TI-84 Plus
TI-84 Plus Silver Edition
Guidebook
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USA FCC Information Concerning Radio Frequency
Interference
This equipment has been tested and found to comply with the limits for a Class B digital
device, pursuant to Part 15 of the FCC rules. These limits are designed to provide
reasonable protection against harmful interference in a residential installation. This
equipment generates, uses, and can radiate radio frequency energy and, if not installed
and used in accordance with the instructions, may cause harmful interference to radio
communications. However, there is no guarantee that interference will not occur in a
particular installation.
If this equipment does cause harmful interference to radio or television reception, which
can be determined by turning the equipment off and on, you can try to correct the
interference by one or more of the following measures:
•
•
•
Reorient or relocate the receiving antenna.
Increase the separation between the equipment and receiver.
Connect the equipment into an outlet on a circuit different from that to which the
receiver is connected.
•
Consult the dealer or an experienced radio/television technician for help.
Caution: Any changes or modifications to this equipment not expressly approved
by Texas Instruments may void your authority to operate the equipment.
iii
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Chapter 1:
Operating the TI-84 Plus Silver Edition
Documentation Conventions
In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition.
Sometimes, as in Chapter 19, the full name TI-84 Plus Silver Edition is used to
distinguish it from the TI-84 Plus.
All the instructions and examples in this guidebook also work for the TI-84 Plus. All the
functions of the TI-84 Plus Silver Edition and the TI-84 Plus are the same. The two
graphing calculators differ only in available RAM memory, interchangeable faceplates,
and Flash application ROM memory.
TI-84 Plus Keyboard
Generally, the keyboard is divided into these zones: graphing keys, editing keys,
advanced function keys, and scientific calculator keys.
Keyboard Zones
Graphing — Graphing keys access the interactive graphing features.
Editing — Editing keys allow you to edit expressions and values.
Advanced — Advanced function keys display menus that access the advanced
functions.
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Scientific — Scientific calculator keys access the capabilities of a standard scientific
calculator.
TI-84 Plus
Graphing Keys
Editing Keys
Advanced
Function Keys
Scientific
Calculator Keys
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Using the Color.Coded Keyboard
The keys on the TI-84 Plus are color-coded to help you easily locate the key you need.
The light colored keys are the number keys. The light gray keys along the right side of the
keyboard are the common math functions. The light gray keys across the top set up and
display graphs. The Πkey with the purple lettering provides access to applications such
as the Inequality Graphing application.
The primary function of each key is printed on the keys. For example, when you press
, the MATH menu is displayed.
Using the y and ƒ Keys
The secondary function of each key is printed in blue above the key. When you press the
blue y key, the character, abbreviation, or word printed in blue above the other keys
becomes active for the next keystroke. For example, when you press y and then
, the TEST menu is displayed. This guidebook describes this keystroke combination
as y :.
The alpha function of each key is printed in green above the key. When you press the
green ƒ key, the alpha character printed in green above the other keys becomes
active for the next keystroke. For example, when you press ƒ and then , the
letter A is entered. This guidebook describes this keystroke combination as ƒ [A].
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The y key
accesses the
second function
printed in blue
above each key.
The ƒ key
accesses the alpha
function printed in
green above each
key.
Turning On and Turning Off the TI-84 Plus
Turning On the Graphing Calculator
To turn on the TI-84 Plus, press É.
•
If you previously had turned off the graphing calculator by pressing y M, the
TI-84 Plus displays the home screen as it was when you last used it and clears any
error.
Chapter 1: Operating the TI-84 Plus Silver Edition
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•
•
If Automatic Power Down™ (APD™) had previously turned off the graphing
calculator, the TI-84 Plus will return exactly as you left it, including the display, cursor,
and any error.
If the TI-84 Plus is turned off and connected to another graphing calculator or
personal computer, any communication activity will “wake up” the TI-84 Plus.
To prolong the life of the batteries, APD turns off the TI-84 Plus automatically after about
five minutes without any activity.
Turning Off the Graphing Calculator
To turn off the TI-84 Plus manually, press y M.
•
•
All settings and memory contents are retained by Constant Memory™.
Any error condition is cleared.
Batteries
The TI-84 Plus uses five batteries: four AAA alkaline batteries and one SR44SW or 303
silver oxide backup battery. The silver oxide battery provides auxiliary power to retain
memory while you replace the AAA batteries. To replace batteries without losing any
information stored in memory, follow the steps in Appendix C.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Setting the Display Contrast
Adjusting the Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting conditions. As
you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right
corner indicates the current level. You may not be able to see the number if contrast is too
light or too dark.
Note: The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents
four settings.
The TI-84 Plus retains the contrast setting in memory when it is turned off.
To adjust the contrast, follow these steps.
1. Press and release the y key.
2. Press and hold † or }, which are below and above the contrast symbol (blue, half-
shaded circle).
•
•
† lightens the screen.
} darkens the screen.
Note: If you adjust the contrast setting to 0, the display may become completely blank. To
restore the screen, press and release y, and then press and hold } until the display
reappears.
Chapter 1: Operating the TI-84 Plus Silver Edition
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When to Replace Batteries
When the batteries are low, a low-battery message is displayed when you turn on the
graphing calculator.
To replace the batteries without losing any information in memory, follow the steps in
Appendix C.
Generally, the graphing calculator will continue to operate for one or two weeks after the
low-battery message is first displayed. After this period, the TI-84 Plus will turn off
automatically and the unit will not operate. Batteries must be replaced. All memory
should be retained.
Note: The operating period following the first low-battery message could be longer than
two weeks if you use the graphing calculator infrequently.
The Display
Types of Displays
The TI-84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9
describes how the TI-84 Plus can display a horizontally or vertically split screen to show
graphs and text simultaneously.
Home Screen
The home screen is the primary screen of the TI-84 Plus. On this screen, enter
instructions to execute and expressions to evaluate. The answers are displayed on the
same screen.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Displaying Entries and Answers
When text is displayed, the TI-84 Plus screen can display a maximum of 8 lines with a
maximum of 16 characters per line. If all lines of the display are full, text scrolls off the
top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the
program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next
line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls
to the right and left.
When an entry is executed on the home screen, the answer is displayed on the right side
of the next line.
Entry
Answer
The mode settings control the way the TI-84 Plus interprets expressions and displays
answers.
If an answer, such as a list or matrix, is too long to display entirely on one line, an ellipsis
(...) is displayed to the right or left. Press ~ and | to display the answer.
Entry
Answer
Returning to the Home Screen
To return to the home screen from any other screen, press y 5.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Busy Indicator
When the TI-84 Plus is calculating or graphing, a vertical moving line is displayed as a
busy indicator in the top-right corner of the screen. When you pause a graph or a
program, the busy indicator becomes a vertical moving dotted line.
Display Cursors
In most cases, the appearance of the cursor indicates what will happen when you press
the next key or select the next menu item to be pasted as a character.
Cursor
Appearance
Effect of Next Keystroke
Entry
Solid rectangle
$
A character is entered at the cursor; any existing
character is overwritten
Insert
Second
Alpha
Full
Underline
__
A character is inserted in front of the cursor
location
Reverse arrow
Þ
A 2nd character (blue on the keyboard) is entered
or a 2nd operation is executed
Reverse A
Ø
An alpha character (green on the keyboard) is
entered or SOLVE is executed
Checkerboard rectangle No entry; the maximum characters are entered at
a prompt or memory is full
#
If you press ƒ during an insertion, the cursor becomes an underlined A (A). If you
press y during an insertion, the underlined cursor becomes an underlined # (#).
Graphs and editors sometimes display additional cursors, which are described in other
chapters.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Interchangeable Faceplates
The TI-84 Plus Silver Edition has interchangeable faceplates that let you customize the
appearance of your unit. To purchase additional faceplates, refer to the TI Online Store
Removing a Faceplate
1. Lift the tab at the bottom edge of
the faceplate away from the TI-84
Plus Silver Edition case.
2. Carefully lift the faceplate away
from the unit until it releases. Be
careful not to damage the
faceplate or the keyboard.
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Installing New Faceplates
1. Align the top of the faceplate in the
corresponding grooves of the TI-84
Plus Silver Edition case.
2. Gently click the faceplate into
place. Do not force.
3. Make sure you gently press each
of the grooves to ensure the
faceplate is installed properly. See
the diagram for proper groove
placement.
Using the Clock
Use the Clock to set the time and date, select the clock display format, and turn the clock
on and off. The clock is turned on by default and is accessed from the mode screen.
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Displaying the Clock Settings
1. Press z
2. Press the † to move the cursor to SET CLOCK.
3. Press Í.
Changing the Clock settings
1. Press the ~ or | to highlight the date format you
want, example: M/D/Y. Press Í.
2. Press † to highlight YEAR. Press ‘ and type
the year, example: 2004.
3. Press † to highlight MONTH. Press ‘ and
type the number of the month (a number from 1–
12).
4. Press † to highlight DAY. Press ‘ and type
the date.
5. Press † to highlight TIME. Press ~ or | to
highlight the time format you want. Press Í.
6. Press † to highlight HOUR. Press ‘ and type
the hour. A number from 1–12 or 0–23.
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7. Press † to highlight MINUTE. Press ‘ and
type the minutes. A number from 0–59.
8. Press † to highlight AM/PM. Press ~ or | to
highlight the format. Press Í.
9. To Save changes, press † to select SAVE. Press
Í.
Error Messages
If you type the wrong date for the month, for example:
June 31, June does not have 31 days, you will receive
an error message with two choices:
•
To Quit the Clock application and return to the
Home screen, select 1: Quit. Press Í.
— or —
•
To return to the clock application and correct the
error, select 2: Goto. Press Í.
Turning the Clock On
There are two options to turn the clock on. One option is through the MODE screen, the
other is through the Catalog.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Using the Mode Screen to turn the clock on
1. If the Clock is turned off, Press † to highlight
TURN CLOCK ON.
2. Press Í Í.
Using the Catalog to turn the clock on
1. If the Clock is turned off, Press y N
2. Press † or } to scroll the CATALOG until the
selection cursor points to ClockOn.
3. Press Í Í.
Turning the Clock Off
1. Press y N.
2. Press † or } to scroll the CATALOG until the
selection cursor points to ClockOff.
3. Press Í.
ClockOff will turn off the Clock display.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Entering Expressions and Instructions
What Is an Expression?
An expression is a group of numbers, variables, functions and their arguments, or a
combination of these elements. An expression evaluates to a single answer. On the
TI-84 Plus, you enter an expression in the same order as you would write it on paper. For
2
example, pR is an expression.
You can use an expression on the home screen to calculate an answer. In most places
where a value is required, you can use an expression to enter a value.
Entering an Expression
To create an expression, you enter numbers, variables, and functions from the keyboard
and menus. An expression is completed when you press Í, regardless of the cursor
location. The entire expression is evaluated according to Equation Operating System
(EOS™) rules, and the answer is displayed.
Most TI-84 Plus functions and operations are symbols comprising several characters.
You must enter the symbol from the keyboard or a menu; do not spell it out. For
example, to calculate the log of 45, you must press « 45. Do not enter the letters L, O,
and G. If you enter LOG, the TI-84 Plus interprets the entry as implied multiplication of the
variables L, O, and G.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Calculate 3.76 P (L7.9 + ‡5) + 2 log 45.
3 Ë 76 ¥ £ Ì 7 Ë 9 Ã
y C 5 ¤ ¤ Ã 2 « 45 ¤
Í
Multiple Entries on a Line
To enter two or more expressions or instructions on a line, separate them with colons
(ƒ [:]). All instructions are stored together in last entry (ENTRY).
Entering a Number in Scientific Notation
To enter a number in scientific notation, follow these steps.
1. Enter the part of the number that precedes the exponent. This value can be an
expression.
2. Press y D. â is pasted to the cursor location.
3. If the exponent is negative, press Ì, and then enter the exponent, which can be one
or two digits.
Chapter 1: Operating the TI-84 Plus Silver Edition
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When you enter a number in scientific notation, the TI-84 Plus does not automatically
display answers in scientific or engineering notation. The mode settings and the size of
the number determine the display format.
Functions
A function returns a value. For example, ÷, L, +, ‡(, and log( are the functions in the
example on the previous page. In general, the first letter of each function is lowercase on
the TI-84 Plus. Most functions take at least one argument, as indicated by an open
parenthesis ( ( ) following the name. For example, sin( requires one argument, sin(value).
Instructions
An instruction initiates an action. For example, ClrDraw is an instruction that clears any
drawn elements from a graph. Instructions cannot be used in expressions. In general,
the first letter of each instruction name is uppercase. Some instructions take more than
one argument, as indicated by an open parenthesis ( ( ) at the end of the name. For
example, Circle( requires three arguments, Circle(X,Y,radius).
Interrupting a Calculation
To interrupt a calculation or graph in progress, which is indicated by the busy indicator,
press É.
When you interrupt a calculation, a menu is displayed.
•
•
To return to the home screen, select 1:Quit.
To go to the location of the interruption, select 2:Goto.
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When you interrupt a graph, a partial graph is displayed.
•
•
To return to the home screen, press ‘ or any nongraphing key.
To restart graphing, press a graphing key or select a graphing instruction.
TI-84 Plus Edit Keys
Keystrokes
~ or |
Result
Moves the cursor within an expression; these keys repeat.
Moves the cursor from line to line within an expression that occupies
more than one line; these keys repeat.
} or †
On the top line of an expression on the home screen, } moves the
cursor to the beginning of the expression.
On the bottom line of an expression on the home screen, † moves the
cursor to the end of the expression.
Moves the cursor to the beginning of an expression.
Moves the cursor to the end of an expression.
Evaluates an expression or executes an instruction.
y |
y ~
Í
‘
On a line with text on the home screen, clears the current line.
On a blank line on the home screen, clears everything on the home
screen.
In an editor, clears the expression or value where the cursor is located; it
does not store a zero.
Deletes a character at the cursor; this key repeats.
{
Changes the cursor to an underline (__); inserts characters in front of the
y 6
underline cursor; to end insertion, press y 6 or press |, }, ~, or
†.
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Keystrokes
Result
y
Changes the cursor to Þ; the next keystroke performs a 2nd operation
(an operation in blue above a key and to the left); to cancel 2nd, press
y again.
ƒ
Changes the cursor to Ø; the next keystroke pastes an alpha character
(a character in green above a key and to the right) or executes SOLVE
(Chapters 10 and 11); to cancel ƒ, press ƒ or press |, },
~, or †.
y 7
„
Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes (on an
alpha key) paste alpha characters; to cancel alpha-lock, press ƒ. If
you are prompted to enter a name such as for a group or a program,
alpha-lock is set automatically.
Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in
Seq mode with one keystroke.
Setting Modes
Checking Mode Settings
Mode settings control how the TI-84 Plus displays and interprets numbers and graphs.
Mode settings are retained by the Constant Memory feature when the TI-84 Plus is
turned off. All numbers, including elements of matrices and lists, are displayed according
to the current mode settings.
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To display the mode settings, press z. The current settings are highlighted. Defaults
are highlighted below. The following pages describe the mode settings in detail.
Numeric notation
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected Dot
Sequential Simul
Real a+bi re^qi
Full Horiz G-T
Set Clock
Number of decimal places
Unit of angle measure
Type of graphing
Whether to connect graph points
Whether to plot simultaneously
Real, rectangular complex, or polar complex
Full screen, two split-screen modes
01/01/01 12:00 AM
Changing Mode Settings
To change mode settings, follow these steps.
1. Press † or } to move the cursor to the line of the setting that you want to change.
2. Press ~ or | to move the cursor to the setting you want.
3. Press Í.
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Setting a Mode from a Program
You can set a mode from a program by entering the name of the mode as an instruction;
for example, Func or Float. From a blank program command line, select the mode setting
from the mode screen; the instruction is pasted to the cursor location.
Normal, Sci, Eng
Notation modes only affect the way an answer is displayed on the home screen.
Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You
can enter a number in any format.
Normal notation mode is the usual way we express numbers, with digits to the left and
right of the decimal, as in 12345.67.
Sci (scientific) notation mode expresses numbers in two parts. The significant digits
display with one digit to the left of the decimal. The appropriate power of 10 displays to
the right of å, as in 1.234567â4.
Eng (engineering) notation mode is similar to scientific notation. However, the number
can have one, two, or three digits before the decimal; and the power-of-10 exponent is a
multiple of three, as in 12.34567â3.
Note: If you select Normal notation, but the answer cannot display in 10 digits (or the
absolute value is less than .001), the TI-84 Plus expresses the answer in scientific
notation.
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Float, 0123456789
Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal.
0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display
to the right of the decimal. Place the cursor on the desired number of decimal digits, and
then press Í.
The decimal setting applies to Normal, Sci, and Eng notation modes.
The decimal setting applies to these numbers:
•
•
•
•
•
An answer displayed on the home screen
Coordinates on a graph (Chapters 3, 4, 5, and 6)
The Tangent( DRAW instruction equation of the line, x, and dy/dx values (Chapter 8)
Results of CALCULATE operations (Chapters 3, 4, 5, and 6)
The regression equation stored after the execution of a regression model
(Chapter 12)
Radian, Degree
Angle modes control how the TI-84 Plus interprets angle values in trigonometric
functions and polar/rectangular conversions.
Radian mode interprets angle values as radians. Answers display in radians.
Degree mode interprets angle values as degrees. Answers display in degrees.
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Func, Par, Pol, Seq
Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these
modes in detail.
Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3).
Par (parametric) graphing mode plots relations, where X and Y are functions of T
(Chapter 4).
Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5).
Seq (sequence) graphing mode plots sequences (Chapter 6).
Connected, Dot
Connected plotting mode draws a line connecting each point calculated for the selected
functions.
Dot plotting mode plots only the calculated points of the selected functions.
Sequential, Simul
Sequential graphing-order mode evaluates and plots one function completely before the
next function is evaluated and plotted.
Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for
a single value of X and then evaluates and plots them for the next value of X.
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Note: Regardless of which graphing mode is selected, the TI-84 Plus will sequentially
graph all stat plots before it graphs any functions.
Real, a+bi, re^qi
Real mode does not display complex results unless complex numbers are entered as
input.
Two complex modes display complex results.
•
•
a+bi (rectangular complex mode) displays complex numbers in the form a+bi.
re^qi (polar complex mode) displays complex numbers in the form re^qi.
Full, Horiz, G-T
Full screen mode uses the entire screen to display a graph or edit screen.
Each split-screen mode displays two screens simultaneously.
•
•
Horiz (horizontal) mode displays the current graph on the top half of the screen; it
displays the home screen or an editor on the bottom half (Chapter 9).
G-T (graph-table) mode displays the current graph on the left half of the screen; it
displays the table screen on the right half (Chapter 9).
Set Clock
Use the clock to set the time, date, and clock display formats.
Chapter 1: Operating the TI-84 Plus Silver Edition
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Using TI-84 Plus Variable Names
Variables and Defined Items
On the TI-84 Plus you can enter and use several types of data, including real and
complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures,
and strings.
The TI-84 Plus uses assigned names for variables and other items saved in memory. For
lists, you also can create your own five-character names.
Variable Type
Real numbers
Complex numbers
Matrices
Names
A, B, ... , Z
A, B, ... , Z
ãAä, ãBä, ãCä, ... , ãJä
L1, L2, L3, L4, L5, L6, and user-defined names
Y1, Y2, ... , Y9, Y0
Lists
Functions
Parametric equations
Polar functions
Sequence functions
Stat plots
X1T and Y1T, ... , X6T and Y6T
r1, r2, r3, r4, r5, r6
u, v, w
Plot1, Plot2, Plot3
Graph databases
Graph pictures
Strings
GDB1, GDB2, ... , GDB9, GDB0
Pic1, Pic2, ... , Pic9, Pic0
Str1, Str2, ... , Str9, Str0
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Variable Type
Apps
Names
Applications
AppVars
Application variables
Grouped variables
Xmin, Xmax, and others
Groups
System variables
Notes about Variables
•
•
•
You can create as many list names as memory will allow (Chapter 11).
Programs have user-defined names and share memory with variables (Chapter 16).
From the home screen or from a program, you can store to matrices (Chapter 10),
lists (Chapter 11), strings (Chapter 15), system variables such as Xmax (Chapter 1),
TblStart (Chapter 7), and all Y= functions (Chapters 3, 4, 5, and 6).
•
•
From an editor, you can store to matrices, lists, and Y= functions (Chapter 3).
From the home screen, a program, or an editor, you can store a value to a matrix
element or a list element.
•
•
•
You can use DRAW STO menu items to store and recall graph databases and
pictures (Chapter 8).
Although most variables can be archived, system variables including r, t, x, y, and q
cannot be archived (Chapter 18)
Apps are independent applications.which are stored in Flash ROM. AppVars is a
variable holder used to store variables created by independent applications. You
cannot edit or change variables in AppVars unless you do so through the application
which created them.
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Storing Variable Values
Storing Values in a Variable
Values are stored to and recalled from memory using variable names. When an
expression containing the name of a variable is evaluated, the value of the variable at
that time is used.
To store a value to a variable from the home screen or a program using the ¿ key,
begin on a blank line and follow these steps.
1. Enter the value you want to store. The value can be an expression.
2. Press ¿. ! is copied to the cursor location.
3. Press ƒ and then the letter of the variable to which you want to store the value.
4. Press Í. If you entered an expression, it is evaluated. The value is stored to the
variable.
Displaying a Variable Value
To display the value of a variable, enter the name on a blank line on the home screen,
and then press Í.
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Archiving Variables (Archive, Unarchive)
You can archive data, programs, or other variables in a section of memory called user
data archive where they cannot be edited or deleted inadvertently. Archived variables
are indicated by asterisks (ä) to the left of the variable names. Archived variables cannot
be edited or executed. They can only be seen and unarchived. For example, if you
archive list L1, you will see that L1 exists in memory but if you select it and paste the
name L1 to the home screen, you won’t be able to see its contents or edit it until they are
unarchived.
Recalling Variable Values
Using Recall (RCL)
To recall and copy variable contents to the current cursor location, follow these steps. To
leave RCL, press ‘.
1. Press y K. RCL and the edit cursor are displayed on the bottom line of the
screen.
2. Enter the name of the variable in any of five ways.
•
•
•
•
Press ƒ and then the letter of the variable.
Press y 9, and then select the name of the list, or press y [Ln].
Press y >, and then select the name of the matrix.
Press to display the VARS menu or ~ to display the VARS Y-VARS
menu; then select the type and then the name of the variable or function.
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•
Press |, and then select the name of the program (in the program editor
only).
The variable name you selected is displayed on the bottom line and the cursor
disappears.
3. Press Í. The variable contents are inserted where the cursor was located
before you began these steps.
Note: You can edit the characters pasted to the expression without affecting the
value in memory.
ENTRY (Last Entry) Storage Area
Using ENTRY (Last Entry)
When you press Í on the home screen to evaluate an expression or execute an
instruction, the expression or instruction is placed in a storage area called ENTRY (last
entry). When you turn off the TI-84 Plus, ENTRY is retained in memory.
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To recall ENTRY, press y [. The last entry is pasted to the current cursor location,
where you can edit and execute it. On the home screen or in an editor, the current line is
cleared and the last entry is pasted to the line.
Because the TI-84 Plus updates ENTRY only when you press Í, you can recall the
previous entry even if you have begun to enter the next expression.
5 Ã 7
Í
y [
Accessing a Previous Entry
The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity
of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more
than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage
area.
1 ¿ ƒ A
Í
2 ¿ ƒ B
Í
y [
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If you press y [ after displaying the oldest stored entry, the newest stored entry is
displayed again, then the next-newest entry, and so on.
y [
Reexecuting the Previous Entry
After you have pasted the last entry to the home screen and edited it (if you chose to edit
it), you can execute the entry. To execute the last entry, press Í.
To reexecute the displayed entry, press Í again. Each reexecution displays an
answer on the right side of the next line; the entry itself is not redisplayed.
0 ¿ ƒ N
Í
ƒ N Ã 1 ¿ ƒ N
ƒ ã:䊃ÄN ¡ Í
Í
Í
Multiple Entry Values on a Line
To store to ENTRY two or more expressions or instructions, separate each expression or
instruction with a colon, then press Í. All expressions and instructions separated by
colons are stored in ENTRY.
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When you press y [, all the expressions and instructions separated by colons are
pasted to the current cursor location. You can edit any of the entries, and then execute all
of them when you press Í.
2
For the equation A=pr , use trial and error to find the radius of a circle that covers 200
square centimeters. Use 8 as your first guess.
8 ¿ ƒ R ƒ ã:ä
y B ƒ R ¡ Í
y [
y | 7 y 6 Ë 95
Í
Continue until the answer is as accurate as you want.
Clearing ENTRY
Clear Entries (Chapter 18) clears all data that the TI-84 Plus is holding in the ENTRY
storage area.
Using Ans in an Expression
When an expression is evaluated successfully from the home screen or from a program,
the TI-84 Plus stores the answer to a storage area called Ans (last answer). Ans may be
a real or complex number, a list, a matrix, or a string. When you turn off the TI-84 Plus,
the value in Ans is retained in memory.
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You can use the variable Ans to represent the last answer in most places. Press y Z to
copy the variable name Ans to the cursor location. When the expression is evaluated, the
TI-84 Plus uses the value of Ans in the calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield
per square meter if the plot produces a total of 147 tomatoes.
1 Ë 7 ¯ 4 Ë 2
Í
147 ¥ y Z
Í
Continuing an Expression
You can use Ans as the first entry in the next expression without entering the value again
or pressing y Z. On a blank line on the home screen, enter the function. The TI-84
Plus pastes the variable name Ans to the screen, then the function.
5 ¥ 2
Í
¯ 9 Ë 9
Í
Storing Answers
To store an answer, store Ans to a variable before you evaluate another expression.
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Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder
of radius 5 meters and height 3.3 meters, and then store the result in the variable V.
y B 5 ¡
Í
¯ 3 Ë 3
Í
¿ ƒ V
Í
TI-84 Plus Menus
Using a TI-84 Plus Menu
You can access most TI-84 Plus operations using menus. When you press a key or key
combination to display a menu, one or more menu names appear on the top line of the
screen.
•
•
The menu name on the left side of the top line is highlighted. Up to seven items in
that menu are displayed, beginning with item 1, which also is highlighted.
A number or letter identifies each menu item’s place in the menu. The order is 1
through 9, then 0, then A, B, C, and so on. The LIST NAMES, PRGM EXEC, and
PRGM EDIT menus only label items 1 through 9 and 0.
•
•
When the menu continues beyond the displayed items, a down arrow ($) replaces
the colon next to the last displayed item.
When a menu item ends in an ellipsis (...), the item displays a secondary menu or
editor when you select it.
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•
When an asterisk (ä) appears to the left of a menu item, that item is stored in user
data archive (Chapter 18).
To display any other menu listed on the top line, press ~ or | until that menu name is
highlighted. The cursor location within the initial menu is irrelevant. The menu is
displayed with the cursor on the first item.
Displaying a Menu
While using your TI-84 Plus, you often will need to
access items from its menus.
When you press a key that displays a menu, that
menu temporarily replaces the screen where you are
working. For example, when you press , the
MATH menu is displayed as a full screen.
After you select an item from a menu, the screen
where you are working usually is displayed again.
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Moving from One Menu to Another
Some keys access more than one menu. When you
press such a key, the names of all accessible menus
are displayed on the top line. When you highlight a
menu name, the items in that menu are displayed.
Press ~ and | to highlight each menu name.
Scrolling a Menu
To scroll down the menu items, press †. To scroll up the menu items, press }.
To page down six menu items at a time, press ƒ †. To page up six menu items at a
time, press ƒ }. The green arrows on the graphing calculator, between † and },
are the page-down and page-up symbols.
To wrap to the last menu item directly from the first menu item, press }. To wrap to the
first menu item directly from the last menu item, press †.
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Selecting an Item from a Menu
You can select an item from a menu in either of two ways.
•
Press the number or letter of the item you want to
select. The cursor can be anywhere on the menu,
and the item you select need not be displayed on
the screen.
•
Press † or } to move the cursor to the item you
want, and then press Í.
After you select an item from a menu, the TI-84 Plus
typically displays the previous screen.
Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9
and 0 are labeled in such a way that you can select them by pressing the appropriate
number key. To move the cursor to the first item beginning with any alpha character or q,
press the key combination for that alpha character or q. If no items begin with that
character, the cursor moves beyond it to the next item.
3
Calculate ‡27.
† † † Í
27 ¤ Í
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Leaving a Menu without Making a Selection
You can leave a menu without making a selection in any of four ways.
•
•
•
•
Press y 5 to return to the home screen.
Press ‘ to return to the previous screen.
Press a key or key combination for a different menu, such as or y 9.
Press a key or key combination for a different screen, such as o or y 0.
VARS and VARS Y-VARS Menus
VARS Menu
You can enter the names of functions and system variables in an expression or store to
them directly.
To display the VARS menu, press . All VARS menu items display secondary menus,
which show the names of the system variables. 1:Window, 2:Zoom, and 5:Statistics each
access more than one secondary menu.
VARS Y-VARS
1: Window...
X/Y, T/q, and U/V/W variables
2: Zoom...
ZX/ZY, ZT/Zq, and ZU variables
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VARS Y-VARS
3: GDB...
Graph database variables
Picture variables
4: Picture...
5: Statistics...
6: Table...
XY, G, EQ, TEST, and PTS variables
TABLE variables
String variables
7: String...
Selecting a Variable from the VARS Menu or VARS Y-VARS Menu
To display the VARS Y-VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar
display secondary menus of the Y= function variables.
VARS Y-VARS
Yn functions
1: Function...
2: Parametric...
3: Polar...
XnT, YnT functions
rn functions
Lets you select/deselect functions
4: On/Off...
Note: The sequence variables (u, v, w) are located on the keyboard as the second
functions of ¬, −, and ®.
To select a variable from the VARS or VARS Y-VARS menu, follow these steps.
1. Display the VARS or VARS Y-VARS menu.
•
Press to display the VARS menu.
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•
Press ~ to display the VARS Y-VARS menu.
2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the
VARS Y-VARS menu. A secondary menu is displayed.
3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press
~ or | to display other secondary menus.
4. Select a variable name from the menu. It is pasted to the cursor location.
Equation Operating System (EOS™)
Order of Evaluation
The Equation Operating System (EOS) defines the order in which functions in
expressions are entered and evaluated on the TI-84 Plus. EOS lets you enter numbers
and functions in a simple, straightforward sequence.
EOS evaluates the functions in an expression in this order.
Order Number Function
1
2
Functions that precede the argument, such as ‡(, sin(, or log(
2
M1
r
Functions that are entered after the argument, such as , , !, ¡, , and
conversions
x
3
Powers and roots, such as 2^5 or 5 ‡32
4
5
6
Permutations (nPr) and combinations (nCr)
Multiplication, implied multiplication, and division
Addition and subtraction
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Order Number Function
7
8
9
Relational functions, such as > or
Logic operator and
Logic operators or and xor
Note: Within a priority level, EOS evaluates functions from left to right. Calculations
within parentheses are evaluated first.
Implied Multiplication
The TI-84 Plus recognizes implied multiplication, so you need not press ¯ to express
multiplication in all cases. For example, the TI-84 Plus interprets 2p, 4sin(46), 5(1+2), and
(2…5)7 as implied multiplication.
Note: TI-84 Plus implied multiplication rules, although like the TI-83, differ from those of
the TI-82. For example, the TI-84 Plus evaluates 1à2X as (1à2)…X, while the TI-82
evaluates 1à2X as 1à(2…X) (Chapter 2).
Parentheses
All calculations inside a pair of parentheses are completed first. For example, in the
expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then
multiplies the answer, 3, by 4.
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You can omit the close parenthesis ( ) ) at the end of an expression. All open
parenthetical elements are closed automatically at the end of an expression. This is also
true for open parenthetical elements that precede the store or display-conversion
instructions.
Note: An open parenthesis following a list name, matrix name, or Y= function name does
not indicate implied multiplication. It specifies elements in the list (Chapter 11) or matrix
(Chapter 10) and specifies a value for which to solve the Y= function.
Negation
To enter a negative number, use the negation key. Press Ì and then enter the number.
On the TI-84 Plus, negation is in the third level in the EOS hierarchy. Functions in the
first level, such as squaring, are evaluated before negation.
2
For example, MX , evaluates to a negative number (or 0). Use parentheses to square a
negative number.
Note: Use the ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter
a negative number, as in 9 ¯ ¹ 7, or if you press Ì to indicate subtraction, as in 9 Ì 7,
an error occurs. If you press ƒ A Ì ƒ B, it is interpreted as implied
multiplication (A…MB).
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Special Features of the TI-84 Plus
Flash – Electronic Upgradability
The TI-84 Plus uses Flash technology, which lets you upgrade to future software
versions without buying a new graphing calculator.
As new functionality becomes available, you can electronically upgrade your TI-84 Plus
from the Internet. Future software versions include maintenance upgrades that will be
released free of charge, as well as new applications and major software upgrades that
will be available for purchase from the TI Web site: education.ti.com
For details, refer to: Chapter 19
1.5 Megabytes (M) of Available Memory
1.5 M of available memory are built into the TI-84 Plus Silver Edition, and .5 M for the
TI-84 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for
you to compute and store functions, programs, and data.
About 1.5 M of user data archive allow you to store data, programs, applications, or any
other variables to a safe location where they cannot be edited or deleted inadvertently.
You can also free up RAM by archiving variables to user data.
For details, refer to: Chapter 18
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Applications
Applications can be installed to customize the TI-84 Plus to your classroom needs. The
big 1.5 M archive space lets you store up to 94 applications at one time. Applications can
also be stored on a computer for later use or linked unit-to-unit. There are 30 App slots
for the TI-84 Plus.
For details, refer to: Chapter 18
Archiving
You can store variables in the TI-84 Plus user data archive, a protected area of memory
separate from RAM. The user data archive lets you:
•
•
Store data, programs, applications or any other variables to a safe location where
they cannot be edited or deleted inadvertently.
Create additional free RAM by archiving variables.
By archiving variables that do not need to be edited frequently, you can free up RAM for
applications that may require additional memory.
For details, refer to: Chapter 18
Other TI-84 Plus Features
The TI-84 Plus guidebook that is included with your graphing calculator has introduced
you to basic TI-84 Plus operations. This guidebook covers the other features and
capabilities of the TI-84 Plus in greater detail.
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Graphing
You can store, graph, and analyze up to 10 functions, up to six parametric functions, up
to six polar functions, and up to three sequences. You can use DRAW instructions to
annotate graphs.
The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and
DRAW.
For graphing details, refer to: Chapters 3, 4, 5, 6, 8
Sequences
You can generate sequences and graph them over time. Or, you can graph them as web
plots or as phase plots.
For details, refer to: Chapter 6
Tables
You can create function evaluation tables to analyze many functions simultaneously.
For details, refer to: Chapter 7
Split Screen
You can split the screen horizontally to display both a graph and a related editor (such as
the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the
screen vertically to display a graph and its table simultaneously.
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For details, refer to: Chapter 9
Matrices
You can enter and save up to 10 matrices and perform standard matrix operations on
them.
For details, refer to: Chapter 10
Lists
You can enter and save as many lists as memory allows for use in statistical analyses.
You can attach formulas to lists for automatic computation. You can use lists to evaluate
expressions at multiple values simultaneously and to graph a family of curves.
For details, refer to: Chapter 11
Statistics
You can perform one- and two-variable, list-based statistical analyses, including logistic
and sine regression analysis. You can plot the data as a histogram, xyLine, scatter plot,
modified or regular box-and-whisker plot, or normal probability plot. You can define and
store up to three stat plot definitions.
For details, refer to: Chapter 12
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Inferential Statistics
You can perform 16 hypothesis tests and confidence intervals and 15 distribution
functions. You can display hypothesis test results graphically or numerically.
For details, refer to: Chapter 13
Applications
Press Πto see the complete list of applications that came with your graphing
calculator.
Documentation for TI Flash applications are on the product CD. Visit
education.ti.com/calc/guides for additional Flash application guidebooks.
For details, refer to: Chapter 14
CATALOG
The CATALOG is a convenient, alphabetical list of all functions and instructions on the
TI-84 Plus. You can paste any function or instruction from the CATALOG to the current
cursor location.
For details, refer to: Chapter 15
Programming
You can enter and store programs that include extensive control and input/output
instructions.
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For details, refer to: Chapter 16
Archiving
Archiving allows you to store data, programs, or other variables to user data archive
where they cannot be edited or deleted inadvertently. Archiving also allows you to free
up RAM for variables that may require additional memory.
Archived variables are indicated by asterisks (ä) to the
left of the variable names.
For details, refer to: Chapter 16
Communication Link
The TI-84 Plus has a USB port using a USB unit-to-unit cable to connect and
communicate with another TI-84 Plus or TI-84 Plus Silver Edition. The TI-84 Plus also
has an I/O port using an I/O unit-to-unit cable to communicate with a TI-84 Plus Silver
Edition, a TI-84 Plus, a TI-83 Plus Silver Edition, a TI-83 Plus, a TI-83, a TI-82, a TI-73,
CBL 2™, or a CBR™ System.
With TI Connect™ software and a USB computer cable, you can also link the TI-84 Plus
to a personal computer.
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As future software upgrades become available on the TI Web site, you can download the
software to your PC and then use the TI Connect™ software and a USB computer cable
to upgrade your TI-84 Plus.
For details, refer to: Chapter 19
Error Conditions
Diagnosing an Error
The TI-84 Plus detects errors while performing these tasks.
•
•
•
•
Evaluating an expression
Executing an instruction
Plotting a graph
Storing a value
When the TI-84 Plus detects an error, it returns an error message as a menu title, such
as ERR:SYNTAXor ERR:DOMAIN. Appendix B describes each error type and possible
reasons for the error.
•
•
If you select 1:Quit (or press y 5 or ‘), then the home screen is displayed.
If you select 2:Goto, then the previous screen is displayed with the cursor at or near
the error location.
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Note: If a syntax error occurs in the contents of a Y= function during program execution,
then the Goto option returns to the Y= editor, not to the program.
Correcting an Error
To correct an error, follow these steps.
1. Note the error type (ERR:error type).
2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or
near the error location.
3. Determine the error. If you cannot recognize the error, refer to Appendix B.
4. Correct the expression.
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Chapter 2:
Math, Angle, and Test Operations
Getting Started: Coin Flip
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to model flipping a fair coin 10 times. You want to track how many of
those 10 coin flips result in heads. You want to perform this simulation 40 times. With a
fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin
flip resulting in tails is 0.5.
1. Begin on the home screen. Press | to
display the MATH PRB menu. Press 7 to select
7:randBin( (random Binomial). randBin( is pasted
to the home screen. Press 10 to enter the number
of coin flips. Press ¢. Press Ë 5 to enter the
probability of heads. Press ¢. Press 40 to enter
the number of simulations. Press ¤.
2. Press Í to evaluate the expression. A list of
40 elements is generated with the first 7 displayed.
The list contains the count of heads resulting from
each set of 10 coin flips. The list has 40 elements
because this simulation was performed 40 times.
In this example, the coin came up heads five times
in the first set of 10 coin flips, five times in the
second set of 10 coin flips, and so on.
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3. Press ~ or | to view the additional counts in the
list. Ellipses (...) indicate that the list continues
beyond the screen.
4. Press ¿ y d Í to store the data to the
list name L1. You then can use the data for
another activity, such as plotting a histogram
(Chapter 12).
Note: Since randBin( generates random numbers,
your list elements may differ from those in the
example.
Keyboard Math Operations
Using Lists with Math Operations
Math operations that are valid for lists return a list calculated element by element. If you
use two lists in the same expression, they must be the same length.
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Addition, Subtraction, Multiplication, Division
You can use + (addition, Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥)
with real and complex numbers, expressions, lists, and matrices. You cannot use à with
matrices.
valueA+valueB
valueA N valueB
valueA…valueB
valueA à valueB
Trigonometric Functions
You can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š)
with real numbers, expressions, and lists. The current angle mode setting affects
interpretation. For example, sin(30) in Radian mode returns L.9880316241; in Degree
mode it returns .5.
sin(value)
cos(value)
tan(value)
You can use the inverse trig functions (arcsine, y ?; arccosine, y @; and
arctangent, y A) with real numbers, expressions, and lists. The current angle mode
setting affects interpretation.
L1
L1
L1
sin (value)
cos (value)
tan (value)
Note: The trig functions do not operate on complex numbers.
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Power, Square, Square Root
2
You can use ^ (power, ›), (square, ¡), and ‡( (square root, y C) with real and
complex numbers, expressions, lists, and matrices. You cannot use ‡( with matrices.
È
2
È
value^power
value
‡(value)
Inverse
L1
You can use (inverse, œ) with real and complex numbers, expressions, lists, and
matrices. The multiplicative inverse is equivalent to the reciprocal, 1àx.
-1
value
log(, 10^(, ln(
You can use log( (logarithm, «), 10^( (power of 10, y G), and ln( (natural log, µ)
with real or complex numbers, expressions, and lists.
log(value)
10^(power)
ln(value)
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Exponential
e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with
real or complex numbers, expressions, and lists.
e^(power)
Constant
e (constant, y [e]) is stored as a constant on the TI-84 Plus. Press y [e] to copy e to
the cursor location. In calculations, the TI-84 Plus uses 2.718281828459 for e.
Negation
M (negation, Ì) returns the negative of value. You can use M with real or complex
numbers, expressions, lists, and matrices.
Mvalue
2
EOS™ rules (Chapter 1) determine when negation is evaluated. For example, LA
returns a negative number, because squaring is evaluated before negation. Use
2
parentheses to square a negated number, as in (LA) .
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Note: On the TI-84 Plus, the negation symbol (M) is shorter and higher than the
subtraction sign (N), which is displayed when you press ¹.
Pi
p (Pi, y B) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus
uses 3.1415926535898 for p.
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MATH Operations
MATH Menu
To display the MATH menu, press .
MATH NUM CPX PRB
Displays the answer as a fraction.
1: 4Frac
Displays the answer as a decimal.
Calculates the cube.
2: 4Dec
3
3:
3
Calculates the cube root.
4:
5:
‡(
x
th
‡
Calculates the x root.
Finds the minimum of a function.
Finds the maximum of a function.
Computes the numerical derivative.
Computes the function integral.
Displays the equation solver.
6: fMin(
7: fMax(
8: nDeriv(
9: fnInt(
0: Solver...
4Frac, 4Dec
4Frac (display as a fraction) displays an answer as its rational equivalent. You can use
4Frac with real or complex numbers, expressions, lists, and matrices. If the answer
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cannot be simplified or the resulting denominator is more than three digits, the decimal
equivalent is returned. You can only use 4Frac following value.
value 4Frac
4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with
real or complex numbers, expressions, lists, and matrices. You can only use 4Dec
following value.
value 4Dec
Cube, Cube Root
3
3
(cube) returns the cube of value. You can use with real or complex numbers,
expressions, lists, and square matrices.
3
value
3
3
‡( (cube root) returns the cube root of value. You can use ‡( with real or complex
numbers, expressions, and lists.
3‡(value)
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x
‡ (Root)
x
th
th
x
‡ (x root) returns the x root of value. You can use ‡ with real or complex numbers,
expressions, and lists.
th
x
x root ‡value
fMin(, fMax(
fMin( (function minimum) and fMax( (function maximum) return the value at which the
local minimum or local maximum value of expression with respect to variable occurs,
between lower and upper values for variable. fMin( and fMax( are not valid in expression. The
accuracy is controlled by tolerance (if not specified, the default is 1âL5).
fMin(expression,variable,lower,upper[,tolerance])
fMax(expression,variable,lower,upper[,tolerance])
Note: In this guidebook, optional arguments and the commas that accompany them are
enclosed in brackets ([ ]).
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nDeriv(
nDeriv( (numerical derivative) returns an approximate derivative of expression with respect
to variable, given the value at which to calculate the derivative and H (if not specified, the
default is 1âL3). nDeriv( is valid only for real numbers.
nDeriv(expression,variable,value[,H])
nDeriv( uses the symmetric difference quotient method, which approximates the
numerical derivative value as the slope of the secant line through these points.
f(x + ε) – f(x – ε)
f′(x) = ------------------------------------------
2ε
As H becomes smaller, the approximation usually becomes more accurate.
You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(,
the TI-84 Plus can return a false derivative value at a nondifferentiable point.
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fnInt(
fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of
expression with respect to variable, given lower limit, upper limit, and a tolerance (if not
specified, the default is 1âL5). fnInt( is valid only for real numbers.
fnInt(expression,variable,lower,upper[,tolerance])
Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation),
increase the value of the Xres window variable before you press s.
Using the Equation Solver
Solver
Solver displays the equation solver, in which you can solve for any variable in an
equation. The equation is assumed to be equal to zero. Solver is valid only for real
numbers.
When you select Solver, one of two screens is displayed.
•
•
The equation editor (see step 1 picture below) is displayed when the equation
variable eqn is empty.
The interactive solver editor is displayed when an equation is stored in eqn.
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Entering an Expression in the Equation Solver
To enter an expression in the equation solver, assuming that the variable eqn is empty,
follow these steps.
1. Select 0:Solver from the MATH menu to display the equation editor.
2. Enter the expression in any of three ways.
•
•
•
Enter the expression directly into the equation solver.
Paste a Y= variable name from the VARS Y-VARS menu to the equation solver.
Press y K, paste a Y= variable name from the VARS Y-VARS menu, and
press Í. The expression is pasted to the equation solver.
The expression is stored to the variable eqn as you enter it.
3. Press Í or †. The interactive solver editor is displayed.
•
The equation stored in eqn is set equal to zero and displayed on the top line.
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•
•
•
Variables in the equation are listed in the order in which they appear in the
equation. Any values stored to the listed variables also are displayed.
The default lower and upper bounds appear in the last line of the editor
(bound={L1â99,1â99}).
A $ is displayed in the first column of the bottom line if the editor continues
beyond the screen.
2
2
Note: To use the solver to solve an equation such as K=.5MV , enter eqn:0=KN.5MV in
the equation editor.
Entering and Editing Variable Values
When you enter or edit a value for a variable in the interactive solver editor, the new
value is stored in memory to that variable.
You can enter an expression for a variable value. It is evaluated when you move to the
next variable. Expressions must resolve to real numbers at each step during the
iteration.
You can store equations to any VARS Y-VARS variables, such as Y1 or r6, and then
reference the variables in the equation. The interactive solver editor displays all
variables of all Y= functions referenced in the equation.
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Solving for a Variable in the Equation Solver
To solve for a variable using the equation solver after an equation has been stored to
eqn, follow these steps.
1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not
already displayed.
2. Enter or edit the value of each known variable. All variables, except the unknown
variable, must contain a value. To move the cursor to the next variable, press Í
or †.
3. Enter an initial guess for the variable for which you are solving. This is optional, but it
may help find the solution more quickly. Also, for equations with multiple roots, the
TI-84 Plus will attempt to display the solution that is closest to your guess.
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(upper + lower)
-----------------------------------------
The default guess is calculated as
.
2
4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus
searches for a solution. This is optional, but it may help find the solution more quickly.
The default is bound={L1â99,1â99}.
5. Move the cursor to the variable for which you want to solve and press ƒ \.
•
The solution is displayed next to the variable for which you solved. A solid
square in the first column marks the variable for which you solved and indicates
that the equation is balanced. An ellipsis shows that the value continues beyond
the screen.
Note: When a number continues beyond the screen, be sure to press ~ to scroll
to the end of the number to see whether it ends with a negative or positive
exponent. A very small number may appear to be a large number until you scroll
right to see the exponent.
•
•
The values of the variables are updated in memory.
leftNrt=diff is displayed in the last line of the editor. diff is the difference between
the left and right sides of the equation. A solid square in the first column next to
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leftNrt indicates that the equation has been evaluated at the new value of the
variable for which you solved.
Editing an Equation Stored to eqn
To edit or replace an equation stored to eqn when the interactive equation solver is
displayed, press } until the equation editor is displayed. Then edit the equation.
Equations with Multiple Roots
Some equations have more than one solution. You can enter a new initial guess or new
bounds to look for additional solutions.
Further Solutions
After you solve for a variable, you can continue to explore solutions from the interactive
solver editor. Edit the values of one or more variables. When you edit any variable value,
the solid squares next to the previous solution and leftNrt=diff disappear. Move the cursor
to the variable for which you now want to solve and press ƒ \.
Controlling the Solution for Solver or solve(
The TI-84 Plus solves equations through an iterative process. To control that process,
enter bounds that are relatively close to the solution and enter an initial guess within
those bounds. This will help to find a solution more quickly. Also, it will define which
solution you want for equations with multiple solutions.
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Using solve( on the Home Screen or from a Program
The function solve( is available only from CATALOG or from within a program. It returns a
solution (root) of expression for variable, given an initial guess, and lower and upper bounds
within which the solution is sought. The default for lower is L1â99. The default for upper is
L1â99. solve( is valid only for real numbers.
solve(expression,variable,guess[,{lower,upper}])
expression is assumed equal to zero. The value of variable will not be updated in memory.
guess may be a value or a list of two values. Values must be stored for every variable in
expression, except variable, before expression is evaluated. lower and upper must be entered in
list format.
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MATH NUM (Number) Operations
MATH NUM Menu
To display the MATH NUM menu, press ~.
MATH NUM CPX PRB
Absolute value
Round
1: abs(
2: round(
3: iPart(
4: fPart(
5: int(
6: min(
7: max(
8: lcm(
9: gcd(
Integer part
Fractional part
Greatest integer
Minimum value
Maximum value
Least common multiple
Greatest common divisor
abs(
abs( (absolute value) returns the absolute value of real or complex (modulus) numbers,
expressions, lists, and matrices.
abs(value)
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Note: abs( is also available on the MATH CPX menu.
round(
round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals
is omitted, value is rounded to the digits that are displayed, up to 10 digits.
round(value[,#decimals])
iPart(, fPart(
iPart( (integer part) returns the integer part or parts of real or complex numbers,
expressions, lists, and matrices.
iPart(value)
fPart( (fractional part) returns the fractional part or parts of real or complex numbers,
expressions, lists, and matrices.
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fPart(value)
int(
int( (greatest integer) returns the largest integer real or complex numbers,
expressions, lists, and matrices.
int(value)
Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative
numbers and negative integers, but one integer less than the result of iPart( for negative
noninteger numbers.
min(, max(
min( (minimum value) returns the smaller of valueA and valueB or the smallest element in
list. If listA and listB are compared, min( returns a list of the smaller of each pair of
elements. If list and value are compared, min( compares each element in list with value.
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max( (maximum value) returns the larger of valueA and valueB or the largest element in list.
If listA and listB are compared, max( returns a list of the larger of each pair of elements. If
list and value are compared, max( compares each element in list with value.
min(valueA,valueB)
min(list)
max(valueA,valueB)
max(list)
min(listA,listB)
min(list,value)
max(listA,listB)
max(list,value)
Note: min( and max( also are available on the LIST MATH menu.
lcm(, gcd(
lcm( returns the least common multiple of valueA and valueB, both of which must be
nonnegative integers. When listA and listB are specified, lcm( returns a list of the lcm of
each pair of elements. If list and value are specified, lcm( finds the lcm of each element in
list and value.
gcd( returns the greatest common divisor of valueA and valueB, both of which must be
nonnegative integers. When listA and listB are specified, gcd( returns a list of the gcd of
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each pair of elements. If list and value are specified, gcd( finds the gcd of each element in
list and value.
lcm(valueA,valueB)
lcm(listA,listB)
lcm(list,value)
gcd(valueA,valueB)
gcd(listA,listB)
gcd(list,value)
Entering and Using Complex Numbers
Complex-Number Modes
The TI-84 Plus displays complex numbers in rectangular form and polar form. To select a
complex-number mode, press z, and then select either of the two modes.
•
•
a+bi (rectangular-complex mode)
re^qi (polar-complex mode)
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On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers
are valid list elements.
In Real mode, complex-number results return an error, unless you entered a complex
number as input. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1)
returns an answer.
Real mode
a+bi mode
$
$
Entering Complex Numbers
Complex numbers are stored in rectangular form, but you can enter a complex number
in rectangular form or polar form, regardless of the mode setting. The components of
complex numbers can be real numbers or expressions that evaluate to real numbers;
expressions are evaluated when the command is executed.
Note about Radian Versus Degree Mode
Radian mode is recommended for complex number calculations. Internally, the TI-84
Plus converts all entered trigonometric values to radians, but it does not convert values
for exponential, logarithmic, or hyperbolic functions.
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In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally
true because the values for cos and sin are converted to radians, while those for e^() are
not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as
e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.
Interpreting Complex Results
Complex numbers in results, including list elements, are displayed in either rectangular
or polar form, as specified by the mode setting or by a display conversion instruction. In
the example below, polar-complex (re^qi) and Radian modes are set.
Rectangular-Complex Mode
Rectangular-complex mode recognizes and displays a complex number in the form a+bi,
where a is the real component, b is the imaginary component, and i is a constant equal to
–1 .
To enter a complex number in rectangular form, enter the value of a (real component), press
à or ¹, enter the value of b (imaginary component), and press y V (constant).
real component(+ or N)imaginary component i
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Polar-Complex Mode
Polar-complex mode recognizes and displays a complex number in the form re^qi, where r
is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to
–1 .
To enter a complex number in polar form, enter the value of r (magnitude), press y J
(exponential function), enter the value of q (angle), press y V (constant), and then
press ¤.
magnitudee^(anglei)
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MATH CPX (Complex) Operations
MATH CPX Menu
To display the MATH CPX menu, press ~ ~.
MATH NUM CPX PRB
Returns the complex conjugate.
Returns the real part.
1: conj(
2: real(
3: imag(
4: angle(
5: abs(
Returns the imaginary part.
Returns the polar angle.
Returns the magnitude (modulus).
Displays the result in rectangular form.
Displays the result in polar form.
6: 4Rect
7: 4Polar
conj(
conj( (conjugate) returns the complex conjugate of a complex number or list of complex
numbers.
conj(a+bi) returns aNbi in a+bi mode.
conj(re^(qi)) returns re^(Lqi) in re^qi mode.
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real(
real( (real part) returns the real part of a complex number or list of complex numbers.
real(a+bi) returns a.
real(re^(qi)) returns r†cos(q).
imag(
imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of
complex numbers.
imag(a+bi) returns b.
imag(re^(qi)) returns r†sin(q).
angle(
angle( returns the polar angle of a complex number or list of complex numbers,
L1
calculated as tan (b/a), where b is the imaginary part and a is the real part. The
calculation is adjusted by +p in the second quadrant or Np in the third quadrant.
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L1
angle(a+bi) returns tan (b/a).
angle(re^(qi)) returns q, where Lp<q<p.
abs(
abs( (absolute value) returns the magnitude (modulus), (real2 + imag2)
, of a complex
number or list of complex numbers.
abs(a+bi) returns (a2 + b2)
.
abs(re^(qi)) returns r (magnitude).
4Rect
4Rect (display as rectangular) displays a complex result in rectangular form. It is valid
only at the end of an expression. It is not valid if the result is real.
complex result8Rect returns a+bi.
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4Polar
4Polar (display as polar) displays a complex result in polar form. It is valid only at the end
of an expression. It is not valid if the result is real.
complex result8Polar returns re^(qi).
MATH PRB (Probability) Operations
MATH PRB Menu
To display the MATH PRB menu, press |.
MATH NUM CPX PRB
Random-number generator
Number of permutations
Number of combinations
Factorial
1: rand
2: nPr
3: nCr
4: !
Random-integer generator
Random # from Normal distribution
Random # from Binomial distribution
5: randInt(
6: randNorm(
7: randBin(
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rand
rand (random number) generates and returns one or more random numbers > 0 and < 1.
To generate a list of random-numbers, specify an integer > 1 for numtrials (number of
trials). The default for numtrials is 1.
rand[(numtrials)]
Note: To generate random numbers beyond the range of 0 to 1, you can include rand in
an expression. For example, rand5 generates a random number > 0 and < 5.
With each rand execution, the TI-84 Plus generates the same random-number sequence
for a given seed value. The TI-84 Plus factory-set seed value for rand is 0. To generate a
different random-number sequence, store any nonzero seed value to rand. To restore
the factory-set seed value, store 0 to rand or reset the defaults (Chapter 18).
Note: The seed value also affects randInt(, randNorm(, and randBin( instructions.
nPr, nCr
nPr (number of permutations) returns the number of permutations of items taken number at
a time. items and number must be nonnegative integers. Both items and number can be lists.
items nPr number
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nCr (number of combinations) returns the number of combinations of items taken number
at a time. items and number must be nonnegative integers. Both items and number can be
lists.
items nCr number
Factorial
! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns
factorials for each integer or multiple of .5. value must be ‚ L.5 and 69.
value!
Note: The factorial is computed recursively using the relationship (n+1)! = n…n!, until n is
reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is
used to complete the calculation. Hence:
n!=n…(nN1)…(nN2)… ... …2…1, if n is an integer ‚ 0
n!= n…(nN1)…(nN2)… ... …1à2…‡p, if n+1à2 is an integer ‚ 0
n! is an error, if neither n nor n+1à2 is an integer ‚ 0.
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(The variable n equals value in the syntax description above.)
randInt(
randInt( (random integer) generates and displays a random integer within a range
specified by lower and upper integer bounds. To generate a list of random numbers,
specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.
randInt(lower,upper[,numtrials])
randNorm(
randNorm( (random Normal) generates and displays a random real number from a
specified Normal distribution. Each generated value could be any real number, but most
will be within the interval [mN3(s), m+3(s)]. To generate a list of random numbers, specify
an integer > 1 for numtrials (number of trials); if not specified, the default is 1.
randNorm(m,s[,numtrials])
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randBin(
randBin( (random Binomial) generates and displays a random integer from a specified
Binomial distribution. numtrials (number of trials) must be ‚ 1. prob (probability of success)
must be ‚ 0 and 1. To generate a list of random numbers, specify an integer > 1 for
numsimulations (number of simulations); if not specified, the default is 1.
randBin(numtrials,prob[,numsimulations])
Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin(
instructions.
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ANGLE Operations
ANGLE Menu
To display the ANGLE menu, press y ;. The ANGLE menu displays angle
indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus’s
interpretation of ANGLE menu entries.
ANGLE
Degree notation
1:
¡
DMS minute notation
Radian notation
2: '
3: r
Displays as degree/minute/second
Returns r, given X and Y
4: 8DMS
5: R8Pr(
6: R8Pq( Returns q, given X and Y
7: P8Rx( Returns x, given R and q
8: P8Ry( Returns y, given R and q
Entry Notation
DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (¡), the
minute symbol ('), and the second symbol ("). degrees must be a real number; minutes and
seconds must be real numbers ‚ 0.
degrees¡minutes'seconds"
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For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to
Degree, you must use ¡ so that the TI-84 Plus can interpret the argument as degrees,
minutes, and seconds.
Degree mode
Radian mode
Degree
¡ (degree) designates an angle or list of angles as degrees, regardless of the current
angle mode setting. In Radian mode, you can use ¡ to convert degrees to radians.
value¡
{value1,value2,value3,value4,...,value n}¡
¡ also designates degrees (D) in DMS format.
' (minutes) designates minutes (M) in DMS format.
" (seconds) designates seconds (S) in DMS format.
Note: " is not on the ANGLE menu. To enter ", press ƒ [ã].
Radians
r
(radians) designates an angle or list of angles as radians, regardless of the current
r
angle mode setting. In Degree mode, you can use to convert radians to degrees.
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r
value
Degree mode
8DMS
8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be
Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid
only at the end of a line.
answer8DMS
R8Pr(, R8Pq(, P8Rx(, P8Ry(
R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq(
converts rectangular coordinates to polar coordinates and returns q. x and y can be lists.
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R8Pr(x,y), R8Pq(x,y)
Note: Radian mode is set.
P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry(
converts polar coordinates to rectangular coordinates and returns y. r and q can be lists.
P8Rx(r,q), P8Ry(r,q)
Note: Radian mode is set.
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TEST (Relational) Operations
TEST Menu
To display the TEST menu, press y :.
This operator...
Returns 1 (true) if...
TEST
LOGIC
Equal
1: =
Not equal to
2:
3: >
4:
5: <
6:
ƒ
Greater than
Greater than or equal to
Less than
‚
Less than or equal to
Ä=, ƒ, >, ‚, <,
Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the
test is false. valueA and valueB can be real numbers, expressions, or lists. For = and ƒ
only, valueA and valueB also can be matrices or complex numbers. If valueA and valueB are
matrices, both must have the same dimensions.
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Relational operators are often used in programs to control program flow and in graphing
to control the graph of a function over specific values.
valueA=valueB
valueA>valueB
valueA<valueB
valueAƒvalueB
valueA‚valueB
valueAvalueB
Using Tests
Relational operators are evaluated after mathematical functions according to EOS rules
(Chapter 1).
•
•
The expression 2+2=2+3 returns 0. The TI-84 Plus performs the addition first
because of EOS rules, and then it compares 4 to 5.
The expression 2+(2=2)+3 returns 6. The TI-84 Plus performs the relational test first
because it is in parentheses, and then it adds 2, 1, and 3.
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TEST LOGIC (Boolean) Operations
TEST LOGIC Menu
To display the TEST LOGIC menu, press y : ~.
This operator...
Returns a 1 (true) if...
TEST LOGIC
Both values are nonzero (true).
At least one value is nonzero (true).
Only one value is zero (false).
The value is zero (false).
1: and
2: or
3: xor
4: not(
Boolean Operators
Boolean operators are often used in programs to control program flow and in graphing to
control the graph of the function over specific values. Values are interpreted as zero
(false) or nonzero (true).
and, or, xor
and, or, and xor (exclusive or) return a value of 1 if an expression is true or 0 if an
expression is false, according to the table below. valueA and valueB can be real numbers,
expressions, or lists.
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valueA and valueB
valueA or valueB
valueA xor valueB
valueA
valueB
and
1
or
1
xor
0
returns
returns
returns
returns
ƒ0
ƒ0
0
ƒ0
0
0
1
1
0
1
1
ƒ0
0
0
0
0
0
not(
not( returns 1 if value (which can be an expression) is 0.
not(value)
Using Boolean Operations
Boolean logic is often used with relational tests. In the following program, the instructions
store 4 into C.
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Chapter 3:
Function Graphing
Getting Started: Graphing a Circle
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing window. To
graph this circle, you must enter separate formulas for the upper and lower portions of
the circle. Then use ZSquare (zoom square) to adjust the display and make the
functions appear as a circle.
1. In Func mode, press o to display the Y= editor.
Press y C 100 ¹ „ ¡ ¤ Í to enter
2
the expression Y=‡(100NX ), which defines the
top half of the circle.
2
The expression Y=L‡(100NX ) defines the bottom
half of the circle. On the TI-84 Plus, you can define
one function in terms of another. To define Y2=LY1,
press Ì to enter the negation sign. Press ~
to display the VARS Y-VARS menu. Then press
Í to select 1:Function. The FUNCTION
secondary menu is displayed. Press 1 to select
1:Y1.
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2. Press q 6 to select 6:ZStandard. This is a
quick way to reset the window variables to the
standard values. It also graphs the functions; you
do not need to press s.
Notice that the functions appear as an ellipse in
the standard viewing window.
3. To adjust the display so that each pixel represents
an equal width and height, press q 5 to select
5:ZSquare. The functions are replotted and now
appear as a circle on the display.
4. To see the ZSquare window variables, press
p and notice the new values for Xmin, Xmax,
Ymin, and Ymax.
Defining Graphs
TI-84 Plus—Graphing Mode Similarities
Chapter 3 specifically describes function graphing, but the steps shown here are similar
for each TI-84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are
unique to parametric graphing, polar graphing, and sequence graphing.
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Defining a Graph
To define a graph in any graphing mode, follow these steps. Some steps are not always
necessary.
1. Press z and set the appropriate graph mode.
2. Press o and enter, edit, or select one or more functions in the Y= editor.
3. Deselect stat plots, if necessary.
4. Set the graph style for each function.
5. Press p and define the viewing window variables.
6. Press y . and select the graph format settings.
Displaying and Exploring a Graph
After you have defined a graph, press s to display it. Explore the behavior of the
function or functions using the TI-84 Plus tools described in this chapter.
Saving a Graph for Later Use
You can store the elements that define the current graph to any of 10 graph database
variables (GDB1 through GDB9, and GDB0; Chapter 8). To recreate the current graph
later, simply recall the graph database to which you stored the original graph.
These types of information are stored in a GDB.
•
•
Y= functions
Graph style settings
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•
•
Window settings
Format settings
You can store a picture of the current graph display to any of 10 graph picture variables
(Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored
pictures onto the current graph.
Setting the Graph Modes
Checking and Changing the Graphing Mode
To display the mode screen, press z. The default settings are highlighted below. To
graph functions, you must select Func mode before you enter values for the window
variables and before you enter the functions.
The TI-84 Plus has four graphing modes.
•
•
•
•
Func (function graphing)
Par (parametric graphing; Chapter 4)
Pol (polar graphing; Chapter 5)
Seq (sequence graphing; Chapter 6)
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Other mode settings affect graphing results. Chapter 1 describes each mode setting.
•
•
•
•
Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates.
Radian or Degree angle mode affects interpretation of some functions.
Connected or Dot plotting mode affects plotting of selected functions.
Sequential or Simul graphing-order mode affects function plotting when more than
one function is selected.
Setting Modes from a Program
To set the graphing mode and other modes from a program, begin on a blank line in the
program editor and follow these steps.
1. Press z to display the mode settings.
2. Press †, ~, |, and } to place the cursor on the mode that you want to select.
3. Press Í to paste the mode name to the cursor location.
The mode is changed when the program is executed.
Defining Functions
Displaying Functions in the Y= Editor
To display the Y= editor, press o. You can store up to 10 functions to the function
variables Y1 through Y9, and Y0. You can graph one or more defined functions at once.
In this example, functions Y1 and Y2 are defined and selected.
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Defining or Editing a Function
To define or edit a function, follow these steps.
1. Press o to display the Y= editor.
2. Press † to move the cursor to the function you want to define or edit. To erase a
function, press ‘.
3. Enter or edit the expression to define the function.
•
You may use functions and variables (including matrices and lists) in the
expression. When the expression evaluates to a nonreal number, the value is
not plotted; no error is returned.
•
•
The independent variable in the function is X. Func mode defines „ as X.
To enter X, press „ or press ƒ [X].
When you enter the first character, the = is highlighted, indicating that the
function is selected.
As you enter the expression, it is stored to the variable Yn as a user-defined function
in the Y= editor.
4. Press Í or † to move the cursor to the next function.
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Defining a Function from the Home Screen or a Program
To define a function from the home screen or a program, begin on a blank line and follow
these steps.
1. Press ƒ [ã], enter the expression, and then press ƒ [ã] again.
2. Press ¿.
3. Press ~ 1 to select 1:Function from the VARS Y-VARS menu.
4. Select the function name, which pastes the name to the cursor location on the home
screen or program editor.
5. Press Í to complete the instruction.
"expression"!Yn
When the instruction is executed, the TI-84 Plus stores the expression to the designated
variable Yn, selects the function, and displays the message Done.
Evaluating Y= Functions in Expressions
You can calculate the value of a Y= function Yn at a specified value of X. A list of values
returns a list.
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Yn(value)
Yn({value1,value2,value3, . . .,value n})
Selecting and Deselecting Functions
Selecting and Deselecting a Function
You can select and deselect (turn on and turn off) a function in the Y= editor. A function
is selected when the = sign is highlighted. The TI-84 Plus graphs only the selected
functions. You can select any or all functions Y1 through Y9, and Y0.
To select or deselect a function in the Y= editor, follow these steps.
1. Press o to display the Y= editor.
2. Move the cursor to the function you want to select or deselect.
3. Press | to place the cursor on the function’s = sign.
4. Press Í to change the selection status.
When you enter or edit a function, it is selected automatically. When you clear a function,
it is deselected.
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Turning On or Turning Off a Stat Plot in the Y= Editor
To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3
(the top line of the Y= editor). When a plot is on, its name is highlighted on this line.
To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the
cursor on Plot1, Plot2, or Plot3, and then press Í.
Plot1 is turned on.
Plot2 and Plot3 are turned off.
Selecting and Deselecting Functions from the Home Screen or a
Program
To select or deselect a function from the home screen or a program, begin on a blank
line and follow these steps.
1. Press ~ to display the VARS Y-VARS menu.
2. Select 4:On/Off to display the ON/OFF secondary menu.
3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more
functions. The instruction you select is copied to the cursor location.
4. Enter the number (1 through 9, or 0; not the variable Yn) of each function you want to
turn on or turn off.
•
If you enter two or more numbers, separate them with commas.
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•
To turn on or turn off all functions, do not enter a number after FnOn or FnOff.
FnOn[function#,function#, . . .,function n]
FnOff[function#,function#, . . .,function n]
5. Press Í. When the instruction is executed, the status of each function in the
current mode is set and Doneis displayed.
For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and
then turns on Y1 and Y3.
Setting Graph Styles for Functions
MATH Graph Style Icons in the Y= Editor
This table describes the graph styles available for function graphing. Use the styles to
visually differentiate functions to be graphed together. For example, you can set Y1 as a
solid line, Y2 as a dotted line, and Y3 as a thick line.
Icon Style
Description
Line
A solid line connects plotted points; this is the default in
Connected mode
ç
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Icon Style
Description
Thick
A thick solid line connects plotted points
Shading covers the area above the graph
Shading covers the area below the graph
è
Above
é
Below
ê
Path
A circular cursor traces the leading edge of the graph and draws
a path
ë
Animate
A circular cursor traces the leading edge of the graph without
drawing a path
ì
Dot
A small dot represents each plotted point; this is the default in Dot
mode
í
Note: Some graph styles are not available in all graphing modes. Chapters 4, 5, and 6
list the styles for Par, Pol, and Seq modes.
Setting the Graph Style
To set the graph style for a function, follow these steps.
1. Press o to display the Y= editor.
2. Press † and } to move the cursor to the function.
3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first
column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.)
4. Press Í repeatedly to rotate through the graph styles. The seven styles rotate in
the same order in which they are listed in the table above.
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5. Press ~, }, or † when you have selected a style.
Shading Above and Below
When you select é or ê for two or more functions, the TI-84 Plus rotates through four
shading patterns.
•
•
•
•
•
Vertical lines shade the first function with a é or ê graph style.
Horizontal lines shade the second.
Negatively sloping diagonal lines shade the third.
Positively sloping diagonal lines shade the fourth.
The rotation returns to vertical lines for the fifth é or ê function, repeating the order
described above.
When shaded areas intersect, the patterns overlap.
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Note: When é or ê is selected for a Y= function that graphs a family of curves, such as
Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves.
Setting a Graph Style from a Program
To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu.
To display this menu, press while in the program editor. function# is the number of
the Y= function name in the current graphing mode. graphstyle# is an integer from 1 to 7
that corresponds to the graph style, as shown below.
1 = ç (line)
5 = ë (path)
6 = ì (animate)
7 = í (dot)
2 = è (thick)
3 = é (above)
4 = ê (below)
GraphStyle(function#,graphstyle#)
For example, when this program is executed in Func mode, GraphStyle(1,3) sets Y1 to
é (above).
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Setting the Viewing Window Variables
The TI-84 Plus Viewing Window
The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin,
and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y
scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set
Xscl=0 and Yscl=0.
Displaying the Window Variables
To display the current window variable values, press p. The window editor above
and to the right shows the default values in Func graphing mode and Radian angle
mode. The window variables differ from one graphing mode to another.
Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1.
•
•
At Xres=1, functions are evaluated and graphed at each pixel on the x-axis.
At Xres=8, functions are evaluated and graphed at every eighth pixel along the
x-axis.
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Note: Small Xres values improve graph resolution but may cause the TI-84 Plus to draw
graphs more slowly.
Changing a Window Variable Value
To change a window variable value from the window editor, follow these steps.
1. Press † or } to move the cursor to the window variable you want to change.
2. Edit the value, which can be an expression.
•
•
Enter a new value, which clears the original value.
Move the cursor to a specific digit, and then edit it.
3. Press Í, †, or }. If you entered an expression, the TI-84 Plus evaluates it. The
new value is stored.
Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.
Storing to a Window Variable from the Home Screen or a Program
To store a value, which can be an expression, to a window variable, begin on a blank line
and follow these steps.
1. Enter the value you want to store.
2. Press ¿.
3. Press to display the VARS menu.
4. Select 1:Window to display the Func window variables (X/Y secondary menu).
•
Press ~ to display the Par and Pol window variables (T/q secondary menu).
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•
Press ~ ~ to display the Seq window variables (U/V/W secondary menu).
5. Select the window variable to which you want to store a value. The name of the
variable is pasted to the current cursor location.
6. Press Í to complete the instruction.
When the instruction is executed, the TI-84 Plus stores the value to the window variable
and displays the value.
@X and @Y
The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y secondary menu)
define the distance from the center of one pixel to the center of any adjacent pixel on a
graph (graphing accuracy). @X and @Y are calculated from Xmin, Xmax, Ymin, and Ymax
when you display a graph.
(Xmax – Xmin)
(Ymax – Ymin)
∆X = -------------------------------------- ∆Y = --------------------------------------
94 62
You can store values to @X and @Y. If you do, Xmax and Ymax are calculated from @X,
Xmin, @Y, and Ymin.
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Setting the Graph Format
Displaying the Format Settings
To display the format settings, press y .. The default settings are highlighted
below.
Sets cursor coordinates.
Sets coordinates display on or off.
Sets grid off or on.
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
ExprOn ExprOff
Sets axes on or off.
Sets axes label off or on.
Sets expression display on or off.
Format settings define a graph’s appearance on the display. Format settings apply to all
graphing modes. Seq graphing mode has an additional mode setting (Chapter 6).
Changing a Format Setting
To change a format setting, follow these steps.
1. Press †, ~, }, and | as necessary to move the cursor to the setting you want to
select.
2. Press Í to select the highlighted setting.
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RectGC, PolarGC
RectGC (rectangular graphing coordinates) displays the cursor location as rectangular
coordinates X and Y.
PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R
and q.
The RectGC/PolarGC setting determines which variables are updated when you plot the
graph, move the free-moving cursor, or trace.
•
•
RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.
PolarGC updates X, Y, R, and q; if CoordOn format is selected, R and q are
displayed.
CoordOn, CoordOff
CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If
ExprOff format is selected, the function number is displayed in the top-right corner.
CoordOff (coordinates off) does not display the function number or coordinates.
GridOff, GridOn
Grid points cover the viewing window in rows that correspond to the tick marks on each
axis.
GridOff does not display grid points.
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GridOn displays grid points.
AxesOn, AxesOff
AxesOn displays the axes.
AxesOff does not display the axes.
This overrides the LabelOff/LabelOn format setting.
LabelOff, LabelOn
LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if
AxesOn format is also selected.
ExprOn, ExprOff
ExprOn and ExprOff determine whether to display the Y= expression when the trace
cursor is active. This format setting also applies to stat plots.
When ExprOn is selected, the expression is displayed in the top-left corner of the graph
screen.
When ExprOff and CoordOn both are selected, the number in the top-right corner
specifies which function is being traced.
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Displaying Graphs
Displaying a New Graph
To display the graph of the selected function or functions, press s. TRACE, ZOOM
instructions, and CALC operations display the graph automatically. As the TI-84 Plus
plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated.
Pausing or Stopping a Graph
While plotting a graph, you can pause or stop graphing.
•
•
Press Í to pause; then press Í to resume.
Press É to stop; then press s to redraw.
Smart Graph
Smart Graph is a TI-84 Plus feature that redisplays the last graph immediately when you
press s, but only if all graphing factors that would cause replotting have remained
the same since the graph was last displayed.
If you performed any of these actions since the graph was last displayed, the TI-84 Plus
will replot the graph based on new values when you press s.
•
•
•
Changed a mode setting that affects graphs
Changed a function in the current picture
Selected or deselected a function or stat plot
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•
•
•
•
Changed the value of a variable in a selected function
Changed a window variable or graph format setting
Cleared drawings by selecting ClrDraw
Changed a stat plot definition
Overlaying Functions on a Graph
On the TI-84 Plus, you can graph one or more new functions without replotting existing
functions. For example, store sin(X) to Y1 in the Y= editor and press s. Then store
cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the
original function.
Graphing a Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the TI-84 Plus plots the
function for each value in the list, thereby graphing a family of curves. In Simul graphing-
order mode, it graphs all functions sequentially for the first element in each list, and then
for the second, and so on.
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{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X).
{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X) .
Note: When using more than one list, the lists must have the same dimensions.
Exploring Graphs with the Free-Moving Cursor
Free-Moving Cursor
When a graph is displayed, press |, ~, }, or † to move the cursor around the graph.
When you first display the graph, no cursor is visible. When you press |, ~, }, or †,
the cursor moves from the center of the viewing window.
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As you move the cursor around the graph, the coordinate values of the cursor location
are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix
decimal mode setting determines the number of decimal digits displayed for the
coordinate values.
To display the graph with no cursor and no coordinate values, press ‘ or Í.
When you press |, ~, }, or †, the cursor moves from the same position.
Graphing Accuracy
The free-moving cursor moves from pixel to pixel on the screen. When you move the
cursor to a pixel that appears to be on the function, the cursor may be near, but not
actually on, the function. The coordinate value displayed at the bottom of the screen
actually may not be a point on the function. To move the cursor along a function, use
r.
The coordinate values displayed as you move the cursor approximate actual math
coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin,
and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the
coordinate values more closely approximate the math coordinates.
Free- moving cursor “on”
the curve
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Exploring Graphs with TRACE
Beginning a Trace
Use TRACE to move the cursor from one plotted point to the next along a function. To
begin a trace, press r. If the graph is not displayed already, press r to display
it. The trace cursor is on the first selected function in the Y= editor, at the middle X value
on the screen. The cursor coordinates are displayed at the bottom of the screen if
CoordOn format is selected. The Y= expression is displayed in the top-left corner of the
screen, if ExprOn format is selected.
Moving the Trace Cursor
To move the TRACE cursor
do this:
To the previous or next plotted point,
press | or ~.
press y | or y ~.
Five plotted points on a function (Xres
affects this),
To any valid X value on a function,
From one function to another,
enter a value, and then press Í.
press } or †.
When the trace cursor moves along a function, the Y value is calculated from the X
value; that is, Y=Yn(X). If the function is undefined at an X value, the Y value is blank.
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Trace cursor on the curve
If you move the trace cursor beyond the top or bottom of the screen, the coordinate
values at the bottom of the screen continue to change appropriately.
Moving the Trace Cursor from Function to Function
To move the trace cursor from function to function, press † and }. The cursor follows
the order of the selected functions in the Y= editor. The trace cursor moves to each
function at the same X value. If ExprOn format is selected, the expression is updated.
Moving the Trace Cursor to Any Valid X Value
To move the trace cursor to any valid X value on the current function, enter the value.
When you enter the first digit, an X= prompt and the number you entered are displayed in
the bottom-left corner of the screen. You can enter an expression at the X= prompt. The
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value must be valid for the current viewing window. When you have completed the entry,
press Í to move the cursor.
Note: This feature does not apply to stat plots.
Panning to the Left or Right
If you trace a function beyond the left or right side of the screen, the viewing window
automatically pans to the left or right. Xmin and Xmax are updated to correspond to the
new viewing window.
Quick Zoom
While tracing, you can press Í to adjust the viewing window so that the cursor
location becomes the center of the new viewing window, even if the cursor is above or
below the display. This allows panning up and down. After Quick Zoom, the cursor
remains in TRACE.
Leaving and Returning to TRACE
When you leave and return to TRACE, the trace cursor is displayed in the same location
it was in when you left TRACE, unless Smart Graph has replotted the graph.
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Using TRACE in a Program
On a blank line in the program editor, press r. The instruction Trace is pasted to the
cursor location. When the instruction is encountered during program execution, the
graph is displayed with the trace cursor on the first selected function. As you trace, the
cursor coordinate values are updated. When you finish tracing the functions, press
Í to resume program execution.
Exploring Graphs with the ZOOM Instructions
ZOOM Menu
To display the ZOOM menu, press q. You can adjust the viewing window of the graph
quickly in several ways. All ZOOM instructions are accessible from programs.
ZOOM MEMORY
Draws a box to define the viewing window.
Magnifies the graph around the cursor.
Views more of a graph around the cursor.
Sets @X and @Y to 0.1.
1: ZBox
2: Zoom In
3: Zoom Out
4: ZDecimal
5: ZSquare
Sets equal-size pixels on the X and Y axes.
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ZOOM MEMORY
6: ZStandard
7: ZTrig
Sets the standard window variables.
Sets the built-in trig window variables.
Sets integer values on the X and Y axes.
Sets the values for current stat lists.
8: ZInteger
9: ZoomStat
0: ZoomFit
Fits YMin and YMax between XMin and XMax.
Zoom Cursor
When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the
zoom cursor (+), a smaller version of the free-moving cursor (+).
ZBox
To define a new viewing window using ZBox, follow these steps.
1. Select 1:ZBox from the ZOOM menu. The zoom cursor is displayed at the center of
the screen.
2. Move the zoom cursor to any spot you want to define as a corner of the box, and
then press Í. When you move the cursor away from the first defined corner, a
small, square dot indicates the spot.
3. Press |, }, ~, or †. As you move the cursor, the sides of the box lengthen or
shorten proportionately on the screen.
Note: To cancel ZBox before you press Í, press ‘.
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4. When you have defined the box, press Í to replot the graph.
To use ZBox to define another box within the new graph, repeat steps 2 through 4. To
cancel ZBox, press ‘.
Zoom In, Zoom Out
Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out
displays a greater portion of the graph, centered on the cursor location. The XFact and
YFact settings determine the extent of the zoom.
To zoom in on a graph, follow these steps.
1. Check XFact and YFact; change as needed.
2. Select 2:Zoom In from the ZOOM menu. The zoom cursor is displayed.
3. Move the zoom cursor to the point that is to be the center of the new viewing
window.
4. Press Í. The TI-83 Plus adjusts the viewing window by XFact and YFact;
updates the window variables; and replots the selected functions, centered on the
cursor location.
5. Zoom in on the graph again in either of two ways.
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•
•
To zoom in at the same point, press Í.
To zoom in at a new point, move the cursor to the point that you want as the
center of the new viewing window, and then press Í.
To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5.
To cancel Zoom In or Zoom Out, press ‘.
ZDecimal
ZDecimal replots the functions immediately. It updates the window variables to preset
values, as shown below. These values set @X and @Y equal to 0.1 and set the X and Y
value of each pixel to one decimal place.
Xmin=L4.7
Xmax=4.7
Xscl=1
Ymin=L3.1
Ymax=3.1
Yscl=1
ZSquare
ZSquare replots the functions immediately. It redefines the viewing window based on the
current values of the window variables. It adjusts in only one direction so that @X=@Y,
which makes the graph of a circle look like a circle. Xscl and Yscl remain unchanged.
The midpoint of the current graph (not the intersection of the axes) becomes the
midpoint of the new graph.
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ZStandard
ZStandard replots the functions immediately. It updates the window variables to the
standard values shown below.
Xres=1
Xmin=L10
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
ZTrig
ZTrig replots the functions immediately. It updates the window variables to preset values
that are appropriate for plotting trig functions. Those preset values in Radian mode are
shown below.
Xmin=L(47à24)p
Xmax=(47à24)p
Xscl=p/2
Ymin=L4
Ymax=4
Yscl=1
ZInteger
ZInteger redefines the viewing window to the dimensions shown below. To use ZInteger,
move the cursor to the point that you want to be the center of the new window, and then
press Í; ZInteger replots the functions.
Xscl=10
Yscl=10
@X=1
@Y=1
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ZoomStat
ZoomStat redefines the viewing window so that all statistical data points are displayed.
For regular and modified box plots, only Xmin and Xmax are adjusted.
ZoomFit
ZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to
include the minimum and maximum Y values of the selected functions between the
current XMin and XMax. XMin and XMax are not changed.
Using ZOOM MEMORY
ZOOM MEMORY Menu
To display the ZOOM MEMORY menu, press q ~.
ZOOM MEMORY
Uses the previous viewing window.
Stores the user-defined window.
1: ZPrevious
2: ZoomSto
Recalls the user-defined window.
Changes Zoom In and Zoom Out factors.
3: ZoomRcl
4: SetFactors...
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ZPrevious
ZPrevious replots the graph using the window variables of the graph that was displayed
before you executed the last ZOOM instruction.
ZoomSto
ZoomSto immediately stores the current viewing window. The graph is displayed, and the
values of the current window variables are stored in the user-defined ZOOM variables
ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres.
These variables apply to all graphing modes. For example, changing the value of ZXmin
in Func mode also changes it in Par mode.
ZoomRcl
ZoomRcl graphs the selected functions in a user-defined viewing window. The user-
defined viewing window is determined by the values stored with the ZoomSto instruction.
The window variables are updated with the user-defined values, and the graph is plotted.
ZOOM FACTORS
The zoom factors, XFact and YFact, are positive numbers (not necessarily integers)
greater than or equal to 1. They define the magnification or reduction factor used to
Zoom In or Zoom Out around a point.
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Checking XFact and YFact
To display the ZOOM FACTORS screen, where you can review the current values for
XFact and YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown
are the defaults.
Changing XFact and YFact
You can change XFact and YFact in either of two ways.
•
•
Enter a new value. The original value is cleared automatically when you enter the
first digit.
Place the cursor on the digit you want to change, and then enter a value or press
{ to delete it.
Using ZOOM MEMORY Menu Items from the Home Screen or a Program
From the home screen or a program, you can store directly to any of the user-defined
ZOOM variables.
From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM
MEMORY menu.
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Using the CALC (Calculate) Operations
CALCULATE Menu
To display the CALCULATE menu, press y /. Use the items on this menu to
analyze the current graph functions.
CALCULATE
Calculates a function Y value for a given X.
Finds a zero (x-intercept) of a function.
Finds a minimum of a function.
1: value
2: zero
3: minimum
4: maximum
5: intersect
6: dy/dx
Finds a maximum of a function.
Finds an intersection of two functions.
Finds a numeric derivative of a function.
Finds a numeric integral of a function.
7: ‰f(x)dx
value
value evaluates one or more currently selected functions for a specified value of X.
Note: When a value is displayed for X, press ‘ to clear the value. When no value is
displayed, press ‘ to cancel the value operation.
To evaluate a selected function at X, follow these steps.
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1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the
bottom-left corner.
2. Enter a real value, which can be an expression, for X between Xmin and Xmax.
3. Press Í.
The cursor is on the first selected function in the Y= editor at the X value you entered,
and the coordinates are displayed, even if CoordOff format is selected.
To move the cursor from function to function at the entered X value, press } or †. To
restore the free-moving cursor, press | or ~.
zero
zero finds a zero (x-intercept or root) of a function using solve(. Functions can have more
than one x-intercept value; zero finds the zero closest to your guess.
The time zero spends to find the correct zero value depends on the accuracy of the
values you specify for the left and right bounds and the accuracy of your guess.
To find a zero of a function, follow these steps.
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1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left
Bound?in the bottom-left corner.
2. Press } or † to move the cursor onto the function for which you want to find a zero.
3. Press | or ~ (or enter a value) to select the x-value for the left bound of the
interval, and then press Í. A 4 indicator on the graph screen shows the left
bound. Right Bound?is displayed in the bottom-left corner. Press | or ~ (or enter
a value) to select the x-value for the right bound, and then press Í. A 3 indicator
on the graph screen shows the right bound. Guess?is then displayed in the bottom-
left corner.
4. Press | or ~ (or enter a value) to select a point near the zero of the function,
between the bounds, and then press Í.
The cursor is on the solution and the coordinates are displayed, even if CoordOff format
is selected. To move to the same x-value for other selected functions, press } or †. To
restore the free-moving cursor, press | or ~.
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minimum, maximum
minimum and maximum find a minimum or maximum of a function within a specified
interval to a tolerance of 1âL5.
To find a minimum or maximum, follow these steps.
1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is
displayed.
2. Select the function and set left bound, right bound, and guess as described for zero.
The cursor is on the solution, and the coordinates are displayed, even if you have
selected CoordOff format; Minimum or Maximum is displayed in the bottom-left corner.
To move to the same x-value for other selected functions, press } or †. To restore the
free-moving cursor, press | or ~.
intersect
intersect finds the coordinates of a point at which two or more functions intersect using
solve(. The intersection must appear on the display to use intersect.
To find an intersection, follow these steps.
1. Select 5:intersect from the CALCULATE menu. The current graph is displayed with
First curve?in the bottom-left corner.
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2. Press † or }, if necessary, to move the cursor to the first function, and then press
Í. Second curve?is displayed in the bottom-left corner.
3. Press † or }, if necessary, to move the cursor to the second function, and then
press Í.
4. Press ~ or | to move the cursor to the point that is your guess as to location of the
intersection, and then press Í.
The cursor is on the solution and the coordinates are displayed, even if CoordOff format
is selected. Intersection is displayed in the bottom-left corner. To restore the free-moving
cursor, press |, }, ~, or †.
dy/dx
dy/dx (numerical derivative) finds the numerical derivative (slope) of a function at a point,
with H=1âL3.
To find a function’s slope at a point, follow these steps.
1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed.
2. Press } or † to select the function for which you want to find the numerical
derivative.
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3. Press | or ~ (or enter a value) to select the X value at which to calculate the
derivative, and then press Í.
The cursor is on the solution and the numerical derivative is displayed.
To move to the same x-value for other selected functions, press } or †. To restore the
free-moving cursor, press | or ~.
‰f(x)dx
‰f(x)dx (numerical integral) finds the numerical integral of a function in a specified
interval. It uses the fnInt( function, with a tolerance of H=1âL3.
To find the numerical integral of a function, follow these steps.
1. Select 7:‰f(x)dx from the CALCULATE menu. The current graph is displayed with
Lower Limit?in the bottom-left corner.
2. Press } or † to move the cursor to the function for which you want to calculate the
integral.
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3. Set lower and upper limits as you would set left and right bounds for zero. The
integral value is displayed, and the integrated area is shaded.
Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that
invokes Smart Graph to clear the shaded area.
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Chapter 4:
Parametric Graphing
Getting Started: Path of a Ball
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the path of a ball hit at an initial speed of
30 meters per second, at an initial angle of 25 degrees with the horizontal from ground
level. How far does the ball travel? When does it hit the ground? How high does it go?
Ignore all forces except gravity.
For initial velocity v and angle q, the position of the ball as a function of time has
o
horizontal and vertical components.
1
2
2
--
Vertical: Y1(t)=tv sin(q)N gt
Horizontal: X1(t)=tv cos(q)
0
0
The vertical and horizontal vectors of the ball’s motion also will be graphed.
Vertical vector:
Horizontal vector:
X2(t)=0
X3(t)=X1(t)
Y2(t)=Y1(t)
Y3(t)=0
2
Gravity constant:
g=9.8 m/sec
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1. Press z. Press † † † ~ Í to select Par
mode. Press † † ~ Í to select Simul for
simultaneous graphing of all three parametric
equations in this example.
2. Press o. Press 30 „ ™ 25 y ; 1 (to
select ¡) ¤ Í to define X1T in terms of T.
3. Press 30 „ ˜ 25 y ; 1 ¤ ¹ 9.8 ¥ 2
„ ¡ Í to define Y1T.
The vertical component vector is defined by X2T
and Y2T.
4. Press 0 Í to define X2T.
5. Press ~ to display the VARS Y-VARS menu.
Press 2 to display the PARAMETRIC secondary
menu. Press 2 Í to define Y2T.
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The horizontal component vector is defined by X3T
and Y3T.
6. Press ~ 2, and then press 1 Í to define
X3T. Press 0 Í to define Y3T.
7. Press | | } Í to change the graph style to
è for X3T and Y3T. Press } Í Í to
change the graph style to ë for X2T and Y2T. Press
} Í Í to change the graph style to ë for
X1T and Y1T. (These keystrokes assume that all
graph styles were set to ç originally.)
8. Press p. Enter these values for the window
variables.
Tmin=0
Tmax=5
Tstep=.1
Xmin=L10
Xmax=100
Xscl=50
Ymin=L5
Ymax=15
Yscl=10
9. Press y . † † † ~ Í to set AxesOff,
which turns off the axes.
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10. Press s. The plotting action simultaneously
shows the ball in flight and the vertical and
horizontal component vectors of the motion.
Note: To simulate the ball flying through the air, set
graph style to ì (animate) for X1T and Y1T.
11. Press r to obtain numerical results and
answer the questions at the beginning of this
section.
Tracing begins at Tmin on the first parametric
equation (X1T and Y1T). As you press ~ to trace
the curve, the cursor follows the path of the ball
over time. The values for X (distance), Y (height),
and T (time) are displayed at the bottom of the
screen.
Defining and Displaying Parametric Graphs
TI-84 Plus Graphing Mode Similarities
The steps for defining a parametric graph are similar to the steps for defining a function
graph. Chapter 4 assumes that you are familiar with Chapter 3: Function Graphing.
Chapter 4 details aspects of parametric graphing that differ from function graphing.
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Setting Parametric Graphing Mode
To display the mode screen, press z. To graph parametric equations, you must select
Par graphing mode before you enter window variables and before you enter the
components of parametric equations.
Displaying the Parametric Y= Editor
After selecting Par graphing mode, press o to display the parametric Y= editor.
In this editor, you can display and enter both the X and Y components of up to six
equations, X1T and Y1T through X6T and Y6T. Each is defined in terms of the
independent variable T. A common application of parametric graphs is graphing
equations over time.
Selecting a Graph Style
The icons to the left of X1T through X6T represent the graph style of each parametric
equation. The default in Par mode is ç (line), which connects plotted points. Line,
è (thick), ë (path), ì (animate), and í (dot) styles are available for parametric graphing.
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Defining and Editing Parametric Equations
To define or edit a parametric equation, follow the steps in Chapter 3 for defining a
function or editing a function. The independent variable in a parametric equation is T. In
Par graphing mode, you can enter the parametric variable T in either of two ways.
•
•
Press „.
Press ƒ [T].
Two components, X and Y, define a single parametric equation. You must define both of
them.
Selecting and Deselecting Parametric Equations
The TI-84 Plus graphs only the selected parametric equations. In the Y= editor, a
parametric equation is selected when the = signs of both the X and Y components are
highlighted. You may select any or all of the equations X1T and Y1T through X6T and Y6T.
To change the selection status, move the cursor onto the = sign of either the X or Y
component and press Í. The status of both the X and Y components is changed.
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Setting Window Variables
To display the window variable values, press p. These variables define the viewing
window. The values below are defaults for Par graphing in Radian angle mode.
Smallest T value to evaluate
Tmin=0
Tmax=6.2831853...
Tstep=.1308996...
Xmin=L10
Largest T value to evaluate (2p)
T value increment (pà24)
Smallest X value to be displayed
Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Note: To ensure that sufficient points are plotted, you may want to change the T window
variables.
Setting the Graph Format
To display the current graph format settings, press y .. Chapter 3 describes the
format settings in detail. The other graphing modes share these format settings; Seq
graphing mode has an additional axes format setting.
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Displaying a Graph
When you press s, the TI-84 Plus plots the selected parametric equations. It
evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of
Tstep), and then plots each point defined by X and Y. The window variables define the
viewing window.
As the graph is plotted, X, Y, and T are updated.
Smart Graph applies to parametric graphs.
Window Variables and Y.VARS Menus
You can perform these actions from the home screen or a program.
•
Access functions by using the name of the X or Y component of the equation as a
variable.
•
Store parametric equations.
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•
•
Select or deselect parametric equations.
Store values directly to window variables.
Exploring Parametric Graphs
Free-Moving Cursor
The free-moving cursor in Par graphing works the same as in Func graphing.
In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is
selected, X and Y are displayed.
In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are
displayed.
TRACE
To activate TRACE, press r. When TRACE is active, you can move the trace cursor
along the graph of the equation one Tstep at a time. When you begin a trace, the trace
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cursor is on the first selected function at Tmin. If ExprOn is selected, then the function is
displayed.
In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn
format is on.
In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and
T are displayed. The X and Y (or R and q) values are calculated from T.
To move five plotted points at a time on a function, press y | or y ~. If you move
the cursor beyond the top or bottom of the screen, the coordinate values at the bottom of
the screen continue to change appropriately.
Quick Zoom is available in Par graphing; panning is not.
Moving the Trace Cursor to Any Valid T Value
To move the trace cursor to any valid T value on the current function, enter the number.
When you enter the first digit, a T= prompt and the number you entered are displayed in
the bottom-left corner of the screen. You can enter an expression at the T= prompt. The
value must be valid for the current viewing window. When you have completed the entry,
press Í to move the cursor.
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ZOOM
ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin,
Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
The T window variables (Tmin, Tmax, and Tstep) are only affected when you select
ZStandard. The VARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and
3:ZTstep are the zoom memory variables for Par graphing.
CALC
CALC operations in Par graphing work the same as in Func graphing. The CALCULATE
menu items available in Par graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.
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Chapter 5:
Polar Graphing
Getting Started: Polar Rose
Getting Started is a fast-paced introduction. Read the chapter for details.
The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and
then explore the appearance of the rose for other values of A and B.
1. Press z to display the MODE screen. Press †
† † ~ ~ Í to select Pol graphing mode.
Select the defaults (the options on the left) for the
other mode settings.
2. Press o to display the polar Y= editor. Press 8
˜ 2.5 „ ¤ Í to define r1.
3. Press q 6 to select 6:ZStandard and graph the
equation in the standard viewing window. The
graph shows only five petals of the rose, and the
rose does not appear to be symmetrical. This is
because the standard window sets qmax=2p and
defines the window, rather than the pixels, as
square.
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4. Press p to display the window variables.
Press † 4 y B to increase the value of qmax to
4p.
5. Press q 5 to select 5:ZSquare and plot the
graph.
6. Repeat steps 2 through 5 with new values for the
variables A and B in the polar equation
r1=Asin(Bq). Observe how the new values affect
the graph.
Defining and Displaying Polar Graphs
TI-84 Plus Graphing Mode Similarities
The steps for defining a polar graph are similar to the steps for defining a function graph.
Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5
details aspects of polar graphing that differ from function graphing.
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Setting Polar Graphing Mode
To display the mode screen, press z. To graph polar equations, you must select Pol
graphing mode before you enter values for the window variables and before you enter
polar equations.
Displaying the Polar Y= Editor
After selecting Pol graphing mode, press o to display the polar Y= editor.
In this editor, you can enter and display up to six polar equations, r1 through r6. Each is
defined in terms of the independent variable q.
Selecting Graph Styles
The icons to the left of r1 through r6 represent the graph style of each polar equation.
The default in Pol graphing mode is ç (line), which connects plotted points. Line,
è (thick), ë (path), ì (animate), and í (dot) styles are available for polar graphing.
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Defining and Editing Polar Equations
To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or
editing a function. The independent variable in a polar equation is q. In Pol graphing
mode, you can enter the polar variable q in either of two ways.
•
•
Press „.
Press ƒ [q].
Selecting and Deselecting Polar Equations
The TI-84 Plus graphs only the selected polar equations. In the Y= editor, a polar
equation is selected when the = sign is highlighted. You may select any or all of the
equations.
To change the selection status, move the cursor onto the = sign, and then press Í.
Setting Window Variables
To display the window variable values, press p. These variables define the viewing
window. The values below are defaults for Pol graphing in Radian angle mode.
qmin=0
Smallest q value to evaluate
qmax=6.2831853...
qstep=.1308996...
Xmin=L10
Largest q value to evaluate (2p)
Increment between q values (pà24)
Smallest X value to be displayed
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Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
Note: To ensure that sufficient points are plotted, you may want to change the q window
variables.
Setting the Graph Format
To display the current graph format settings, press y .. Chapter 3 describes the
format settings in detail. The other graphing modes share these format settings.
Displaying a Graph
When you press s, the TI-84 Plus plots the selected polar equations. It evaluates R
for each value of q (from qmin to qmax in intervals of qstep) and then plots each point.
The window variables define the viewing window.
As the graph is plotted, X, Y, R, and q are updated.
Smart Graph applies to polar graphs.
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Window Variables and Y.VARS Menus
You can perform these actions from the home screen or a program.
•
Access functions by using the name of the equation as a variable.
•
Store polar equations.
•
•
Select or deselect polar equations.
Store values directly to window variables.
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Exploring Polar Graphs
Free-Moving Cursor
The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC
format, moving the cursor updates the values of X and Y; if CoordOn format is selected,
X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format
is selected, R and q are displayed.
TRACE
To activate TRACE, press r. When TRACE is active, you can move the trace cursor
along the graph of the equation one qstep at a time. When you begin a trace, the trace
cursor is on the first selected function at qmin. If ExprOn format is selected, then the
equation is displayed.
In RectGC format, TRACE updates the values of X, Y, and q; if CoordOn format is
selected, X, Y, and q are displayed. In PolarGC format, TRACE updates X, Y, R, and q; if
CoordOn format is selected, R and q are displayed.
To move five plotted points at a time on a function, press y | or y ~. If you move
the trace cursor beyond the top or bottom of the screen, the coordinate values at the
bottom of the screen continue to change appropriately.
Quick Zoom is available in Pol graphing mode; panning is not.
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Moving the Trace Cursor to Any Valid Theta Value
To move the trace cursor to any valid q value on the current function, enter the number.
When you enter the first digit, a q= prompt and the number you entered are displayed in
the bottom-left corner of the screen. You can enter an expression at the q= prompt. The
value must be valid for the current viewing window. When you complete the entry, press
Í to move the cursor.
ZOOM
ZOOM operations in Pol graphing work the same as in Func graphing. Only the X (Xmin,
Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
The q window variables (qmin, qmax, and qstep) are not affected, except when you select
ZStandard. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and
6:Zqstep are zoom memory variables for Pol graphing.
CALC
CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE
menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq.
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Chapter 6:
Sequence Graphing
Getting Started: Forest and Trees
Note: Getting Started is a fast-paced introduction. Read the chapter for details.
A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the
trees will be harvested and 1,000 new trees will be planted. Will the forest eventually
disappear? Will the forest size stabilize? If so, in how many years and with how many
trees?
1. Press z. Press † † † ~ ~ ~ Í to select
Seq graphing mode.
2. Press y . and select Time axes format and
ExprOn format if necessary.
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3. Press o. If the graph-style icon is not ç (dot),
press | |, press Í until ç is displayed, and
then press ~ ~.
4. Press ~ 3 to select iPart( (integer part)
because only whole trees are harvested. After
each annual harvest, 80 percent (.80) of the trees
remain.
Press Ë 8 y [u] £ „ ¹ 1 ¤ to define the
number of trees after each harvest. Press à 1000
¤ to define the new trees. Press † 4000 to define
the number of trees at the beginning of the
program.
5. Press p 0 to set nMin=0. Press † 50 to set
nMax=50. nMin and nMax evaluate forest size over
50 years. Set the other window variables.
PlotStart=1 Xmin=0
PlotStep=1 Xmax=50 Ymax=6000
Xscl=10 Yscl=1000
Ymin=0
6. Press r. Tracing begins at nMin (the start of
the forestry plan). Press ~ to trace the sequence
year by year. The sequence is displayed at the top
of the screen. The values for n (number of years),
X (X=n, because n is plotted on the x-axis), and Y
(tree count) are displayed at the bottom. When will
the forest stabilize? With how many trees?
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Defining and Displaying Sequence Graphs
TI-84 Plus Graphing Mode Similarities
The steps for defining a sequence graph are similar to the steps for defining a function
graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing.
Chapter 6 details aspects of sequence graphing that differ from function graphing.
Setting Sequence Graphing Mode
To display the mode screen, press z. To graph sequence functions, you must select
Seq graphing mode before you enter window variables and before you enter sequence
functions.
Sequence graphs automatically plot in Simul mode, regardless of the current plotting-
order mode setting.
TI-84 Plus Sequence Functions u, v, and w
The TI-84 Plus has three sequence functions that you can enter from the keyboard: u, v,
and w. They are above the ¬, −, and ® keys.
You can define sequence functions in terms of:
•
•
•
The independent variable n
The previous term in the sequence function, such as u(nN1)
The term that precedes the previous term in the sequence function, such as u(nN2)
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•
The previous term or the term that precedes the previous term in another sequence
function, such as u(nN1) or u(nN2) referenced in the sequence v(n).
Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements
about u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for
v(nN2) and w(nN2).
Displaying the Sequence Y= Editor
After selecting Seq mode, press o to display the sequence Y= editor.
In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can
edit the value for nMin, which is the sequence window variable that defines the minimum
n value to evaluate.
The sequence Y= editor displays the nMin value because of its relevance to u(nMin),
v(nMin), and w(nMin), which are the initial values for the sequence equations u(n), v(n),
and w(n), respectively.
nMin in the Y= editor is the same as nMin in the window editor. If you enter a new value
for nMin in one editor, the new value for nMin is updated in both editors.
Note: Use u(nMin), v(nMin), or w(nMin) only with a recursive sequence, which requires an
initial value.
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Selecting Graph Styles
The icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence
(Chapter 3). The default in Seq mode is í (dot), which shows discrete values. Dot,
ç (line), and è (thick) styles are available for sequence graphing. Graph styles are
ignored in Web format.
Selecting and Deselecting Sequence Functions
The TI-84 Plus graphs only the selected sequence functions. In the Y= editor, a
sequence function is selected when the = signs of both u(n)= and u(nMin)= are
highlighted.
To change the selection status of a sequence function, move the cursor onto the = sign
of the function name, and then press Í. The status is changed for both the
sequence function u(n) and its initial value u(nMin).
Defining and Editing a Sequence Function
To define or edit a sequence function, follow the steps in Chapter 3 for defining a
function. The independent variable in a sequence is n.
In Seq graphing mode, you can enter the sequence variable in either of two ways.
•
•
Press „.
Press y N [N].
You can enter the function name from the keyboard.
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•
•
•
To enter the function name u, press y [u] (above ¬).
To enter the function name v, press y [v] (above −).
To enter the function name w, press y [w] (above ®).
Generally, sequences are either nonrecursive or recursive. Sequences are evaluated
only at consecutive integer values. n is always a series of consecutive integers, starting
at zero or any positive integer.
Nonrecursive Sequences
In a nonrecursive sequence, the nth term is a function of the independent variable n.
Each term is independent of all other terms.
For example, in the nonrecursive sequence below, you can calculate u(5) directly,
without first calculating u(1) or any previous term.
The sequence equation above returns the sequence 2, 4, 6, 8, 10, … for
n = 1, 2, 3, 4, 5, … .
Note: You may leave blank the initial value u(nMin) when calculating nonrecursive
sequences.
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Recursive Sequences
In a recursive sequence, the nth term in the sequence is defined in relation to the
previous term or the term that precedes the previous term, represented by u(nN1) and
u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n.
For example, in the sequence below you cannot calculate u(5) without first calculating
u(1), u(2), u(3), and u(4).
Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... .
Note: On the TI-84 Plus, you must type each character of the terms. For example, to
enter u(nN1), press y [u] £ „ ¹ À ¤.
Recursive sequences require an initial value or values, since they reference undefined
terms.
•
If each term in the sequence is defined in relation to the previous term, as in u(nN1),
you must specify an initial value for the first term.
•
If each term in the sequence is defined in relation to the term that precedes the
previous term, as in u(nN2), you must specify initial values for the first two terms.
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Enter the initial values as a list enclosed in braces ({ }) with commas separating the
values.
The value of the first term is 0 and the value of the second term is 1 for the sequence
u(n).
Setting Window Variables
To display the window variables, press p. These variables define the viewing
window. The values below are defaults for Seq graphing in both Radian and Degree
angle modes.
Smallest n value to evaluate
nMin=1
Largest n value to evaluate
nMax=10
First term number to be plotted
Incremental n value (for graphing only)
Smallest X value to be displayed
PlotStart=1
PlotStep=1
Xmin=L10
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Largest X value to be displayed
Spacing between the X tick marks
Smallest Y value to be displayed
Largest Y value to be displayed
Spacing between the Y tick marks
Xmax=10
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
nMin must be an integer | 0. nMax, PlotStart, and PlotStep must be integers | 1.
nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor.
nMax is the largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1),
u(nMin+2), ... , u(nMax).
PlotStart is the first term to be plotted. PlotStart=1 begins plotting on the first term in the
sequence. If you want plotting to begin with the fifth term in a sequence, for example, set
PlotStart=5. The first four terms are evaluated but are not plotted on the graph.
PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence
evaluation; it only designates which points are plotted on the graph. If you specify
PlotStep=2, the sequence is evaluated at each consecutive integer, but it is plotted on the
graph only at every other integer.
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Selecting Axes Combinations
Setting the Graph Format
To display the current graph format settings, press y .. Chapter 3 describes the
format settings in detail. The other graphing modes share these format settings. The
axes setting on the top line of the screen is available only in Seq mode.
Type of sequence plot (axes)
Rectangular or polar output
Cursor coordinate display on/off
Grid display off or on
Time Web uv vw uw
RectGC
Polar GC
CoordOn
GridOff
AxesOn
CoordOff
GridOn
Axes display on or off
AxesOff
LabelOn
ExprOff
Axes label display off or on
Expression display on or off
LableOff
ExprOn
Setting Axes Format
For sequence graphing, you can select from five axes formats. The table below shows
the values that are plotted on the x-axis and y-axis for each axes setting.
Axes Setting
Time
x-axis
y-axis
n
u(n), v(n), w(n)
u(n), v(n), w(n)
Web
u(nN1), v(nN1), w(nN1)
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Axes Setting
x-axis
u(n)
y-axis
v(n)
uv
vw
uw
v(n)
w(n)
w(n)
u(n)
Displaying a Sequence Graph
To plot the selected sequence functions, press s. As a graph is plotted, the TI-84
Plus updates X, Y, and n.
Smart Graph applies to sequence graphs (Chapter 3).
Exploring Sequence Graphs
Free-Moving Cursor
The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC
format, moving the cursor updates the values of X and Y; if CoordOn format is selected,
X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format
is selected, R and q are displayed.
TRACE
The axes format setting affects TRACE.
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When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the
sequence one PlotStep increment at a time. To move five plotted points at once, press
y ~ or y |.
•
•
When you begin a trace, the trace cursor is on the first selected sequence at the
term number specified by PlotStart, even if it is outside the viewing window.
Quick Zoom applies to all directions. To center the viewing window on the current
cursor location after you have moved the trace cursor, pressÍÍ. The trace cursor
returns to nMin.
In Web format, the trail of the cursor helps identify points with attracting and repelling
behavior in the sequence. When you begin a trace, the cursor is on the x-axis at the
initial value of the first selected function.
Note: To move the cursor to a specified n during a trace, enter a value for n, and press
Í. For example, to quickly return the cursor to the beginning of the sequence, paste
nMin to the n= prompt and press Í.
Moving the Trace Cursor to Any Valid n Value
To move the trace cursor to any valid n value on the current function, enter the number.
When you enter the first digit, an n= prompt and the number you entered are displayed in
the bottom-left corner of the screen. You can enter an expression at the n= prompt. The
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value must be valid for the current viewing window. When you have completed the entry,
press Í to move the cursor.
ZOOM
ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin,
Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected.
PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The
VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for
Seq graphing.
CALC
The only CALC operation available in Seq graphing is value.
•
•
When Time axes format is selected, value displays Y (the u(n) value) for a specified n
value.
When Web axes format is selected, value draws the web and displays Y (the u(n)
value) for a specified n value.
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•
When uv, vw, or uw axes format is selected, value displays X and Y according to the
axes format setting. For example, for uv axes format, X represents u(n) and Y
represents v(n).
Evaluating u, v, and w
To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can evaluate these
names in any of three ways.
•
•
•
Calculate the nth value in a sequence.
Calculate a list of values in a sequence.
Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.
Graphing Web Plots
Graphing a Web Plot
To select Web axes format, press y . ~ Í. A web plot graphs u(n) versus
u(nN1), which you can use to study long-term behavior (convergence, divergence, or
oscillation) of a recursive sequence. You can see how the sequence may change
behavior as its initial value changes.
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Valid Functions for Web Plots
When Web axes format is selected, a sequence will not graph properly or will generate
an error.
•
•
•
It must be recursive with only one recursion level (u(nN1) but not u(nN2)).
It cannot reference n directly.
It cannot reference any defined sequence except itself.
Displaying the Graph Screen
In Web format, press s to display the graph screen. The TI-84 Plus:
•
•
Draws a y=x reference line in AxesOn format.
Plots the selected sequences with u(nN1) as the independent variable.
Note: A potential convergence point occurs whenever a sequence intersects the y=x
reference line. However, the sequence may or may not actually converge at that point,
depending on the sequence’s initial value.
Drawing the Web
To activate the trace cursor, press r. The screen displays the sequence and the
current n, X, and Y values (X represents u(nN1) and Y represents u(n)). Press ~
repeatedly to draw the web step by step, starting at nMin. In Web format, the trace cursor
follows this course.
1. It starts on the x-axis at the initial value u(nMin) (when PlotStart=1).
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2. It moves vertically (up or down) to the sequence.
3. It moves horizontally to the y=x reference line.
4. It repeats this vertical and horizontal movement as you continue to press ~.
Using Web Plots to Illustrate Convergence
Example: Convergence
1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is
set to í (dot), and then define nMin, u(n) and u(nMin) as shown below.
2. Press y . Í to set Time axes format.
3. Press p and set the variables as shown below.
nMin=1
Xmin=0
Xmax=25
Xscl=1
Ymin=L10
Ymax=10
Yscl=1
nMax=25
PlotStart=1
PlotStep=1
4. Press s to graph the sequence.
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5. Press y . and select the Web axes setting.
6. Press p and change the variables below.
Xmax=10
Xmin=L10
7. Press s to graph the sequence.
8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n,
X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n value is
displayed, and the trace cursor is on the sequence. When you press ~ again, the n
value remains the same, and the cursor moves to the y=x reference line. This pattern
repeats as you trace the web.
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Graphing Phase Plots
Graphing with uv, vw, and uw
The phase-plot axes settings uv, vw, and uw show relationships between two
sequences. To select a phase-plot axes setting, press y ., press ~ until the
cursor is on uv, vw, or uw, and then press Í.
Axes Setting
x-axis
u(n)
y-axis
v(n)
uv
vw
uw
v(n)
w(n)
w(n)
u(n)
Example: Predator-Prey Model
Use the predator-prey model to determine the regional populations of a predator and its
prey that would maintain population equilibrium for the two species.
This example uses the model to determine the equilibrium populations of foxes and
rabbits, with initial populations of 200 rabbits (u(nMin)) and 50 foxes (v(nMin)).
These are the variables (given values are in parentheses):
R
M
K
=
=
=
number of rabbits
rabbit population growth rate without foxes
rabbit population death rate with foxes
(.05)
(.001)
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W
G
D
n
=
=
=
=
=
number of foxes
fox population growth rate with rabbits
fox population death rate without rabbits
time (in months)
(.0002)
(.03)
R
R
(1+MNKW
)
nN1
n
nN1
W
n
=
W
(1+GR ND)
nN1
nN1
1. Press o in Seq mode to display the sequence Y= editor. Define the sequences and
initial values for R and W as shown below. Enter the sequence R as u(n) and enter
n
n
n
the sequence W as v(n).
n
2. Press y . Í to select Time axes format.
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3. Press p and set the variables as shown below.
nMin=0
Xmin=0
Ymin=0
nMax=400
PlotStart=1
PlotStep=1
Xmax=400
Xscl=100
Ymax=300
Yscl=100
4. Press s to graph the sequence.
5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over
time (n).
Note: Press a number, and then press Í to jump to a specific n value (month)
while in TRACE.
6. Press y . ~ ~ Í to select uv axes format.
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7. Press p and change these variables as shown below.
Xmin=84
Xmax=237
Xscl=50
Ymin=25
Ymax=75
Yscl=10
8. Press r. Trace both the number of rabbits (X) and the number of foxes (Y)
through 400 generations.
Note: When you press r, the equation for u is
displayed in the
top-left corner. Press } or † to
see the equation for v.
Comparing TI-84 Plus and TI-82 Sequence Variables
Sequences and Window Variables
Refer to the table if you are familiar with the TI-82. It shows TI-84 Plus sequences and
sequence window variables, as well as their TI-82 counterparts.
TI-84 Plus
In the Y= editor:
u(n)
TI-82
Un
u(nMin)
UnStart (window variable)
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TI-84 Plus
v(n)
TI-82
Vn
v(nMin)
w(n)
VnStart (window variable)
not available
not available
w(nMin)
In the window editor:
nMin
nStart
nMax
nMax
PlotStart
PlotStep
nMin
not available
Keystroke Differences Between TI-84 Plus
and TI-82
Sequence Keystroke Changes
Refer to the table if you are familiar with the TI-82. It compares TI-84 Plus sequence-
name syntax and variable syntax with TI-82 sequence-name syntax and variable syntax.
TI-84 Plus / TI-82
n / n
On TI-84 Plus, press:
On TI-82, press:
y ô
„
u(n) / Un
y [u]
£ „ ¤
y ó ¶¦À
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TI-84 Plus / TI-82
On TI-84 Plus, press:
On TI-82, press:
v(n) / Vn
y [v]
£ „ ¤
y ó ¶¦Á
w(n)
not available
y õ
y [w]
£ „ ¤
u(nN1) / UnN1
v(nN1) / VnN1
w(nN1)
y [u]
£ „ ¹ À ¤
y [v]
£ „ ¹ À ¤
y ö
not available
y [w]
£ „ ¹ À ¤
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Chapter 7:
Tables
Getting Started: Roots of a Function
Getting Started is a fast-paced introduction. Read the chapter for details.
3
Evaluate the function Y = X N 2X at each integer between L10 and 10. How many sign
changes occur, and at what X values?
1. Press z † † † Í to set Func graphing
mode.
3
2. Press o. Press „ 3 to select . Then
3
press ¹ 2 „ to enter the function Y1=X N2X.
3. Press y - to display the TABLE SETUP
screen. Press Ì 10 Í to set TblStart=L10.
Press 1 Í to set @Tbl=1.
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Press Í to select Indpnt: Auto (automatically
generated independent values). Press † Í to
select Depend: Auto (automatically generated
dependent values).
4. Press y 0 to display the table screen.
5. Press † until you see the sign changes in the
value of Y1. How many sign changes occur, and at
what X values?
Setting Up the Table
TABLE SETUP Screen
To display the TABLE SETUP screen, press y -.
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TblStart, @Tbl
TblStart (table start) defines the initial value for the independent variable. TblStart applies
only when the independent variable is generated automatically (when Indpnt: Auto is
selected).
@Tbl (table step) defines the increment for the independent variable.
Note: In Seq mode, both TblStart and @Tbl must be integers.
Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask
Selections
Table Characteristics
Indpnt: Auto
Depend: Auto
Values are displayed automatically in both the independent-
variable column and in all dependent-variable columns.
Indpnt: Ask
Depend: Auto
The table is empty; when you enter a value for the independent
variable, all corresponding dependent-variable values are
calculated and displayed automatically.
Indpnt: Auto
Depend: Ask
Values are displayed automatically for the independent variable;
to generate a value for a dependent variable, move the cursor to
that cell and press Í.
Indpnt: Ask
Depend: Ask
The table is empty; enter values for the independent variable; to
generate a value for a dependent variable, move the cursor to
that cell and press Í.
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Setting Up the Table from the Home Screen or a Program
To store a value to TblStart, @Tbl, or TbYZnput from the home screen or a program, select
the variable name from the VARS TABLE secondary menu. TblZnput is a list of
independent-variable values in the current table.
When you press y - in the program editor, you can select IndpntAuto, IndpntAsk,
DependAuto, and DependAsk.
Defining the Dependent Variables
Defining Dependent Variables from the Y= Editor
In the Y= editor, enter the functions that define the dependent variables. Only functions
that are selected in the Y= editor are displayed in the table. The current graphing mode
is used. In Par mode, you must define both components of each parametric equation
(Chapter 4).
Editing Dependent Variables from the Table Editor
To edit a selected Y= function from the table editor, follow these steps.
1. Press y 0 to display the table, then press ~ or | to move the cursor to a
dependent-variable column.
2. Press } until the cursor is on the function name at the top of the column. The
function is displayed on the bottom line.
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3. Press Í. The cursor moves to the bottom line. Edit the function.
4. Press Í or †. The new values are calculated. The table and the Y= function are
updated automatically.
Note: You also can use this feature to view the function that defines a dependent
variable without having to leave the table.
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Displaying the Table
The Table
To display the table, press y 0.
Note: The table abbreviates the values, if necessary.
Current cell
Dependent-variable
values in the second
and third columns
Independent-variable
values in the first
column
Current cell’s full value
Independent and Dependent Variables
The current graphing mode determines which independent and dependent variables are
displayed in the table (Chapter 1). In the table above, for example, the independent
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variable X and the dependent variables Y1 and Y2 are displayed because Func graphing
mode is set.
Independent Variable
Graphing Mode
Func (function)
Par (parametric)
Pol (polar)
Dependent Variable
Y1 through Y9, and Y0
X1T/Y1T through X6T/Y6T
r1 through r6
X
T
q
n
Seq (sequence)
u(n), v(n), and w(n)
Clearing the Table from the Home Screen or a Program
From the home screen, select the ClrTable instruction from the CATALOG. To clear the
table, press Í.
From a program, select 9:ClrTable from the PRGM I/O menu or from the CATALOG. The
table is cleared upon execution. If IndpntAsk is selected, all independent and dependent
variable values on the table are cleared. If DependAsk is selected, all dependent variable
values on the table are cleared.
Scrolling Independent-Variable Values
If Indpnt: Auto is selected, you can press } and † in the independent-variable column
to display more values. As you scroll the column, the corresponding dependent-variable
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values also are displayed. All dependent-variable values may not be displayed if
Depend: Ask is selected.
Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is
updated automatically to the value shown on the top line of the table. In the example
above, TblStart=0 and @Tbl=1 generates and displays values of X=0, …, 6; but you can
press } to scroll back and display the table for X=M1, …, 5.
Displaying Other Dependent Variables
If you have defined more than two dependent variables, the first two selected Y=
functions are displayed initially. Press ~ or | to display dependent variables defined by
other selected Y= functions. The independent variable always remains in the left column,
except during a trace with Par graphing mode and G-T split-screen mode set.
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Note: To simultaneously display two dependent variables on the table that are not defined
as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between
the two you want to display. For example, to simultaneously display Y4 and Y7 on the
table, go to the Y= editor and deselect Y5 and Y6.
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Chapter 8:
Draw Instructions
Getting Started: Drawing a Tangent Line
Getting Started is a fast-paced introduction. Read the chapter for details.
2
2
------
Suppose you want to find the equation of the tangent line at X =
Y=sin(X).
for the function
Before you begin, select Radian and Func mode from
the mode screen, if necessary.
1. Press o to display the Y= editor. Press
˜ „ ¤ to store sin(X) in Y1.
2. Press q 7 to select 7:ZTrig, which graphs the
equation in the Zoom Trig window.
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3. Press y < 5 to select 5:Tangent(. The
tangent instruction is initiated.
4. Press y C 2 ¤ ¥ 2.
5. Press Í. The tangent line is drawn; the X
value and the tangent-line equation are displayed
on the graph.
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Using the DRAW Menu
DRAW Menu
To display the DRAW menu, press y <. The TI-84 Plus’s interpretation of these
instructions depends on whether you accessed the menu from the home screen or the
program editor or directly from a graph.
DRAW
POINTS STO
Clears all drawn elements.
1: ClrDraw
2: Line(
Draws a line segment between 2 points.
Draws a horizontal line.
3: Horizontal
4: Vertical
5: Tangent(
6: DrawF
Draws a vertical line.
Draws a line segment tangent to a function.
Draws a function.
Shades an area between two functions.
Draws the inverse of a function.
Draws a circle.
7: Shade(
8: DrawInv
9: Circle(
0: Text(
Draws text on a graph screen.
Activates the free-form drawing tool.
A: Pen
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Before Drawing on a Graph
The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW
instructions, consider whether you want to perform one or more of the following actions.
•
•
•
•
•
•
•
Change the mode settings on the mode screen.
Change the format settings on the format screen.
Enter or edit functions in the Y= editor.
Select or deselect functions in the Y= editor.
Change the window variable values.
Turn stat plots on or off.
Clear existing drawings with ClrDraw.
Note: If you draw on a graph and then perform any of the actions listed above, the graph
is replotted without the drawings when you display the graph again.
Drawing on a Graph
You can use any DRAW menu instructions except DrawInv to draw on Func, Par, Pol, and
Seq graphs. DrawInv is valid only in Func graphing. The coordinates for all DRAW
instructions are the display’s x-coordinate and y-coordinate values.
You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on
a graph, using the cursor to identify the coordinates. You also can execute these
instructions from the home screen or from within a program. If a graph is not displayed
when you select a DRAW menu instruction, the home screen is displayed.
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Clearing Drawings
Clearing Drawings When a Graph Is Displayed
All points, lines, and shading drawn on a graph with DRAW instructions are temporary.
To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW
menu. The current graph is replotted and displayed with no drawn elements.
Clearing Drawings from the Home Screen or a Program
To clear drawings on a graph from the home screen or a program, begin on a blank line
on the home screen or in the program editor. Select 1:ClrDraw from the DRAW menu.
The instruction is copied to the cursor location. Press Í.
When ClrDraw is executed, it clears all drawings from the current graph and displays the
message Done. When you display the graph again, all drawn points, lines, circles, and
shaded areas will be gone.
Note: Before you clear drawings, you can store them with StorePic.
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Drawing Line Segments
Drawing a Line Segment Directly on a Graph
To draw a line segment when a graph is displayed, follow these steps.
1. Select 2:Line( from the DRAW menu.
2. Place the cursor on the point where you want the line segment to begin, and then
press Í.
3. Move the cursor to the point where you want the line segment to end. The line is
displayed as you move the cursor. Press Í.
To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press ‘.
Drawing a Line Segment from the Home Screen or a Program
Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The values
may be entered as expressions.
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Line(X1,Y1,X2,Y2)
To erase a line segment, enter Line(X1,Y1,X2,Y2,0)
Drawing Horizontal and Vertical Lines
Drawing a Line Directly on a Graph
To draw a horizontal or vertical line when a graph is displayed, follow these steps.
1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves
as you move the cursor.
2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical
lines) through which you want the drawn line to pass.
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3. Press Í to draw the line on the graph.
To continue drawing lines, repeat steps 2 and 3.
To cancel Horizontal or Vertical, press ‘.
Drawing a Line from the Home Screen or a Program
Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not
a list.
Horizontal y
Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list.
Vertical x
To instruct the TI-84 Plus to draw more than one horizontal or vertical line, separate each
instruction with a colon ( : ).
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Drawing Tangent Lines
Drawing a Tangent Line Directly on a Graph
To draw a tangent line when a graph is displayed, follow these steps.
1. Select 5:Tangent( from the DRAW menu.
2. Press † and } to move the cursor to the function for which you want to draw the
tangent line. The current graph’s Y= function is displayed in the top-left corner, if
ExprOn is selected.
3. Press ~ and | or enter a number to select the point on the function at which you
want to draw the tangent line.
4. Press Í. In Func mode, the X value at which the tangent line was drawn is
displayed on the bottom of the screen, along with the equation of the tangent line. In
all other modes, the dy/dx value is displayed.
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Note: Change the fixed decimal setting on the mode screen if you want to see fewer
digits displayed for X and the equation for Y.
Drawing a Tangent Line from the Home Screen or a Program
2
Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X ,
at point X=value. X can be an expression. expression is interpreted as being in Func mode.
Tangent(expression,value)
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Drawing Functions and Inverses
Drawing a Function
DrawF (draw function) draws expression as a function in terms of X on the current graph.
When you select 6:DrawF from the DRAW menu, the TI-84 Plus returns to the home
screen or the program editor. DrawF is not interactive.
DrawF expression
Note: You cannot use a list in expression to draw a family of curves.
Drawing an Inverse of a Function
DrawInv (draw inverse) draws the inverse of expression by plotting X values on the y-axis
and Y values on the x-axis. When you select 8:DrawInv from the DRAW menu, the TI-84
Plus returns to the home screen or the program editor. DrawInv is not interactive.
DrawInv works in Func mode only.
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DrawInv expression
Note: You cannot use a list in expression to draw a family of curves.
Shading Areas on a Graph
Shading a Graph
To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is
pasted to the home screen or to the program editor.
Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the
area that is specifically above lowerfunc and below upperfunc. Only the areas where
lowerfunc < upperfunc are shaded.
Xleft and Xright, if included, specify left and right boundaries for the shading. Xleft and
Xright must be numbers between Xmin and Xmax, which are the defaults.
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pattern specifies one of four shading patterns.
pattern=1
pattern=2
pattern=3
pattern=4
vertical (default)
horizontal
negative—slope 45¡
positive—slope 45¡
patres specifies one of eight shading resolutions.
patres=1
patres=2
patres=3
patres=4
patres=5
patres=6
patres=7
patres=8
shades every pixel (default)
shades every second pixel
shades every third pixel
shades every fourth pixel
shades every fifth pixel
shades every sixth pixel
shades every seventh pixel
shades every eighth pixel
Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres])
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Drawing Circles
Drawing a Circle Directly on a Graph
To draw a circle directly on a displayed graph using the cursor, follow these steps.
1. Select 9:Circle( from the DRAW menu.
2. Place the cursor at the center of the circle you want to draw. Press Í.
3. Move the cursor to a point on the circumference. Press Í to draw the circle on
the graph.
Note: This circle is displayed as circular, regardless of the window variable values,
because you drew it directly on the display. When you use the Circle( instruction from the
home screen or a program, the current window variables may distort the shape.
To continue drawing circles, repeat steps 2 and 3. To cancel Circle(, press ‘.
Drawing a Circle from the Home Screen or a Program
Circle( draws a circle with center (X,Y) and radius. These values can be expressions.
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Circle(X,Y,radius)
Note: When you use Circle( on the home screen or from a program, the current window
values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to
adjust the window variables and make the circle circular.
Placing Text on a Graph
Placing Text Directly on a Graph
To place text on a graph when the graph is displayed, follow these steps.
1. Select 0:Text( from the DRAW menu.
2. Place the cursor where you want the text to begin.
3. Enter the characters. Press ƒ or y 7 to enter letters and q. You may
enter TI-84 Plus functions, variables, and instructions. The font is proportional, so
the exact number of characters you can place on the graph varies. As you type, the
characters are placed on top of the graph.
To cancel Text(, press ‘.
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Placing Text on a Graph from the Home Screen or a Program
Text( places on the current graph the characters comprising value, which can include
TI-84 Plus functions and instructions. The top-left corner of the first character is at pixel
(row,column), where row is an integer between 0 and 57 and column is an integer between 0
and 94. Both row and column can be expressions.
Text(row,column,value,value…)
value can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-84
Plus will evaluate an expression and display the result with up to 10 characters.
Split Screen
On a Horiz split screen, the maximum value for row is 25. On a G-T split screen, the
maximum value for row is 45, and the maximum value for column is 46.
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Using Pen to Draw on a Graph
Using Pen to Draw on a Graph
Pen draws directly on a graph only. You cannot execute Pen from the home screen or a
program.
To draw on a displayed graph, follow these steps.
1. Select A:Pen from the DRAW menu.
2. Place the cursor on the point where you want to begin drawing. Press Í to turn
on the pen.
3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel
at a time.
4. Press Í to turn off the pen.
For example, Pen was used to create the arrow pointing to the local minimum of the
selected function.
Note: To continue drawing on the graph, move the
cursor to a new position where you want to begin
drawing again, and then repeat steps 2, 3, and 4. To
cancel Pen, press ‘.
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Drawing Points on a Graph
DRAW POINTS Menu
To display the DRAW POINTS menu, press y < ~. The TI-84 Plus’s interpretation of
these instructions depends on whether you accessed this menu from the home screen
or the program editor or directly from a graph.
DRAW POINTS
1: Pt-On(
STO
Turns on a point.
Turns off a point.
2: Pt-Off(
Toggles a point on or off.
Turns on a pixel.
3: Pt-Change(
4: Pxl-On(
Turns off a pixel.
5: Pxl-Off(
6: Pxl-Change(
7: pxl-Test(
Toggles a pixel on or off.
Returns 1 if pixel on, 0 if pixel off.
Drawing Points Directly on a Graph with Pt-On(
To draw a point on a graph, follow these steps.
1. Select 1:Pt-On( from the DRAW POINTS menu.
2. Move the cursor to the position where you want to draw the point.
3. Press Í to draw the point.
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To continue drawing points, repeat steps 2 and 3. To cancel Pt-On(, press ‘.
Erasing Points with Pt-Off(
To erase (turn off) a drawn point on a graph, follow these steps.
1. Select 2:Pt-Off( (point off) from the DRAW POINTS menu.
2. Move the cursor to the point you want to erase.
3. Press Í to erase the point.
To continue erasing points, repeat steps 2 and 3. To cancel Pt-Off(, press ‘.
Changing Points with Pt-Change(
To change (toggle on or off) a point on a graph, follow these steps.
1. Select 3:Pt-Change( (point change) from the DRAW POINTS menu.
2. Move the cursor to the point you want to change.
3. Press Í to change the point’s on/off status.
To continue changing points, repeat steps 2 and 3. To cancel Pt-Change(, press ‘.
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Drawing Points from the Home Screen or a Program
Pt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off( turns the point off. Pt-Change(
toggles the point on or off. mark is optional; it determines the point’s appearance; specify
1, 2, or 3, where:
1 = ¦ (dot; default)
Pt-On(x,y[,mark])
2 = › (box)
3 = + (cross)
Pt-Off(x,y[,mark])
Pt-Change(x,y)
Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you
turn off the point with Pt-Off(. Pt-Change( does not have the mark option.
Drawing Pixels
TI-84 Plus Pixels
A pixel is a square dot on the TI-84 Plus display. The Pxl- (pixel) instructions let you turn
on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a
pixel instruction from the DRAW POINTS menu, the TI-84 Plus returns to the home screen
or the program editor. The pixel instructions are not interactive.
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Turning On and Off Pixels with Pxl-On( and Pxl-Off(
Pxl-On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and
62 and column is an integer between 0 and 94.
Pxl-Off( turns the pixel off. Pxl-Change( toggles the pixel on and off.
Pxl-On(row,column)
Pxl-Off(row,column)
Pxl-Change(row,column)
Using pxl-Test(
pxl-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is
turned off on the current graph. row must be an integer between 0 and 62. column must be
an integer between 0 and 94.
pxl-Test(row,column)
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Split Screen
On a Horiz split screen, the maximum value for row is 30 for Pxl-On(, Pxl-Off(,
Pxl-Change(, and pxl-Test(.
On a G-T split screen, the maximum value for row is 50 and the maximum value for column
is 46 for Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(.
Storing Graph Pictures (Pic)
DRAW STO Menu
To display the DRAW STO menu, press y < |. When you select an instruction
from the DRAW STO menu, the TI-84 Plus returns to the home screen or the program
editor. The picture and graph database instructions are not interactive.
DRAW POINTS
1: StorePic
2: RecallPic
3: StoreGDB
4: RecallGDB
STO
Stores the current picture.
Recalls a saved picture.
Stores the current graph database.
Recalls a saved graph database.
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Storing a Graph Picture
You can store up to 10 graph pictures, each of which is an image of the current graph
display, in picture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the
stored picture onto a displayed graph from the home screen or a program.
A picture includes drawn elements, plotted functions, axes, and tick marks. The picture
does not include axes labels, lower and upper bound indicators, prompts, or cursor
coordinates. Any parts of the display hidden by these items are stored with the picture.
To store a graph picture, follow these steps.
1. Select 1:StorePic from the DRAW STO menu. StorePic is pasted to the current cursor
location.
2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store
the picture. For example, if you enter 3, the TI-84 Plus will store the picture to Pic3.
Note: You also can select a variable from the PICTURE secondary menu ( 4).
The variable is pasted next to StorePic.
3. Press Í to display the current graph and store the picture.
Recalling Graph Pictures (Pic)
Recalling a Graph Picture
To recall a graph picture, follow these steps.
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1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current
cursor location.
2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to
recall a picture. For example, if you enter 3, the TI-84 Plus will recall the picture
stored to Pic3.
Note: You also can select a variable from the PICTURE secondary menu ( 4).
The variable is pasted next to RecallPic.
3. Press Í to display the current graph with the picture superimposed on it.
Note: Pictures are drawings. You cannot trace a curve that is part of a picture.
Deleting a Graph Picture
To delete graph pictures from memory, use the MEMORY MANAGEMENT/DELETE
secondary menu (Chapter 18).
Storing Graph Databases (GDB)
What Is a Graph Database?
A graph database (GDB) contains the set of elements that defines a particular graph.
You can recreate the graph from these elements. You can store up to 10 GDBs in
variables GDB1 through GDB9, or GDB0 and recall them to recreate graphs.
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A GDB stores five elements of a graph.
•
•
•
•
•
Graphing mode
Window variables
Format settings
All functions in the Y= editor and the selection status of each
Graph style for each Y= function
GDBs do not contain drawn items or stat plot definitions.
Storing a Graph Database
To store a graph database, follow these steps.
1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current
cursor location.
2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store
the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB to
GDB7.
Note: You also can select a variable from the GDB secondary menu ( 3). The
variable is pasted next to StoreGDB.
3. Press Í to store the current database to the specified GDB variable.
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Recalling Graph Databases (GDB)
Recalling a Graph Database
CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing
the current Y= functions to another database before recalling a stored GDB.
To recall a graph database, follow these steps.
1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current
cursor location.
2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to
recall a GDB. For example, if you enter 7, the TI-84 Plus will recall the GDB stored to
GDB7.
Note: You also can select a variable from the GDB secondary menu ( 3). The
variable is pasted next to RecallGDB.
3. Press Í to replace the current GDB with the recalled GDB. The new graph is not
plotted. The TI-84 Plus changes the graphing mode automatically, if necessary.
Deleting a Graph Database
To delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary
menu (Chapter 18).
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Chapter 9:
Split Screen
Getting Started: Exploring the Unit Circle
Getting Started is a fast-paced introduction. Read the chapter for details.
Use G-T (graph-table) split-screen mode to explore the unit circle and its relationship to
the numeric values for the commonly used trigonometric angles of 0¡ 30¡, 45¡, 60¡, 90¡,
and so on.
1. Press z to display the mode screen. Press †
† ~ Í to select Degree mode. Press † ~
Í to select Par (parametric) graphing mode.
Press † † † † ~ ~ Í to select G-T (graph-
table) split-screen mode.
2. Press y . to display the format screen.
Press † † † † † ~ Í to select ExprOff.
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3. Press o to display the Y= editor for Par graphing
mode. Press ™ „ ¤ Í to store cos(T)
to X1T. Press ÷ ˜ „ ¤ Í to store sin(T)
to Y1T.
4. Press p to display the window editor. Enter
these values for the window variables.
Tmin=0
Tmax=360 Xmax=2.3 Ymax=2.5
Tstep=15 Xscl=1 Yscl=1
Xmin=L2.3 Ymin=L2.5
5. Press r. On the left, the unit circle is graphed
parametrically in Degree mode and the trace
cursor is activated. When T=0 (from the graph
trace coordinates), you can see from the table on
the right that the value of X1T (cos(T)) is 1 and Y1T
(sin(T)) is 0. Press ~ to move the cursor to the
next 15¡ angle increment. As you trace around the
circle in steps of 15¡, an approximation of the
standard value for each angle is highlighted in the
table.
6. Press y - and change Indpnt to Ask.
7. Press y 0 to make the table portion of the
split screen active. Press † or } to highlight a
value you want to edit, and then enter a new value
directly in the table to overwrite the previous value.
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Using Split Screen
Setting a Split-Screen Mode
To set a split-screen mode, press z, and then move the cursor to the next-to-last line
on the mode screen.
•
•
Select Horiz (horizontal) to display the graph screen and another screen split
horizontally.
Select G-T (graph-table) to display the graph screen and table screen split vertically.
$
$
The split screen is activated when you press any key that applies to either half of the split
screen.
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If stat plots are turned on, the plots are shown along with the x-y plots in graphs. Press
y 0 to make the table portion of the split screen active and to display the list data.
Press † or } to highlight a value you want to edit, and then enter a new value directly in
the table to overwrite the previous value. Press ~ repeatedly to display each column of
data (both table and list data).
Split-screen display with both x-y plots and stat plots
Some screens are never displayed as split screens. For example, if you press z in
Horiz or G-T mode, the mode screen is displayed as a full screen. If you then press a key
that displays either half of a split screen, such as r, the split screen returns.
When you press a key or key combination in either Horiz or G-T mode, the cursor is
placed in the half of the display for which that key applies. For example, if you press
r, the cursor is placed in the half in which the graph is displayed. If you press
y 0, the cursor is placed in the half in which the table is displayed.
The TI-84 Plus will remain in split-screen mode until you change back to Full screen
mode.
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Horiz (Horizontal) Split Screen
Horiz Mode
In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and
bottom halves.
The top half displays the graph.
The bottom half displays any of these editors.
•
•
•
•
•
Home screen (four lines)
Y= editor (four lines)
Stat list editor (two rows)
Window editor (three settings)
Table editor (two rows)
Moving from Half to Half in Horiz Mode
To use the top half of the split screen:
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•
•
Press s or r.
Select a ZOOM or CALC operation.
To use the bottom half of the split screen:
•
•
•
•
•
Press any key or key combination that displays the home screen.
Press o (Y= editor).
Press … Í (stat list editor).
Press p (window editor).
Press y 0 (table editor).
Full Screens in Horiz Mode
All other screens are displayed as full screens in Horiz split-screen mode.
To return to the Horiz split screen from a full screen when in Horiz mode, press any key
or key combination that displays the graph, home screen, Y= editor, stat list editor,
window editor, or table editor.
G-T (Graph-Table) Split Screen
G-T Mode
In G-T (graph-table) split-screen mode, a vertical line splits the screen into left and right
halves.
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The left half displays all active graphs and plots.
The right half displays either table data corresponding to the graph at the left or list data
corresponding to the plot at the left.
Moving from Half to Half in G-T Mode
To use the left half of the split screen:
•
•
Press s or r.
Select a ZOOM or CALC operation.
To use the right half of the split screen, press y 0. If the values at the right are list
data, these values can be edited similarly to using the Stat List Editor.
Using TRACE in G-T Mode
As you press | or ~ to move the trace cursor along a graph in the split screen’s left half
in G-T mode, the table on the right half automatically scrolls to match the current cursor
values. If more than one graph or plot is active, you can press } or † to select a
different graph or plot.
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Note: When you trace in Par graphing mode, both components of an equation (XnT and
YnT) are displayed in the two columns of the table. As you trace, the current value of the
independent variable T is displayed on the graph.
Full Screens in G-T Mode
All screens other than the graph and the table are displayed as full screens in G-T split-
screen mode.
To return to the G-T split screen from a full screen when in G-T mode, press any key or
key combination that displays the graph or the table.
TI-84 Plus Pixels in Horiz and G-T Modes
TI-84 Plus Pixels in Horiz and G-T Modes
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Note: Each set of numbers in parentheses above represents the row and column of a
corner pixel, which is turned on.
DRAW POINTS Menu Pixel Instructions
For Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(:
•
•
In Horiz mode, row must be {30; column must be {94.
In G-T mode, row must be {50; column must be {46.
Pxl-On(row,column)
DRAW Menu Text( Instruction
For the Text( instruction:
•
•
In Horiz mode, row must be {25; column must be {94.
In G-T mode, row must be {45; column must be {46.
Text(row,column,"text")
PRGM I/O Menu Output( Instruction
For the Output( instruction:
•
•
In Horiz mode, row must be {4; column must be {16.
In G-T mode, row must be {8; column must be {16.
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Output(row,column,"text")
Note: The Output( instruction can only be used within a program.
Setting a Split-Screen Mode from the Home Screen or a Program
To set Horiz or G-T from a program, follow these steps.
1. Press z while the cursor is on a blank line in the program editor.
2. Select Horiz or G-T.
The instruction is pasted to the cursor location. The mode is set when the instruction is
encountered during program execution. It remains in effect after execution.
Note: You also can paste Horiz or G-T to the home screen or program editor from the
CATALOG (Chapter 15).
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Chapter 10:
Matrices
Getting Started: Systems of Linear Equations
Getting Started is a fast-paced introduction. Read the chapter for details.
Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can
solve a system of linear equations by entering the coefficients as elements in a matrix,
and then using rref( to obtain the reduced row-echelon form.
1. Press y . Press ~ ~ to display the
MATRX EDIT menu. Press 1 to select 1: [A].
2. Press 2 Í 4 Í to define a 2×4 matrix. The
rectangular cursor indicates the current element.
Ellipses (...) indicate additional columns beyond
the screen.
3. Press 1 Í to enter the first element. The
rectangular cursor moves to the second column of
the first row.
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4. Press 2 Í 3 Í 3 Í to complete the first
row for X + 2Y + 3Z = 3.
5. Press 2 Í 3 Í 4 Í 3 Í to enter the
second row for 2X + 3Y + 4Z = 3.
6. Press y 5 to return to the home screen. If
necessary, press ‘ to clear the home screen.
Press y ~ to display the MATRX MATH
menu. Press } to wrap to the end of the menu.
Select B:rref( to copy rref( to the home screen.
7. Press y 1 to select 1: [A] from the
MATRX NAMES menu. Press ¤ Í. The
reduced row-echelon form of the matrix is
displayed and stored in Ans.
1X N 1Z = L3
1Y + 2Z = 3
therefore
therefore
X = L3 + Z
Y = 3 N 2Z
Defining a Matrix
What Is a Matrix?
A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix
editor. The TI-84 Plus has 10 matrix variables, [A] through [J]. You can define a matrix
directly in an expression. A matrix, depending on available memory, may have up to 99
rows or columns. You can store only real numbers in TI-84 Plus matrices.
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Selecting a Matrix
Before you can define or display a matrix in the editor, you first must select the matrix
name. To do so, follow these steps.
1. Press y | to display the MATRX EDIT menu. The dimensions of any
previously defined matrices are displayed.
2. Select the matrix you want to define. The MATRX EDIT screen is displayed.
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (row × column) are displayed on the top line. The dimensions
of a new matrix are 1 × 1. You must accept or change the dimensions each time you edit
a matrix. When you select a matrix to define, the cursor highlights the row dimension.
•
•
To accept the row dimension, press Í.
To change the row dimension, enter the number of rows (up to 99), and then press
Í.
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The cursor moves to the column dimension, which you must accept or change the same
way you accepted or changed the row dimension. When you press Í, the
rectangular cursor moves to the first matrix element.
Viewing and Editing Matrix Elements
Displaying Matrix Elements
After you have set the dimensions of the matrix, you can view the matrix and enter
values for the matrix elements. In a new matrix, all values are zero.
Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The
center portion of the matrix editor displays up to seven rows and three columns of a
matrix, showing the values of the elements in abbreviated form if necessary. The full
value of the current element, which is indicated by the rectangular cursor, is displayed on
the bottom line.
This is an 8 × 4 matrix. Ellipses in the left or right column indicate additional columns. #
or $ in the right column indicate additional rows.
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Deleting a Matrix
To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE secondary
menu (Chapter 18).
Viewing a Matrix
The matrix editor has two contexts, viewing and editing. In viewing context, you can use
the cursor keys to move quickly from one matrix element to the next. The full value of the
highlighted element is displayed on the bottom line.
Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.
Viewing-Context Keys
Key
Function
Moves the rectangular cursor within the current row
| or ~
† or }
Moves the rectangular cursor within the current column; on the top
row, } moves the cursor to the column dimension; on the column
dimension, } moves the cursor to the row dimension
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Key
Function
Switches to editing context; activates the edit cursor on the bottom
line
Í
Switches to editing context; clears the value on the bottom line
‘
Any entry character
Switches to editing context; clears the value on the bottom line;
copies the character to the bottom line
Nothing
Nothing
y 6
{
Editing a Matrix Element
In editing context, an edit cursor is active on the bottom line. To edit a matrix element
value, follow these steps.
1. Select the matrix from the MATRX EDIT menu, and then enter or accept the
dimensions.
2. Press |, }, ~, and † to move the cursor to the matrix element you want to
change.
3. Switch to editing context by pressing Í, ‘, or an entry key.
4. Change the value of the matrix element using the editing-context keys described
below. You may enter an expression, which is evaluated when you leave editing
context.
Note: You can press ‘ Í to restore the value at the rectangular cursor if you
make a mistake.
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5. Press Í, }, or † to move to another element.
Editing-Context Keys
Key
Function
Moves the edit cursor within the value
| or ~
† or }
Stores the value displayed on the bottom line to the matrix
element; switches to viewing context and moves the rectangular
cursor within the column
Stores the value displayed on the bottom line to the matrix
element; switches to viewing context and moves the rectangular
cursor to the next row element
Í
Clears the value on the bottom line
‘
Any entry character
Copies the character to the location of the edit cursor on the
bottom line
Activates the insert cursor
y 6
{
Deletes the character under the edit cursor on the bottom line
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Using Matrices with Expressions
Using a Matrix in an Expression
To use a matrix in an expression, you can do any of the following.
•
•
•
Copy the name from the MATRX NAMES menu.
Recall the contents of the matrix into the expression with y K (Chapter 1).
Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix
directly in an expression.
To enter a matrix in an expression, follow these steps.
1. Press y [ [ ] to indicate the beginning of the matrix.
2. Press y [ [ ] to indicate the beginning of a row.
3. Enter a value, which can be an expression, for each element in the row. Separate
the values with commas.
4. Press y [ ] ] to indicate the end of a row.
5. Repeat steps 2 through 4 to enter all of the rows.
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6. Press y [ ] ] to indicate the end of the matrix.
Note: The closing ]] are not necessary at the end of an expression or preceding !.
The resulting matrix is displayed in the form:
[[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]]
Any expressions are evaluated when the entry is executed.
Note: The commas that you must enter to separate elements are not displayed on
output.
Displaying and Copying Matrices
Displaying a Matrix
To display the contents of a matrix on the home screen, select the matrix from the
MATRX NAMES menu, and then press Í.
Ellipses in the left or right column indicate additional columns. # or $ in the right column
indicate additional rows. Press ~, |, †, and } to scroll the matrix.
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Copying One Matrix to Another
To copy a matrix, follow these steps.
1. Press y > to display the MATRX NAMES menu.
2. Select the name of the matrix you want to copy.
3. Press ¿.
4. Press y > again and select the name of the new matrix to which you want to
copy the existing matrix.
5. Press Í to copy the matrix to the new matrix name.
Accessing a Matrix Element
On the home screen or from within a program, you can store a value to, or recall a value
from, a matrix element. The element must be within the currently defined matrix
dimensions. Select matrix from the MATRX NAMES menu.
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[matrix](row,column)
Using Math Functions with Matrices
Using Math Functions with Matrices
You can use many of the math functions on the TI-84 Plus keyboard, the MATH menu, the
MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions
must be appropriate. Each of the functions below creates a new matrix; the original matrix
remains the same.
Addition, Subtraction, Multiplication
To add (Ã) or subtract (¹) matrices, the dimensions must be the same. The answer is a
matrix in which the elements are the sum or difference of the individual corresponding
elements.
matrixA+matrixB
matrixANmatrixB
To multiply (¯) two matrices together, the column dimension of matrixA must match the
row dimension of matrixB.
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matrixA…matrixB
Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element
of matrix is multiplied by value.
matrix…value
value…matrix
Negation
Negating a matrix (Ì) returns a matrix in which the sign of every element is changed
(reversed).
Lmatrix
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abs(
abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of
each element of matrix.
abs(matrix)
round(
round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals
( 9). If #decimals is omitted, the elements are rounded to 10 digits.
round(matrix[,#decimals])
Inverse
L1
Use the function (œ) to invert a matrix (^L1 is not valid). matrix must be square. The
determinant cannot equal zero.
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1
L
matrix
Powers
2
3
To raise a matrix to a power, matrix must be square. You can use (¡), (MATH menu),
or ^power (›) for integer power between 0 and 255.
2
matrix
3
matrix
matrix^power
Relational Operations
To compare two matrices using the relational operations = and ƒ (TEST menu), they must
have the same dimensions. = and ƒ compare matrixA and matrixB on an element-by-
element basis. The other relational operations are not valid with matrices.
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matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is
false.
matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison
is false.
iPart(, fPart(, int(
iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the
MATH NUM menu.
iPart( returns a matrix containing the integer part of each element of matrix.
fPart( returns a matrix containing the fractional part of each element of matrix.
int( returns a matrix containing the greatest integer of each element of matrix.
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iPart(matrix)
fPart(matrix)
int(matrix)
Using the MATRX MATH Operations
MATRX MATH Menu
To display the MATRX MATH menu, press y ~.
NAMES MATH EDIT
Calculates the determinant.
Transposes the matrix.
1: det(
T
2:
Returns the matrix dimensions.
Fills all elements with a constant.
Returns the identity matrix.
Returns a random matrix.
Appends two matrices.
3: dim(
4: Fill(
5: identity(
6: randM(
7: augment(
8: Matr4list(
Stores a matrix to a list.
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NAMES MATH EDIT
9: List4matr(
0: cumSum(
A: ref(
Stores a list to a matrix.
Returns the cumulative sums of a matrix.
Returns the row-echelon form of a matrix.
Returns the reduced row-echelon form.
Swaps two rows of a matrix.
B: rref(
C: rowSwap(
D: row+(
Adds two rows; stores in the second row.
Multiplies the row by a number.
E: …row(
Multiplies the row, adds to the second row.
F: …row+(
det(
det( (determinant) returns the determinant (a real number) of a square matrix.
det(matrix)
Transpose
T
(transpose) returns a matrix in which each element (row, column) is swapped with the
corresponding element (column, row) of matrix.
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T
matrix
Accessing Matrix Dimensions with dim(
dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix.
dim(matrix)
Note: dim(matrix)"Ln:Ln(1) returns the number of rows. dim(matrix)"Ln:Ln(2) returns the
number of columns.
Creating a Matrix with dim(
Use dim( with ¿ to create a new matrixname of dimensions rows × columns with 0 as
each element.
{rows,columns}"dim(matrixname)
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Redimensioning a Matrix with dim(
Use dim( with ¿ to redimension an existing matrixname to dimensions rows × columns.
The elements in the old matrixname that are within the new dimensions are not changed.
Additional created elements are zeros. Matrix elements that are outside the new
dimensions are deleted.
{rows,columns}"dim(matrixname)
Fill(
Fill( stores value to every element in matrixname.
Fill(value,matrixname)
identity(
identity( returns the identity matrix of dimension rows × dimension columns.
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identity(dimension)
randM(
L
randM( (create random matrix) returns a rows × columns random matrix of integers ‚ 9
and 9. The seed value stored to the rand function controls the values (Chapter 2).
randM(rows,columns)
augment(
augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have
the same number of rows.
augment(matrixA,matrixB)
Matr4list(
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Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix.
Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix
columns.
Matr4list(matrix,listnameA,...,listname n)
Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with
a specific column from matrix, you must enter column# after matrix.
Matr4list(matrix,column#,listname)
List4matr(
List4matr( (lists stored to matrix) fills matrixname column by column with the elements from
each list. If dimensions of all lists are not equal, List4matr( fills each extra matrixname row with
0. Complex lists are not valid.
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List4matr(listA,...,list n,matrixname)
cumSum(
cumSum( returns cumulative sums of the elements in matrix, starting with the first
element. Each element is the cumulative sum of the column from top to bottom.
cumSum(matrix)
Row Operations
MATRX MATH menu items A through F are row operations. You can use a row operation
in an expression. Row operations do not change matrix in memory. You can enter all row
numbers and values as expressions. You can select the matrix from the MATRX NAMES
menu.
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ref(, rref(
ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of
columns must be greater than or equal to the number of rows.
ref(matrix)
rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix.
The number of columns must be greater than or equal to the number of rows.
rref(matrix)
rowSwap(
rowSwap( returns a matrix. It swaps rowA and rowB of matrix.
rowSwap(matrix,rowA,rowB)
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row+(
row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the
results in rowB.
row+(matrix,rowA,rowB)
…row(
…row( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the
results in row.
…row(value,matrix,row)
…row+(
…row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by
value, adds it to rowB, and stores the results in rowB.
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…row+(value,matrix,rowA,rowB)
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Chapter 11:
Lists
Getting Started: Generating a Sequence
Getting Started is a fast-paced introduction. Read the chapter for details.
2
Calculate the first eight terms of the sequence 1/A . Store the results to a user-created
list. Then display the results in fraction form. Begin this example on a blank line on the
home screen.
1. Press y 9 ~ to display the LIST OPS menu.
2. Press 5 to select 5:seq(, which pastes seq( to the
current cursor location.
3. Press 1 ¥ ƒ [A] ¡ ¢ ƒ [A] ¢ 1 ¢ 8 ¢
1 ¤ Í to enter the sequence.
4. Press ¿, and then press y ƒ to turn on
alpha-lock. Press [S] [E] [Q], and then press ƒ
to turn off alpha-lock. Press 1 to complete the list
name.
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5. Press Í to generate the list and store it in
SEQ1. The list is displayed on the home screen.
An ellipsis (...) indicates that the list continues
beyond the viewing window. Press ~ repeatedly
(or press and hold ~) to scroll the list and view all
the list elements.
6. Press y 9 to display the LIST NAMES menu.
Press 7 to select 7:seq( to paste ÙSEQ1 to the
current cursor location. (If SEQ1 is not item 7 on
your LIST NAMES menu, move the cursor to SEQ1
before you press Í.)
7. Press to display the MATH menu. Press 1 to
select 1:4Frac, which pastes 4Frac to the current
cursor location.
8. Press Í to show the sequence in fraction
form. Press ~ repeatedly (or press and hold ~) to
scroll the list and view all the list elements.
Naming Lists
Using TI-84 Plus List Names L1 through L6
The TI-84 Plus has six list names in memory: L1, L2, L3, L4, L5, and L6. The list names
L1 through L6 are on the keyboard above the numeric keys À through ¸. To paste one
of these names to a valid screen, press y, and then press the appropriate key. L1
through L6 are stored in stat list editor columns 1 through 6 when you reset memory.
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Creating a List Name on the Home Screen
To create a list name on the home screen, follow these steps.
1. Press y E, enter one or more list elements, and then press y F. Separate list
elements with commas. List elements can be real numbers, complex numbers, or
expressions.
2. Press ¿.
3. Press ƒ [letter from A to Z or q] to enter the first letter of the name.
4. Enter zero to four letters, q, or numbers to complete the name.
5. Press Í. The list is displayed on the next line. The list name and its elements
are stored in memory. The list name becomes an item on the LIST NAMES menu.
Note: If you want to view a user-created list in the stat list editor, you must store it in
the stat list editor (Chapter 12).
You also can create a list name in these four places.
•
At the Name= prompt in the stat list editor
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•
•
At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor
At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt in the inferential
stat editors
•
On the home screen using SetUpEditor
You can create as many list names as your TI-84 Plus memory has space to store.
Storing and Displaying Lists
Storing Elements to a List
You can store list elements in either of two ways.
•
Use braces and ¿ on the home screen.
•
Use the stat list editor (Chapter 12).
The maximum dimension of a list is 999 elements.
Note: When you store a complex number to a list, the entire list is converted to a list of
complex numbers. To convert the list to a list of real numbers, display the home screen,
and then enter real(listname)!listname.
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Displaying a List on the Home Screen
To display the elements of a list on the home screen, enter the name of the list (preceded
by Ù, if necessary, and then press Í. An ellipsis indicates that the list continues
beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list
and view all the list elements.
Copying One List to Another
To copy a list, store it to another list.
Accessing a List Element
You can store a value to or recall a value from a specific list element. You can store to any
element within the current list dimension or one element beyond.
listname(element)
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Deleting a List from Memory
To delete lists from memory, including L1 through L6, use the
MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Resetting memory
restores L1 through L6. Removing a list from the stat list editor does not delete it from
memory.
Using Lists in Graphing
You can use lists to graph a family of curves (Chapter 3).
Entering List Names
Using the LIST NAMES Menu
To display the LIST NAMES menu, press y 9. Each item is a user-created list name
except for L1 through L6. LIST NAMES menu items are sorted automatically in
alphanumerical order. Only the first 10 items are labeled, using 1 through 9, then 0. To
jump to the first list name that begins with a particular alpha character or q, press ƒ
[letter from A to Z or q].
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Note: From the top of a menu, press } to move to the bottom. From the bottom, press †
to move to the top.
When you select a list name from the LIST NAMES menu, the list name is pasted to the
current cursor location.
•
•
The list name symbol Ù precedes a list name when the name is pasted where non-
list name data also is valid, such as the home screen.
The Ù symbol does not precede a list name when the name is pasted where a list
name is the only valid input, such as the stat list editor’s Name= prompt or the stat
plot editor’s XList: and YList: prompts.
Entering a User-Created List Name Directly
To enter an existing list name directly, follow these steps.
1. Press y 9 ~ to display the LIST OPS menu.
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2. Select B:Ù, which pastes Ù to the current cursor location. Ù is not always necessary.
Note: You also can paste Ù to the current cursor
location from the CATALOG.
3. Enter the characters that comprise the list name.
Attaching Formulas to List Names
Attaching a Formula to a List Name
You can attach a formula to a list name so that each list element is a result of the
formula. When executed, the attached formula must resolve to a list.
When anything in the attached formula changes, the list to which the formula is attached
is updated automatically.
•
•
When you edit an element of a list that is referenced in the formula, the
corresponding element in the list to which the formula is attached is updated.
When you edit the formula itself, all elements in the list to which the formula is
attached are updated.
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For example, the first screen below shows that elements are stored to L3, and the
formula L3+10 is attached to the list name ÙADD10. The quotation marks designate the
formula to be attached to ÙADD10. Each element of ÙADD10 is the sum of an element in
L3 and 10.
The next screen shows another list, L4. The elements of L4 are the sum of the same
formula that is attached to L3. However, quotation marks are not entered, so the formula
is not attached to L4.
On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and then redisplays
L3.
The last screen shows that editing L3 updated ÙADD10, but did not change L4. This is
because the formula L3+10 is attached to ÙADD10, but it is not attached to L4.
Note: To view a formula that is attached to a list name, use the stat list editor
(Chapter 12).
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Attaching a Formula to a List on the Home Screen or in a Program
To attach a formula to a list name from a blank line on the home screen or from a
program, follow these steps.
1. Press ƒ [ã], enter the formula (which must resolve to a list), and press ƒ [ã]
again.
Note: When you include more than one list name in a formula, each list must have
the same dimension.
2. Press ¿.
3. Enter the name of the list to which you want to attach the formula.
•
•
•
Press y, and then enter a TI-84 Plus list name L1 through L6.
Press y 9 and select a user.created list name from the LIST NAMES menu.
Enter a user.created list name directly using Ù.
4. Press Í.
Note: The stat list editor displays a formula-lock symbol next to each list name that has
an attached formula. Chapter 12 describes how to use the stat list editor to attach
formulas to lists, edit attached formulas, and detach formulas from lists.
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Detaching a Formula from a List
You can detach (clear) an attached formula from a list in several ways.
For example:
•
•
•
•
Enter ã ã !listname on the home screen.
Edit any element of a list to which a formula is attached.
Use the stat list editor (Chapter 12).
Use ClrList or ClrAllList to detach a formula from a list (Chapter 18).
Using Lists in Expressions
Using a List in an Expression
You can use lists in an expression in any of three ways. When you press Í, any
expression is evaluated for each list element, and a list is displayed.
•
•
Use L1–L6 or any user-created list name in an expression.
Enter the list elements directly.
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•
Use y K to recall the contents of the list into an expression at the cursor location
(Chapter 1).
Note: You must paste user-created list names to the Rcl prompt by selecting them from
the LIST NAMES menu. You cannot enter them directly using Ù.
Using Lists with Math Functions
You can use a list to input several values for some math functions. Other chapters and
Appendix A specify whether a list is valid. The function is evaluated for each list element,
and a list is displayed.
•
When you use a list with a function, the function must be valid for every element in
the list. In graphing, an invalid element, such as L1 in ‡({1,0,L1}), is ignored.
This returns an error.
This graphs X…‡(1) and X…‡(0), but skips
X…‡(L1).
•
When you use two lists with a two-argument function, the dimension of each list
must be the same. The function is evaluated for corresponding elements.
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•
When you use a list and a value with a two-argument function, the value is used with
each element in the list.
LIST OPS Menu
LIST OPS Menu
To display the LIST OPS menu, press y 9 ~.
NAMES OPS MATH
Sorts lists in ascending order.
Sorts lists in descending order.
Sets the list dimension.
1: SortA(
2: SortD(
3: dim(
Fills all elements with a constant.
Creates a sequence.
4: Fill(
5: seq(
Returns a list of cumulative sums.
Returns difference of successive elements.
6: cumSum(
7: @List(
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NAMES OPS MATH
8: Select(
Selects specific data points.
Concatenates two lists.
9: augment(
0: List4matr(
A: Matr4list(
Stores a list to a matrix.
Stores a matrix to a list.
Designates the list-name data type.
B:
Ù
SortA(, SortD(
SortA( (sort ascending) sorts list elements from low to high values. SortD( (sort
descending) sorts list elements from high to low values. Complex lists are sorted based
on magnitude (modulus).
With one list, SortA( and SortD( sort the elements of listname and update the list in
memory.
SortA(listname)
SortD(listname)
With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist by
placing its elements in the same order as the corresponding elements in keylistname. All
lists must have the same dimension.
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SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])
SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])
Note:
•
In the example, 5 is the first element in L4, and 1 is the first element in L5. After
SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1 becomes the
second element of L5.
•
SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu
(Chapter 12).
Using dim( to Find List Dimensions
dim( (dimension) returns the length (number of elements) of list.
dim(list)
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Using dim( to Create a List
You can use dim( with ¿ to create a new listname with dimension length from 1 to 999.
The elements are zeros.
length!dim(listname)
Using dim( to Redimension a List
You can use dim with ¿ to redimension an existing listname to dimension length from 1
to 999.
•
•
•
The elements in the old listname that are within the new dimension are not changed.
Extra list elements are filled by 0.
Elements in the old list that are outside the new dimension are deleted.
length!dim(listname)
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Fill(
Fill( replaces each element in listname with value.
Fill(value,listname)
Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu
(Chapter 10).
seq(
seq( (sequence) returns a list in which each element is the result of the evaluation of
expression with regard to variable for the values ranging from begin to end at steps of
increment. variable need not be defined in memory. increment can be negative; the default
value for increment is 1. seq( is not valid within expression. Complex lists are not valid.
seq(expression,variable,begin,end[,increment])
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cumSum(
cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting
with the first element. list elements can be real or complex numbers.
cumSum(list)
@List(
@List( returns a list containing the differences between consecutive elements in list. @List
subtracts the first element in list from the second element, subtracts the second element
from the third, and so on. The list of differences is always one element shorter than the
original list. list elements can be a real or complex numbers.
@List(list)
Select(
Select( selects one or more specific data points from a scatter plot or xyLine plot (only),
and then stores the selected data points to two new lists, xlistname and ylistname. For
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example, you can use Select( to select and then analyze a portion of plotted
CBL 2™/CBL™ or CBR™ data.
Select(xlistname,ylistname)
Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine
plot. Also, the plot must be displayed in the current viewing window.
Before Using Select(
Before using Select(, follow these steps.
1. Create two list names and enter the data.
2. Turn on a stat plot, select " (scatter plot) or Ó (xyLine), and enter the two list names
for Xlist: and Ylist: (Chapter 12).
3. Use ZoomStat to plot the data (Chapter 3).
Using Select( to Select Data Points from a Plot
To select data points from a scatter plot or xyLine plot, follow these steps.
1. Press y 9 ~ 8 to select 8:Select( from the LIST OPS menu. Select( is pasted to
the home screen.
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2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names
into which you want the selected data to be stored.
3. Press Í. The graph screen is displayed with Left Bound?in the bottom-left
corner.
4. Press } or † (if more than one stat plot is selected) to move the cursor onto the stat
plot from which you want to select data points.
5. Press | and ~ to move the cursor to the stat plot data point that you want as the left
bound.
6. Press Í. A 4 indicator on the graph screen shows the left bound. Right Bound?
is displayed in the bottom-left corner.
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7. Press | or ~ to move the cursor to the stat plot point that you want for the right
bound, and then press Í.
The x-values and y-values of the selected points are stored in xlistname and ylistname.
A new stat plot of xlistname and ylistname replaces the stat plot from which you
selected data points. The list names are updated in the stat plot editor.
Note: The two new lists (xlistname and ylistname) will include the points you select as left
bound and right bound. Also, left-bound x-value { right-bound x-value must be true.
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augment(
augment( concatenates the elements of listA and listB. The list elements can be real or
complex numbers.
augment(listA,listB)
List4matr(
List4matr( (lists stored to matrix) fills matrixname column by column with the elements from
each list. If the dimensions of all lists are not equal, then List4matr( fills each extra
matrixname row with 0. Complex lists are not valid.
List4matr(list1,list2, ... ,list n,matrixname)
Matr4list(
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Matr4list( (matrix stored to lists) fills each listname with elements from each column in
matrix. If the number of listname arguments exceeds the number of columns in matrix, then
Matr4list( ignores extra listname arguments. Likewise, if the number of columns in matrix
exceeds the number of listname arguments, then Matr4list( ignores extra matrix columns.
Matr4list(matrix,listname1,listname2, . . . ,listname n)
Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list
with a specific column from matrix, you must enter a column# after matrix.
Matr4list(matrix,column#,listname)
Ù preceding one to five characters identifies those characters as a user-created listname.
listname may comprise letters, q, and numbers, but it must begin with a letter from A to Z
or q.
Ùlistname
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Generally, Ù must precede a user-created list name when you enter a user-created list
name where other input is valid, for example, on the home screen. Without the Ù, the
TI-84 Plus may misinterpret a user-created list name as implied multiplication of two or
more characters.
Ù need not precede a user-created list name where a list name is the only valid input, for
example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the
stat plot editor. If you enter Ù where it is not necessary, the TI-84 Plus will ignore the
entry.
LIST MATH Menu
LIST MATH Menu
To display the LIST MATH menu, press y 9 |.
NAMES OPS MATH
Returns minimum element of a list.
Returns maximum element of a list.
Returns mean of a list.
1: min(
2: max(
3: mean(
4: median(
5: sum(
Returns median of a list.
Returns sum of elements in a list.
Returns product of elements in list.
Returns standard deviation of a list.
Returns the variance of a list.
6: prod(
7: stdDev(
8: variance(
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min(, max(
min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two
lists are compared, it returns a list of the smaller or larger of each pair of elements in listA
and listB. For a complex list, the element with smallest or largest magnitude (modulus) is
returned.
min(listA[,listB])
max(listA[,listB])
Note: min( and max( are the same as min( and max( on the MATH NUM menu.
mean(, median(
mean( returns the mean value of list. median( returns the median value of list. The default
value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences
of the corresponding element in list. Complex lists are not valid.
mean(list[,freqlist])
median(list[,freqlist])
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sum(, prod(
sum( (summation) returns the sum of the elements in list. start and end are optional; they
specify a range of elements. list elements can be real or complex numbers.
prod( returns the product of all elements of list. start and end elements are optional; they
specify a range of list elements. list elements can be real or complex numbers.
sum(list[,start,end])
prod(list[,start,end])
Sums and Products of Numeric Sequences
You can combine sum( or prod( with seq( to obtain:
upper
upper
∏
expression(x)
expression(x)
G
x=lower
x=lower
(N–1)
To evaluate G 2
from N=1 to 4:
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stdDev(, variance(
stdDev( returns the standard deviation of the elements in list. The default value for freqlist is
1. Each freqlist element counts the number of consecutive occurrences of the
corresponding element in list. Complex lists are not valid.
•
variance( returns the variance of the elements in list. The default value for freqlist is 1.
Each freqlist element counts the number of consecutive occurrences of the
corresponding element in list. Complex lists are not valid.
stdDev(list[,freqlist])
variance(list[,freqlist])
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Chapter 12:
Statistics
Getting Started: Pendulum Lengths and Periods
Getting Started is a fast-paced introduction. Read the chapter for details.
A group of students is attempting to determine the mathematical relationship between
the length of a pendulum and its period (one complete swing of a pendulum). The group
makes a simple pendulum from string and washers and then suspends it from the
ceiling. They record the pendulum’s period for each of 12 string lengths.*
Length (cm)
6.5
Time (sec)
0.51
Length (cm)
24.4
Time (sec)
1.01
11.0
0.68
26.6
1.08
13.2
0.73
30.5
1.13
15.0
0.79
34.3
1.26
18.0
0.88
37.6
1.28
23.1
0.99
41.5
1.32
*This example is quoted and adapted from Contemporary Precalculus Through Applications, by
the North Carolina School of Science and Mathematics, by permission of Janson Publications,
Inc., Dedham, MA. 1-800-322-MATH. © 1992. All rights reserved.
1. Press z † † † Í to set Func graphing
mode.
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2. Press … 5 to select 5:SetUpEditor. SetUpEditor
is pasted to the home screen.
Press Í. This removes lists from stat list editor
columns 1 through 20, and then stores lists L1
through L6 in columns 1 through 6.
Note: Removing lists from the stat list editor does
not delete them from memory.
3. Press … 1 to select 1:Edit from the STAT EDIT
menu. The stat list editor is displayed. If elements
are stored in L1 and L2, press } to move the
cursor onto L1, and then press ‘ Í ~ }
‘ Í to clear both lists. Press | to move
the rectangular cursor back to the first row in L1.
4. Press 6 Ë 5 Í to store the first pendulum
string length (6.5 cm) in L1. The rectangular cursor
moves to the next row. Repeat this step to enter
each of the 12 string length values in the table.
5. Press ~ to move the rectangular cursor to the first
row in L2.
Press Ë 51 Í to store the first time
measurement (.51 sec) in L2. The rectangular
cursor moves to the next row. Repeat this step to
enter each of the 12 time values in the table.
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6. Press o to display the Y= editor.
If necessary, press ‘ to clear the function Y1.
As necessary, press }, Í, and ~ to turn off
Plot1, Plot2, and Plot3 from the top line of the
Y= editor (Chapter 3). As necessary, press †, |,
and Í to deselect functions.
7. Press y , 1 to select 1:Plot1 from the
STAT PLOTS menu. The stat plot editor is
displayed for plot 1.
8. Press Í to select On, which turns on plot 1.
Press † Í to select " (scatter plot). Press
† y d to specify Xlist:L1 for plot 1. Press
† y e to specify Ylist:L2 for plot 1. Press
† ~ Í to select + as the Mark for each data
point on the scatter plot.
9. Press q 9 to select 9:ZoomStat from the ZOOM
menu. The window variables are adjusted
automatically, and plot 1 is displayed. This is a
scatter plot of the time-versus-length data.
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Since the scatter plot of time-versus-length data appears to be approximately linear, fit a
line to the data.
10. Press … ~ 4 to select 4:LinReg(ax+b) (linear
regression model) from the STAT CALC menu.
LinReg(ax+b) is pasted to the home screen.
11. Press y d ¢ y e ¢. Press ~ 1 to
display the VARS Y-VARS FUNCTION secondary
menu, and then press 1 to select 1:Y1. L1, L2, and
Y1 are pasted to the home screen as arguments to
LinReg(ax+b).
12. Press Í to execute LinReg(ax+b). The linear
regression for the data in L1 and L2 is calculated.
Values for a and b are displayed on the home
screen. The linear regression equation is stored in
Y1. Residuals are calculated and stored
automatically in the list name RESID, which
becomes an item on the LIST NAMES menu.
13. Press s. The regression line and the scatter
plot are displayed.
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The regression line appears to fit the central portion of the scatter plot well. However, a
residual plot may provide more information about this fit.
14. Press … 1 to select 1:Edit. The stat list editor is
displayed.
Press ~ and } to move the cursor onto L3.
Press y 6. An unnamed column is displayed
in column 3; L3, L4, L5, and L6 shift right one
column. The Name= prompt is displayed in the
entry line, and alpha-lock is on.
15. Press y 9 to display the LIST NAMES menu.
If necessary, press † to move the cursor onto the
list name RESID.
16. Press Í to select RESID and paste it to the
stat list editor’s Name= prompt.
17. Press Í. RESID is stored in column 3 of the
stat list editor.
Press † repeatedly to examine the residuals.
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Notice that the first three residuals are negative. They correspond to the shortest
pendulum string lengths in L1. The next five residuals are positive, and three of the last
four are negative. The latter correspond to the longer string lengths in L1. Plotting the
residuals will show this pattern more clearly.
18. Press y , 2 to select 2:Plot2 from the
STAT PLOTS menu. The stat plot editor is
displayed for plot 2.
19. Press Í to select On, which turns on plot 2.
Press † Í to select " (scatter plot). Press
† y d to specify Xlist:L1 for plot 2. Press † ãRä
ãEä ãSä ãIä ãDä (alpha-lock is on) to specify
Ylist:RESID for plot 2. Press † Í to select ›
as the mark for each data point on the scatter plot.
20. Press o to display the Y= editor.
Press | to move the cursor onto the = sign, and
then press Í to deselect Y1. Press } Í to
turn off plot 1.
21. Press q 9 to select 9:ZoomStat from the ZOOM
menu. The window variables are adjusted
automatically, and plot 2 is displayed. This is a
scatter plot of the residuals.
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Notice the pattern of the residuals: a group of negative residuals, then a group of positive
residuals, and then another group of negative residuals.
The residual pattern indicates a curvature associated with this data set for which the
linear model did not account. The residual plot emphasizes a downward curvature, so a
model that curves down with the data would be more accurate. Perhaps a function such
b
as square root would fit. Try a power regression to fit a function of the form y = a … x .
22. Press o to display the Y= editor.
Press ‘ to clear the linear regression
equation from Y1. Press } Í to turn on plot 1.
Press ~ Í to turn off plot 2.
23. Press q 9 to select 9:ZoomStat from the ZOOM
menu. The window variables are adjusted
automatically, and the original scatter plot of time-
versus-length data (plot 1) is displayed.
24. Press … ~ ƒ ãAä to select A:PwrReg from
the STAT CALC menu. PwrReg is pasted to the
home screen.
Press y d ¢ y e ¢. Press ~ 1 to
display the VARS Y-VARS FUNCTION secondary
menu, and then press 1 to select 1:Y1. L1, L2, and
Y1 are pasted to the home screen as arguments to
PwrReg.
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25. Press Í to calculate the power regression.
Values for a and b are displayed on the home
screen. The power regression equation is stored
in Y1. Residuals are calculated and stored
automatically in the list name RESID.
26. Press s. The regression line and the scatter
plot are displayed.
.522
The new function y=.192x
examine a residual plot.
appears to fit the data well. To get more information,
27. Press o to display the Y= editor.
Press | Í to deselect Y1.
Press } Í to turn off plot 1. Press ~ Í to
turn on plot 2.
Note: Step 19 defined plot 2 to plot residuals
(RESID) versus string length (L1).
28. Press q 9 to select 9:ZoomStat from the ZOOM
menu. The window variables are adjusted
automatically, and plot 2 is displayed. This is a
scatter plot of the residuals.
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The new residual plot shows that the residuals are random in sign, with the residuals
increasing in magnitude as the string length increases.
To see the magnitudes of the residuals, continue with these steps.
29. Press r.
Press ~ and | to trace the data. Observe the
values for Y at each point.
With this model, the largest positive residual is
about 0.041 and the smallest negative residual is
about L0.027. All other residuals are less than 0.02
in magnitude.
Now that you have a good model for the relationship between length and period, you can
use the model to predict the period for a given string length. To predict the periods for a
pendulum with string lengths of 20 cm and 50 cm, continue with these steps.
30. Press ~ 1 to display the VARS Y-VARS
FUNCTION secondary menu, and then press 1 to
select 1:Y1. Y1 is pasted to the home screen.
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31. Press £ 20 ¤ to enter a string length of 20 cm.
Press Í to calculate the predicted time of
about 0.92 seconds.
Based on the residual analysis, we would expect
the prediction of about 0.92 seconds to be within
about 0.02 seconds of the actual value.
32. Press y [ to recall the Last Entry.
Press | | | 5 to change the string length to 50
cm.
33. Press Í to calculate the predicted time of
about 1.48 seconds.
Since a string length of 50 cm exceeds the lengths
in the data set, and since residuals appear to be
increasing as string length increases, we would
expect more error with this estimate.
Note: You also can make predictions using the
table with the TABLE SETUP settings Indpnt:Ask
and Depend:Auto (Chapter 7).
Setting Up Statistical Analyses
Using Lists to Store Data
Data for statistical analyses is stored in lists, which you can create and edit using the stat
list editor. The TI-84 Plus has six list variables in memory, L1 through L6, to which you
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can store data for statistical calculations. Also, you can store data to list names that you
create (Chapter 11).
Setting Up a Statistical Analysis
To set up a statistical analysis, follow these steps. Read the chapter for details.
1. Enter the statistical data into one or more lists.
2. Plot the data.
3. Calculate the statistical variables or fit a model to the data.
4. Graph the regression equation for the plotted data.
5. Graph the residuals list for the given regression model.
Displaying the Stat List Editor
The stat list editor is a table where you can store, edit, and view up to 20 lists that are in
memory. Also, you can create list names from the stat list editor.
To display the stat list editor, press …, and then select 1:Edit from the STAT EDIT
menu.
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The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a
memory reset. The number of the current column is displayed in the top-right corner.
The bottom line is the entry line. All data entry occurs on this line. The characteristics of
this line change according to the current context.
The center area displays up to seven elements of up to three lists; it abbreviates values
when necessary. The entry line displays the full value of the current element.
Using the Stat List Editor
Entering a List Name in the Stat List Editor
To enter a list name in the stat list editor, follow these steps.
1. Display the Name= prompt in the entry line in either of two ways.
•
•
Move the cursor onto the list name in the column where you want to insert a list,
and then press y 6. An unnamed column is displayed and the remaining lists
shift right one column.
Press } until the cursor is on the top line, and then press ~ until you reach the
unnamed column.
Note: If list names are stored to all 20 columns, you must remove a list name to
make room for an unnamed column.
The Name= prompt is displayed and alpha-lock is on.
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2. Enter a valid list name in any of four ways.
•
•
•
•
Select a name from the LIST NAMES menu (Chapter 11).
Enter L1, L2, L3, L4, L5, or L6 from the keyboard.
Enter an existing user-created list name directly from the keyboard.
Enter a new user-created list name.
3. Press Í or † to store the list name and its elements, if any, in the current
column of the stat list editor.
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To begin entering, scrolling, or editing list elements, press †. The rectangular cursor
is displayed.
Note: If the list name you entered in step 2 already was stored in another stat list
editor column, then the list and its elements, if any, move to the current column from
the previous column. Remaining list names shift accordingly.
Creating a Name in the Stat List Editor
To create a name in the stat list editor, follow these steps.
1. Display the Name= prompt.
2. Press [letter from A to Z or q] to enter the first letter of the name. The first character
cannot be a number.
3. Enter zero to four letters, q, or numbers to complete the new user-created list name.
List names can be one to five characters long.
4. Press Í or † to store the list name in the current column of the stat list editor.
The list name becomes an item on the LIST NAMES menu (Chapter 11).
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Removing a List from the Stat List Editor
To remove a list from the stat list editor, move the cursor onto the list name and then press
{. The list is not deleted from memory; it is only removed from the stat list editor.
Notes:
•
•
To delete a list name from memory, use the MEMORY MANAGEMENT/DELETE
secondary menu (Chapter 18).
If you archive a list, it will be removed from the stat list editor.
Removing All Lists and Restoring L1 through L6
You can remove all user-created lists from the stat list editor and restore list names L1
through L6 to columns 1 through 6 in either of two ways.
•
•
Use SetUpEditor with no arguments.
Reset all memory (Chapter 18).
Clearing All Elements from a List
You can clear all elements from a list in any of five ways.
•
•
Use ClrList to clear specified lists.
In the stat list editor, press } to move the cursor onto a list name, and then press
‘ Í.
•
In the stat list editor, move the cursor onto each element, and then press { one by
one.
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•
•
On the home screen or in the program editor, enter 0!dim(listname) to set the
dimension of listname to 0 (Chapter 11).
Use ClrAllLists to clear all lists in memory (Chapter 18).
Editing a List Element
To edit a list element, follow these steps.
1. Move the rectangular cursor onto the element you want to edit.
2. Press Í to move the cursor to the entry line.
Note: If you want to replace the current value, you can enter a new value without first
pressing Í. When you enter the first character, the current value is cleared
automatically.
3. Edit the element in the entry line.
•
•
•
Press one or more keys to enter the new value. When you enter the first
character, the current value is cleared automatically.
Press ~ to move the cursor to the character before which you want to insert, press
y 6, and then enter one or more characters.
Press ~ to move the cursor to a character you want to delete, and then press {
to delete the character.
To cancel any editing and restore the original element at the rectangular cursor,
press ‘ Í.
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Note: You can enter expressions and variables for elements.
4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated.
If you entered only a variable, the stored value is displayed as a list element.
When you edit a list element in the stat list editor, the list is updated in memory
immediately.
Attaching Formulas to List Names
Attaching a Formula to a List Name in Stat List Editor
You can attach a formula to a list name in the stat list editor, and then display and edit the
calculated list elements. When executed, the attached formula must resolve to a list.
Chapter 11 describes in detail the concept of attaching formulas to list names.
To attach a formula to a list name that is stored in the stat list editor, follow these steps.
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1. Press … Í to display the stat list editor.
2. Press } to move the cursor to the top line.
3. Press | or ~, if necessary, to move the cursor onto the list name to which you want
to attach the formula.
Note: If a formula in quotation marks is displayed on the entry line, then a formula is
already attached to the list name. To edit the formula, press Í, and then edit the
formula.
4. Press ƒ ããä, enter the formula, and press ƒ ããä.
Note: If you do not use quotation marks, the TI-84 Plus calculates and displays the
same initial list of answers, but does not attach the formula for future calculations.
Note: Any user-created list name referenced in a formula must be preceded by an Ù
symbol (Chapter 11).
5. Press Í. The TI-84 Plus calculates each list element and stores it to the list
name to which the formula is attached. A lock symbol is displayed in the stat list
editor, next to the list name to which the formula is attached.
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lock symbol
Using the Stat List Editor When Formula-Generated Lists Are Displayed
When you edit an element of a list referenced in an attached formula, the TI-84 Plus
updates the corresponding element in the list to which the formula is attached
(Chapter 11).
When a list with a formula attached is displayed in the stat list editor and you edit or enter
elements of another displayed list, then the TI-84 Plus takes slightly longer to accept
each edit or entry than when no lists with formulas attached are in view.
Note: To speed editing time, scroll horizontally until no lists with formulas are displayed,
or rearrange the stat list editor so that no lists with formulas are displayed.
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Handling Errors Resulting from Attached Formulas
On the home screen, you can attach to a list a formula that references another list with
dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the
stat list editor or on the home screen until you enter at least one element to the list that
the formula references.
All elements of a list referenced by an attached formula must be valid for the attached
formula. For example, if Real number mode is set and the attached formula is log(L1),
then each element of L1 must be greater than 0, since the logarithm of a negative
number returns a complex result.
Notes:
•
If an error menu is returned when you attempt to display a formula-generated list in
the stat list editor, you can select 2:Goto, write down the formula that is attached to
the list, and then press ‘ Í to detach (clear) the formula. You then can use
the stat list editor to find the source of the error. After making the appropriate
changes, you can reattach the formula to a list.
•
If you do not want to clear the formula, you can select 1:Quit, display the referenced
list on the home screen, and find and edit the source of the error. To edit an element
of a list on the home screen, store the new value to listname(element#) (Chapter 11).
Detaching Formulas from List Names
Detaching a Formula from a List Name
You can detach (clear) a formula from a list name in several ways.
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For example:
•
In the stat list editor, move the cursor onto the name of the list to which a formula is
attached. Press Í ‘ Í. All list elements remain, but the formula is
detached and the lock symbol disappears.
•
In the stat list editor, move the cursor onto an element of the list to which a formula is
attached. Press Í, edit the element, and then press Í. The element
changes, the formula is detached, and the lock symbol disappears. All other list
elements remain.
•
•
Use ClrList. All elements of one or more specified lists are cleared, each formula is
detached, and each lock symbol disappears. All list names remain.
Use ClrAllLists (Chapter 18). All elements of all lists in memory are cleared, all
formulas are detached from all list names, and all lock symbols disappear. All list
names remain.
Editing an Element of a Formula-Generated List
As described above, one way to detach a formula from a list name is to edit an element
of the list to which the formula is attached. The TI-84 Plus protects against inadvertently
detaching the formula from the list name by editing an element of the formula-generated
list.
Because of the protection feature, you must press Í before you can edit an element
of a formula-generated list.
The protection feature does not allow you to delete an element of a list to which a
formula is attached. To delete an element of a list to which a formula is attached, you
must first detach the formula in any of the ways described above.
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Switching Stat List Editor Contexts
Stat List Editor Contexts
The stat list editor has four contexts.
•
•
•
•
View-elements context
View-names context
Edit-elements context
Enter-name context
The stat list editor is first displayed in view-elements context. To switch through the four
contexts, select 1:Edit from the STAT EDIT menu and follow these steps.
1. Press } to move the cursor onto a list name. You are
now in view-names context. Press ~ and | to view list
names stored in other stat list editor columns.
2. Press Í. You are now in edit-elements context. You
may edit any element in a list. All elements of the current
list are displayed in braces ( { } )in the entry line. Press
~ and | to view more list elements.
3. Press Í again. You are now in view-elements
context. Press ~, |, †, and } to view other list
elements. The current element’s full value is displayed in
the entry line.
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4. Press Í again. You are now in edit-elements
context. You may edit the current element in the entry
line.
5. Press } until the cursor is on a list name, then press
y 6. You are now in enter-name context.
6. Press ‘. You are now in view-names context.
7. Press †. You are now back in view-elements context.
Stat List Editor Contexts
View-Elements Context
In view-elements context, the entry line displays the list name, the current element’s
place in that list, and the full value of the current element, up to 12 characters at a time.
An ellipsis (...) indicates that the element continues beyond 12 characters.
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To page down the list six elements, press ƒ †. To page up six elements, press
ƒ }. To delete a list element, press {. Remaining elements shift up one row. To
insert a new element, press y 6. 0 is the default value for a new element.
Edit-Elements Context
In edit-elements context, the data displayed in the entry line depends on the previous
context.
•
When you switch to edit-elements context from view-elements context, the full value
of the current element is displayed. You can edit the value of this element, and then
press † and } to edit other list elements.
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•
When you switch to edit-elements context from view-names context, the full values
of all elements in the list are displayed. An ellipsis indicates that list elements
continue beyond the screen. You can press ~ and | to edit any element in the list.
Note: In edit-elements context, you can attach a formula to a list name only if you
switched to it from view-names context.
View-Names Context
In view-names context, the entry line displays the list name and the list elements.
To remove a list from the stat list editor, press {. Remaining lists shift to the left one
column. The list is not deleted from memory.
To insert a name in the current column, press y 6. Remaining columns shift to the
right one column.
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Enter-Name Context
In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is
on.
At the Name= prompt, you can create a new list name, paste a list name from L1 to L6
from the keyboard, or paste an existing list name from the LIST NAMES menu
(Chapter 11). The Ù symbol is not required at the Name= prompt.
To leave enter-name context without entering a list name, press ‘. The stat list
editor switches to view-names context.
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STAT EDIT Menu
STAT EDIT Menu
To display the STAT EDIT menu, press ….
EDIT CALC TESTS
Displays the stat list editor.
1: Edit...
Sorts a list in ascending order.
Sorts a list in descending order.
Deletes all elements of a list.
2: SortA(
3: SortD(
4: ClrList
5: SetUpEditor
Stores specified lists in the stat list editor.
Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items.
SortA(, SortD(
SortA( (sort ascending) sorts list elements from low to high values. SortD( (sort
descending) sorts list elements from high to low values. Complex lists are sorted based
on magnitude (modulus). SortA( and SortD( each can sort in either of two ways.
•
•
With one listname, SortA( and SortD( sort the elements in listname and update the list
in memory.
With two or more lists, SortA( and SortD( sort keylistname, and then sort each dependlist
by placing its elements in the same order as the corresponding elements in
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keylistname. This lets you sort two-variable data on X and keep the data pairs together.
All lists must have the same dimension.
The sorted lists are updated in memory.
SortA(listname)
SortD(listname)
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])
SortD(keylistname,dependlist1[,dependlist2,...,dependlist n])
Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu.
ClrList
ClrList clears (deletes) from memory the elements of one or more listnames. ClrList also
detaches any formula attached to a listname.
ClrList listname1,listname2,...,listname n
Note: To clear from memory all elements of all list names, use ClrAllLists (Chapter 18).
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SetUpEditor
With SetUpEditor you can set up the stat list editor to display one or more listnames in the
order that you specify. You can specify zero to 20 listnames.
Additionally, if you want to use listnames which happen to be archived, the SetUp Editor
will automatically unarchive the listnames and place them in the stat list editor at the same
time.
SetUpEditor [listname1,listname2,...,listname n]
SetUpEditor with one to 20 listnames removes all list names from the stat list editor and
then stores listnames in the stat list editor columns in the specified order, beginning in
column 1.
If you enter a listname that is not stored in memory already, then listname is created and
stored in memory; it becomes an item on the LIST NAMES menu.
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Restoring L1 through L6 to the Stat List Editor
SetUpEditor with no listnames removes all list names from the stat list editor and restores
list names L1 through L6 in the stat list editor columns 1 through 6.
Regression Model Features
Regression Model Features
STAT CALC menu items 3 through C are regression models. The automatic residual list
and automatic regression equation features apply to all regression models. Diagnostics
display mode applies to some regression models.
Automatic Residual List
When you execute a regression model, the automatic residual list feature computes and
stores the residuals to the list name RESID. RESID becomes an item on the
LIST NAMES menu (Chapter 11).
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The TI-84 Plus uses the formula below to compute RESID list elements. The next
section describes the variable RegEQ.
RESID = Ylistname N RegEQ(Xlistname)
Automatic Regression Equation
Each regression model has an optional argument, regequ, for which you can specify a Y=
variable such as Y1. Upon execution, the regression equation is stored automatically to
the specified Y= variable and the Y= function is selected.
Regardless of whether you specify a Y= variable for regequ, the regression equation
always is stored to the TI-84 Plus variable RegEQ, which is item 1 on the VARS Statistics
EQ secondary menu.
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Note: For the regression equation, you can use the fixed-decimal mode setting to control
the number of digits stored after the decimal point (Chapter 1). However, limiting the
number of digits to a small number could affect the accuracy of the fit.
Diagnostics Display Mode
When you execute some regression models, the TI-84 Plus computes and stores
2
diagnostics values for r (correlation coefficient) and r (coefficient of determination) or for
2
R (coefficient of determination).
2
r and r are computed and stored for these regression models.
LinReg(ax+b)
LinReg(a+bx)
LnReg
ExpReg
PwrReg
2
R is computed and stored for these regression models.
QuadReg
CubicReg
QuartReg
2
The r and r that are computed for LnReg, ExpReg, and PwrReg are based on the linearly
2
transformed data. For example, for ExpReg (y=ab^x), r and r are computed on
ln y=ln a+x(ln b).
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By default, these values are not displayed with the results of a regression model when
you execute it. However, you can set the diagnostics display mode by executing the
DiagnosticOn or DiagnosticOff instruction. Each instruction is in the CATALOG
(Chapter 15).
Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y N,
and then select the instruction for the mode you want. The instruction is pasted to the
home screen. Press Í to set the mode.
When DiagnosticOn is set, diagnostics are displayed with the results when you execute a
regression model.
When DiagnosticOff is set, diagnostics are not displayed with the results when you
execute a regression model.
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STAT CALC Menu
STAT CALC Menu
To display the STAT CALC menu, press … ~.
EDIT
CALC TESTS
Calculates 1-variable statistics.
Calculates 2-variable statistics.
Calculates a median-median line.
Fits a linear model to data.
1: 1-Var Stats
2: 2-Var Stats
3: Med-Med
4: LinReg(ax+b)
5: QuadReg
Fits a quadratic model to data.
Fits a cubic model to data.
6: CubicReg
7: QuartReg
8: LinReg(a+bx)
9: LnReg
Fits a quartic model to data.
Fits a linear model to data.
Fits a logarithmic model to data.
Fits an exponential model to data.
Fits a power model to data.
0: ExpReg
A: PwrReg
Fits a logistic model to data.
B: Logistic
C: SinReg
Fits a sinusoidal model to data.
Fits a linear equation interactively to a scatter plot.
D: Manual Linear Fit
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For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified, then the
default list names are L1 and L2. If you do not specify freqlist, then the default is 1
occurrence of each list element.
Frequency of Occurrence for Data Points
For most STAT CALC menu items, you can specify a list of data occurrences, or
frequencies (freqlist).
Each element in freqlist indicates how many times the corresponding data point or data
pair occurs in the data set you are analyzing.
For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-84 Plus interprets the
instruction 1-Var Stats L1, ÙFREQ to mean that 15 occurs once, 12 occurs four times, 9
occurs once, and 14 occurs three times.
Each element in freqlist must be ‚ 0, and at least one element must be > 0.
Noninteger freqlist elements are valid. This is useful when entering frequencies
expressed as percentages or parts that add up to 1. However, if freqlist contains
noninteger frequencies, Sx and Sy are undefined; values are not displayed for Sx and Sy
in the statistical results.
1-Var Stats
1-Var Stats (one-variable statistics) analyzes data with one measured variable. Each
element in freqlist is the frequency of occurrence for each corresponding data point in
Xlistname. freqlist elements must be real numbers > 0.
1-Var Stats [Xlistname,freqlist]
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2-Var Stats
2-Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent
variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of
occurrence for each data pair (Xlistname,Ylistname).
2-Var Stats [Xlistname,Ylistname,freqlist]
Med-Med (ax+b)
Med-Med (median-median) fits the model equation y=ax+b to the data using the median-
median line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3,
and y3. Med-Med displays values for a (slope) and b (y-intercept).
Med-Med [Xlistname,Ylistname,freqlist,regequ]
LinReg (ax+b)
LinReg(ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-
squares fit. It displays values for a (slope) and b (y-intercept); when DiagnosticOn is set, it
2
also displays values for r and r.
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LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]
2
QuadReg (ax +bx+c)
2
QuadReg (quadratic regression) fits the second-degree polynomial y=ax +bx+c to the
data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value
2
for R . For three data points, the equation is a polynomial fit; for four or more, it is a
polynomial regression. At least three data points are required.
QuadReg [Xlistname,Ylistname,freqlist,regequ]
3
2
CubicReg—(ax +bx +cx+d)
3
2
CubicReg (cubic regression) fits the third-degree polynomial y=ax +bx +cx+d to the
data. It displays values for a, b, c, and d; when DiagnosticOn is set, it also displays a
2
value for R . For four points, the equation is a polynomial fit; for five or more, it is a
polynomial regression. At least four points are required.
CubicReg [Xlistname,Ylistname,freqlist,regequ]
4
3
2
QuartReg—(ax +bx +cx + dx+e)
4
3
2
QuartReg (quartic regression) fits the fourth-degree polynomial y=ax +bx +cx +dx+e to
the data. It displays values for a, b, c, d, and e; when DiagnosticOn is set, it also displays
2
a value for R . For five points, the equation is a polynomial fit; for six or more, it is a
polynomial regression. At least five points are required.
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QuartReg [Xlistname,Ylistname,freqlist,regequ]
LinReg—(a+bx)
LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data using a least-
squares fit. It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it
2
also displays values for r and r.
LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]
LnReg—(a+b ln(x))
LnReg (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a
least-squares fit and transformed values ln(x) and y. It displays values for a and b; when
2
DiagnosticOn is set, it also displays values for r and r.
LnReg [Xlistname,Ylistname,freqlist,regequ]
x
ExpReg—(ab )
x
ExpReg (exponential regression) fits the model equation y=ab to the data using a least-
squares fit and transformed values x and ln(y). It displays values for a and b; when
2
DiagnosticOn is set, it also displays values for r and r.
ExpReg [Xlistname,Ylistname,freqlist,regequ]
b
PwrReg—(ax )
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b
PwrReg (power regression) fits the model equation y=ax to the data using a least-
squares fit and transformed values ln(x) and ln(y). It displays values for a and b; when
2
DiagnosticOn is set, it also displays values for r and r.
PwrReg [Xlistname,Ylistname,freqlist,regequ]
-bx
Logistic—c/(1+a…e
)
L
bx
Logistic fits the model equation y=c/(1+a…e ) to the data using an iterative least-squares
fit. It displays values for a, b, and c.
Logistic [Xlistname,Ylistname,freqlist,regequ]
SinReg—a sin(bx+c)+d
SinReg (sinusoidal regression) fits the model equation y=a sin(bx+c)+d to the data using
an iterative least-squares fit. It displays values for a, b, c, and d. At least four data points
are required. At least two data points per cycle are required in order to avoid aliased
frequency estimates.
SinReg [iterations,Xlistname,Ylistname,period,regequ]
iterations is the maximum number of times the algorithm will iterate to find a solution. The
value for iterations can be an integer ‚ 1 and 16; if not specified, the default is 3. The
algorithm may find a solution before iterations is reached. Typically, larger values for
iterations result in longer execution times and better accuracy for SinReg, and vice versa.
A period guess is optional. If you do not specify period, the difference between time values
in Xlistname must be equal and the time values must be ordered in ascending sequential
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order. If you specify period, the algorithm may find a solution more quickly, or it may find a
solution when it would not have found one if you had omitted a value for period. If you
specify period, the differences between time values in Xlistname can be unequal.
Note: The output of SinReg is always in radians, regardless of the Radian/Degree mode
setting.
SinReg Example: Daylight Hours in Alaska for One Year
Compute the regression model for the number of hours of daylight in Alaska during one
year.
1 period
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With noisy data, you will achieve better convergence results when you specify an
accurate estimate for period. You can obtain a period guess in either of two ways.
•
•
Plot the data and trace to determine the x-distance between the beginning and end
of one complete period, or cycle. The illustration above and to the right graphically
depicts a complete period, or cycle.
Plot the data and trace to determine the x-distance between the beginning and end
of N complete periods, or cycles. Then divide the total distance by N.
After your first attempt to use SinReg and the default value for iterations to fit the data, you
may find the fit to be approximately correct, but not optimal. For an optimal fit, execute
SinReg 16,Xlistname,Ylistname,2p/b where b is the value obtained from the previous SinReg
execution.
Manual Linear Fit
Manual Linear Fit allows you to visually fit a linear function to a scatter plot. Manual
Linear Fit is an option in the … / menu.
After entering List data and viewing the StatPlot, select the Manual-Fit function.
1. Press … to display the Stat menu. Press ~ to select
CALC. Press † several times to scroll down to select
D:Manual-Fit. Press Í. This displays a free-floating
cursor at the center of the display screen
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2. Press the cursor navigation keys (} † | ~ ) to move
the cursor to the desired location. Press Í to select
the first point.
3. Press the cursor navigation keys (} † | ~ ) to move
the cursor to the second location. Press Í. This
displays a line containing the two points selected.
The linear function is displayed. The Manual-Fit Line equation displays in the form of
Y=mX+b. The current value of the first parameter (m) is highlighted in the symbolic
expression.
Modify parameter values
Press the cursor navigation keys ( | ~ ) to move from the first parameter (m) or (b) the
second parameter. You can press Í and type a new parameter value. Press Í
to display the new parameter value. When you edit the value of the selected parameter,
the edit can include insert, delete, type over, or mathematical expression.
The screen dynamically displays the revised parameter value. Press Í to complete
the modification of the selected parameter, save the value, and refresh the displayed
graph. The system displays the revised parameter value in the symbolic expression
Y=mX+B, and refreshes the graph with the updated Manual-Fit Line.
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Select y 5 to finish the Manual Fit function. The calculator stores the current mX+b
expression into Y1 and makes that function active for graphing. You can also select
Manual-Fit while on the Home screen. You can then enter a different Y-Var such as Y4
and then press Í. This takes you to the Graph screen and then pastes the Manual-
Fit equation in the specified Y-Var. In this example, Y4.
Statistical Variables
The statistical variables are calculated and stored as indicated below. To access these
variables for use in expressions, press , and select 5:Statistics. Then select the
VARS menu shown in the column below under VARS menu. If you edit a list or change
the type of analysis, all statistical variables are cleared.
1-Var
Stats
2-Var
Stats
VARS
menu
Variables
Other
mean of x values
sum of x values
XY
G
v
v
Gx
Gx
2
2
2
G
sum of x values
Gx
Gx
sample standard deviation of x
population standard deviation of x
number of data points
mean of y values
Sx
sx
n
Sx
sx
n
XY
XY
XY
XY
w
sum of y values
Gy
G
G
2
2
sum of y values
Gy
sample standard deviation of y
Sy
XY
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1-Var
Stats
2-Var
Stats
VARS
menu
Variables
Other
population standard deviation of y
XY
sy
sum of x … y
Gxy
G
minimum of x values
maximum of x values
minimum of y values
maximum of y values
1st quartile
minX
minX
maxX
minY
maxY
XY
XY
maxX
XY
XY
Q1
Med
Q3
PTS
PTS
PTS
EQ
median
3rd quartile
regression/fit coefficients
a, b
polynomial, Logistic, and SinReg
coefficients
a, b, c,
d, e
EQ
correlation coefficient
r
EQ
EQ
2
2
coefficient of determination
r , R
regression equation
RegEQ
EQ
summary points (Med-Med only)
x1, y1, x2,
y2, x3, y3
PTS
Q1 and Q3
The first quartile (Q1) is the median of points between minX and Med (median). The third
quartile (Q3) is the median of points between Med and maxX.
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Statistical Analysis in a Program
Entering Stat Data
You can enter statistical data, calculate statistical results, and fit models to data from a
program. You can enter statistical data into lists directly within the program (Chapter 11).
Statistical Calculations
To perform a statistical calculation from a program, follow these steps.
1. On a blank line in the program editor, select the type of calculation from the
STAT CALC menu.
2. Enter the names of the lists to use in the calculation. Separate the list names with a
comma.
3. Enter a comma and then the name of a Y= variable, if you want to store the regression
equation to a Y= variable.
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Statistical Plotting
Steps for Plotting Statistical Data in Lists
You can plot statistical data that is stored in lists. The six types of plots available are
scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal
probability plot. You can define up to three plots.
To plot statistical data in lists, follow these steps.
1. Store the stat data in one or more lists.
2. Select or deselect Y= functions as appropriate.
3. Define the stat plot.
4. Turn on the plots you want to display.
5. Define the viewing window.
6. Display and explore the graph.
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Scatter
Scatter (")plots plot the data points from Xlist and Ylist as coordinate pairs, showing
each point as a box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist must be the same length.
You can use the same list for Xlist and Ylist.
xyLine
xyLine (Ó)is a scatter plot in which the data points are plotted and connected in order
of appearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists
before you plot them.
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Histogram
Histogram (Ò) plots one-variable data. The Xscl window variable value determines the
width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to
include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be
true. A value that occurs on the edge of a bar is counted in the bar to the right.
ModBoxplot
ModBoxplot (Õ) (modified box plot) plots one-variable data, like the regular box plot,
except points that are 1.5 … Interquartile Range beyond the quartiles. (The Interquartile
Range is defined as the difference between the third quartile Q3 and the first quartile Q1.)
These points are plotted individually beyond the whisker, using the Mark (› or + or ¦) you
select. You can trace these points, which are called outliers.
The prompt for outlier points is x=, except when the outlier is the maximum point (maxX)
or the minimum point (minX). When outliers exist, the end of each whisker will display x=.
When no outliers exist, minX and maxX are the prompts for the end of each whisker. Q1,
Med (median), and Q3 define the box.
Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When
two box plots are plotted, the first one plots at the top of the screen and the second plots
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in the middle. When three are plotted, the first one plots at the top, the second in the
middle, and the third at the bottom.
Boxplot
Boxplot (Ö)(regular box plot) plots one-variable data. The whiskers on the plot extend
from the minimum data point in the set (minX) to the first quartile (Q1) and from the third
quartile (Q3) to the maximum point (maxX). The box is defined by Q1, Med (median), and
Q3.
Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax. When
two box plots are plotted, the first one plots at the top of the screen and the second plots
in the middle. When three are plotted, the first one plots at the top, the second in the
middle, and the third at the bottom.
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NormProbPlot
NormProbPlot (Ô) (normal probability plot) plots each observation X in Data List versus
the corresponding quantile z of the standard normal distribution. If the plotted points lie
close to a straight line, then the plot indicates that the data are normal.
Enter a valid list name in the Data List field. Select X or Y for the Data Axis setting.
•
•
If you select X, the TI-84 Plus plots the data on the x-axis and the z-values on the
y-axis.
If you select Y, the TI-84 Plus plots the data on the y-axis and the z-values on the
x-axis.
Defining the Plots
To define a plot, follow these steps.
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1. Press y ,. The STAT PLOTS menu is displayed with the current plot
definitions.
2. Select the plot you want to use. The stat plot editor is displayed for the plot you
selected.
3. Press Í to select On if you want to plot the statistical data immediately. The
definition is stored whether you select On or Off.
4. Select the type of plot. Each type prompts for the options checked in this table.
Data
List
Data
Axis
Plot Type
XList
_
YList
_
Mark
_
Freq
œ
" Scatter
œ
œ
œ
œ
œ
œ
Ó xyLine
Ò Histogram
_
_
_
œ
_
œ
œ
_
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Data
List
Data
Axis
Plot Type
XList
_
YList
œ
Mark
_
Freq
_
Õ ModBoxplot
Ö Boxplot
œ
œ
œ
œ
_
œ
œ
_
Ô NormProbPlot
œ
œ
_
œ
_
_
5. Enter list names or select options for the plot type.
•
•
•
•
•
•
Xlist (list name containing independent data)
Ylist (list name containing dependent data)
Mark (› or + or ¦)
Freq (frequency list for Xlist elements; default is 1)
Data List (list name for NormProbPlot)
Data Axis (axis on which to plot Data List)
Displaying Other Stat Plot Editors
Each stat plot has a unique stat plot editor. The name of the current stat plot (Plot1,
Plot2, or Plot3) is highlighted in the top line of the stat plot editor. To display the stat plot
editor for a different plot, press } and ~ to move the cursor onto the name in the top
line, and then press Í. The stat plot editor for the selected plot is displayed, and the
selected name remains highlighted.
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Turning On and Turning Off Stat Plots
PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a
program. With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots.
With one or more plot numbers (1, 2, and 3), PlotsOn turns on specified plots, and
PlotsOff turns off specified plots.
PlotsOff [1,2,3]
PlotsOn [1,2,3]
Note: You also can turn on and turn off stat plots in the top line of the Y= editor
(Chapter 3).
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Defining the Viewing Window
Stat plots are displayed on the current graph. To define the viewing window, press
p and enter values for the window variables. ZoomStat redefines the viewing
window to display all statistical data points.
Tracing a Stat Plot
When you trace a scatter plot or xyLine, tracing begins at the first element in the lists.
When you trace a histogram, the cursor moves from the top center of one column to the
top center of the next, starting at the first column.
When you trace a box plot, tracing begins at Med (the median). Press | to trace to Q1
and minX. Press ~ to trace to Q3 and maxX.
When you press } or † to move to another plot or to another Y= function, tracing
moves to the current or beginning point on that plot (not the nearest pixel).
The ExprOn/ExprOff format setting applies to stat plots (Chapter 3). When ExprOn is
selected, the plot number and plotted data lists are displayed in the top-left corner.
Statistical Plotting in a Program
Defining a Stat Plot in a Program
To display a stat plot from a program, define the plot, and then display the graph.
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To define a stat plot from a program, begin on a blank line in the program editor and
enter data into one or more lists; then, follow these steps.
1. Press y , to display the STAT PLOTS menu.
2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location.
3. Press y , ~ to display the STAT TYPE menu.
4. Select the type of plot, which pastes the name of the plot type to the cursor location.
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5. Press ¢. Enter the list names, separated by commas.
6. Press ¢ y , | to display the STAT PLOT MARK menu. (This step is not
necessary if you selected 3:Histogram or 5:Boxplot in step 4.)
Select the type of mark (› or + or ¦) for each data point. The selected mark symbol is
pasted to the cursor location.
7. Press ¤ Í to complete the command line.
Displaying a Stat Plot from a Program
To display a plot from a program, use the DispGraph instruction (Chapter 16) or any of
the ZOOM instructions (Chapter 3).
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Chapter 13:
Inferential Statistics and Distributions
Getting Started: Mean Height of a Population
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to estimate the mean height of a population of women given the
random sample below. Because heights among a biological population tend to be
normally distributed, a t distribution confidence interval can be used when estimating the
mean. The 10 height values below are the first 10 of 90 values, randomly generated from
a normally distributed population with an assumed mean of 165.1 centimeters and a
standard deviation of 6.35 centimeters (randNorm(165.1,6.35,90) with a seed of 789).
Height (in centimeters) of Each of 10 Women
169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53
1. Press … Í to display the stat list editor.
Press } to move the cursor onto L1, and then
press y 6. The Name= prompt is displayed on
the bottom line. The Ø cursor indicates that alpha-
lock is on. The existing list name columns shift to
the right.
Note: Your stat editor may not look like the one
pictured here, depending on the lists you have
already stored.
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2. Enter [H] [G] [H] [T] at the Name= prompt, and then
press Í. The list to which you will store the
women’s height data is created.
Press † to move the cursor onto the first row of
the list. HGHT(1)= is displayed on the bottom line.
3. Press 169 Ë 43 to enter the first height value. As
you enter it, it is displayed on the bottom line.
Press Í. The value is displayed in the first
row, and the rectangular cursor moves to the next
row.
Enter the other nine height values the same way.
4. Press … | to display the STAT TESTS menu,
and then press † until 8:TInterval is highlighted.
5. Press Í to select 8:TInterval. The inferential
stat editor for TInterval is displayed. If Data is not
selected for Inpt:, press | Í to select Data.
Press † and [H] [G] [H] [T] at the List: prompt
(alpha-lock is on).
Press † † Ë 99 to enter a 99 percent confidence
level at the C-Level: prompt.
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6. Press † to move the cursor onto Calculate, and
then press Í. The confidence interval is
calculated, and the TInterval results are displayed
on the home screen.
Interpret the results.
The first line, (159.74,173.94), shows that the 99 percent confidence interval for the
population mean is between about 159.74 centimeters and 173.94 centimeters. This is
about a 14.2 centimeters spread.
The .99 confidence level indicates that in a very large number of samples, we expect 99
percent of the intervals calculated to contain the population mean. The actual mean of
the population sampled is 165.1 centimeters, which is in the calculated interval.
The second line gives the mean height of the sample v used to compute this interval.
The third line gives the sample standard deviation Sx. The bottom line gives the sample
size n.
To obtain a more precise bound on the population mean m of women’s heights, increase
the sample size to 90. Use a sample mean v of 163.8 and sample standard deviation Sx
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of 7.1 calculated from the larger random sample. This time, use the Stats (summary
statistics) input option.
7. Press … | 8 to display the inferential stat
editor for TInterval.
Press ~ Í to select Inpt:Stats. The editor
changes so that you can enter summary statistics
as input.
8. Press † 163 Ë 8 Í to store 163.8 to v.
Press 7 Ë 1 Í to store 7.1 to Sx.
Press 90 Í to store 90 to n.
9. Press † to move the cursor onto Calculate, and
then press Í to calculate the new 99 percent
confidence interval. The results are displayed on
the home screen.
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If the height distribution among a population of women is normally distributed with a
mean m of 165.1 centimeters and a standard deviation s of 6.35 centimeters, what height
is exceeded by only 5 percent of the women (the 95th percentile)?
10. Press ‘ to clear the home screen.
Press y = to display the DISTR
(distributions) menu.
11. Press 3 to paste invNorm( to the home screen.
Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í.
.95 is the area, 165.1 is m, and 6.35 is s.
The result is displayed on the home screen; it shows that five percent of the women are
taller than 175.5 centimeters.
Now graph and shade the top 5 percent of the population.
12. Press p and set the window variables to
these values.
Xmin=145 Ymin=L.02 Xres=1
Xmax=185 Ymax=.08
Xscl=5
Yscl=0
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13. Press y = ~ to display the DISTR DRAW
menu.
14. Press Í to paste ShadeNorm( to the home
screen.
Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë
35 ¤.
Ans (175.5448205 from step 11) is the lower
bound. 1â99 is the upper bound. The normal curve
is defined by a mean m of 165.1 and a standard
deviation s of 6.35.
15. Press Í to plot and shade the normal curve.
Area is the area above the 95th percentile. low is
the lower bound. up is the upper bound.
Inferential Stat Editors
Displaying the Inferential Stat Editors
When you select a hypothesis test or confidence interval instruction from the home
screen, the appropriate inferential statistics editor is displayed. The editors vary
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according to each test or interval’s input requirements. Below is the inferential stat editor
for T-Test.
Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA(
does not have an editor screen.
Using an Inferential Stat Editor
To use an inferential stat editor, follow these steps.
1. Select a hypothesis test or confidence interval from the STAT TESTS menu. The
appropriate editor is displayed.
2. Select Data or Stats input, if the selection is available. The appropriate editor is
displayed.
3. Enter real numbers, list names, or expressions for each argument in the editor.
4. Select the alternative hypothesis (Ā, <, or >) against which to test, if the selection is
available.
5. Select No or Yes for the Pooled option, if the selection is available.
6. Select Calculate or Draw (when Draw is available) to execute the instruction.
•
•
When you select Calculate, the results are displayed on the home screen.
When you select Draw, the results are displayed in a graph.
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This chapter describes the selections in the above steps for each hypothesis test and
confidence interval instruction.
Select an
alternative
hypothesis
Select Data or
Stats input
Enter values
for arguments
Select
Calculate or
Draw output
Selecting Data or Stats
Most inferential stat editors prompt you to select one of two types of input. (1-PropZInt
2
2
and 2-PropZTest, 1-PropZInt and 2-PropZInt, c -Test, c GOF-Test, LinRegTInt, and
LinRegTTest do not.)
•
•
Select Data to enter the data lists as input.
Select Stats to enter summary statistics, such as v, Sx, and n, as input.
To select Data or Stats, move the cursor to either Data or Stats, and then press Í.
Entering the Values for Arguments
Inferential stat editors require a value for every argument. If you do not know what a
particular argument symbol represents, see the Inferential Statistics Input Descriptions
tables.
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When you enter values in any inferential stat editor, the TI-84 Plus stores them in
memory so that you can run many tests or intervals without having to reenter every
value.
Selecting an Alternative Hypothesis (ă < >)
Most of the inferential stat editors for the hypothesis tests prompt you to select one of
three alternative hypotheses.
•
•
•
The first is a ƒ alternative hypothesis, such as mƒm0 for the Z-Test.
The second is a < alternative hypothesis, such as m1<m2 for the 2-SampTTest.
The third is a > alternative hypothesis, such as p1>p2 for the 2-PropZTest.
To select an alternative hypothesis, move the cursor to the appropriate alternative, and
then press Í.
Selecting the Pooled Option
Pooled (2-SampTTest and 2-SampTInt only) specifies whether the variances are to be
pooled for the calculation.
•
•
Select No if you do not want the variances pooled. Population variances can be
unequal.
Select Yes if you want the variances pooled. Population variances are assumed to
be equal.
To select the Pooled option, move the cursor to Yes, and then press Í.
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Selecting Calculate or Draw for a Hypothesis Test
After you have entered all arguments in an inferential stat editor for a hypothesis test,
you must select whether you want to see the calculated results on the home screen
(Calculate) or on the graph screen (Draw).
•
•
Calculate calculates the test results and displays the outputs on the home screen.
Draw draws a graph of the test results and displays the test statistic and p-value with
the graph. The window variables are adjusted automatically to fit the graph.
To select Calculate or Draw, move the cursor to either Calculate or Draw, and then press
Í. The instruction is immediately executed.
Selecting Calculate for a Confidence Interval
After you have entered all arguments in an inferential stat editor for a confidence interval,
select Calculate to display the results. The Draw option is not available.
When you press Í, Calculate calculates the confidence interval results and displays
the outputs on the home screen.
Bypassing the Inferential Stat Editors
To paste a hypothesis test or confidence interval instruction to the home screen without
displaying the corresponding inferential stat editor, select the instruction you want from
the CATALOG menu. Appendix A describes the input syntax for each hypothesis test and
confidence interval instruction.
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Note: You can paste a hypothesis test or confidence interval instruction to a command
line in a program. From within the program editor, select the instruction from either the
CATALOG (Chapter 15) or the STAT TESTS menu.
STAT TESTS Menu
STAT TESTS Menu
To display the STAT TESTS menu, press … |. When you select an inferential
statistics instruction, the appropriate inferential stat editor is displayed.
Most STAT TESTS instructions store some output variables to memory. For a list of these
variables, see the Test and Interval Output Variables table.
EDIT CALC TESTS
1: Z-Test...
Test for 1 m, known s
2: T-Test...
Test for 1 m, unknown s
3: 2-SampZTest...
4: 2-SampTTest...
5: 1-PropZTest...
6: 2-PropZTest...
7: ZInterval...
8: TInterval...
9: 2-SampZInt...
Test comparing 2 m’s, known s’s
Test comparing 2 m’s, unknown s’s
Test for 1 proportion
Test comparing 2 proportions
Confidence interval for 1 m, known s
Confidence interval for 1 m, unknown s
Confidence interval for difference of 2 m’s, known s’s
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EDIT CALC TESTS
0: 2-SampTInt...
A: 1-PropZInt...
B: 2-PropZInt...
Confidence interval for difference of 2 m’s, unknown s’s
Confidence interval for 1 proportion
Confidence interval for difference of 2 proportions
2
C: c -Test...
Chi-square test for 2-way tables
Chi-square Goodness of Fit test
2
D:
c -GOF Test...
E: 2-SampÛTest...
F: LinRegTTest...
G: LinRegTInt...
H: ANOVA(
Test comparing 2 s’s
t test for regression slope and r
Confidence interval for linear regression slope coefficient b
One-way analysis of variance
Note: When a new test or interval is computed, all previous output variables are
invalidated.
Inferential Stat Editors for the STAT TESTS Instructions
In this chapter, the description of each STAT TESTS instruction shows the unique
inferential stat editor for that instruction with example arguments.
•
•
Descriptions of instructions that offer the Data/Stats input choice show both types of
input screens.
Descriptions of instructions that do not offer the Data/Stats input choice show only
one input screen.
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The description then shows the unique output screen for that instruction with the
example results.
•
•
Descriptions of instructions that offer the Calculate/Draw output choice show both
types of screens: calculated and graphic results.
Descriptions of instructions that offer only the Calculate output choice show the
calculated results on the home screen.
Z-Test
Z-Test (one-sample z test; item 1) performs a hypothesis test for a single unknown
population mean m when the population standard deviation s is known. It tests the null
hypothesis H : m=m against one of the alternatives below.
0
0
•
•
•
H : mƒm (m:ƒm0)
a
0
H : m<m (m:<m0)
a
0
H : m>m (m:>m0)
a
0
In the example:
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L1={299.4 297.7 301 298.9 300.2 297}
Data
Stats
Input:
Calculated
results:
Drawn
results:
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Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4 (Chapter 1). If
you set the decimal mode to Float or a different fixed-decimal setting, your output may
differ from the output in the examples.
T-Test
T-Test (one-sample t test; item 2) performs a hypothesis test for a single unknown
population mean m when the population standard deviation s is unknown. It tests the null
hypothesis H : m=m against one of the alternatives below.
0
0
•
•
•
H : mƒm (m:ƒm0)
a
0
H : m<m (m:<m0)
a
0
H : m>m (m:>m0)
a
0
In the example:
TEST={91.9 97.8 111.4 122.3 105.4 95}
Data
Stats
Input:
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Data
Stats
Calculated
results:
Drawn
results:
2-SampZTest
2-SampZTest (two-sample z test; item 3) tests the equality of the means of two
populations (m and m ) based on independent samples when both population standard
1
2
deviations (s and s ) are known. The null hypothesis H : m =m is tested against one of
1
2
0
1
2
the alternatives below.
•
•
•
H : m ƒm (m1:ƒm2)
a
1
2
H : m <m (m1:<m2)
a
1
2
H : m >m (m1:>m2)
a
1
2
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In the example:
LISTA={154 109 137 115 140}
LISTB={108 115 126 92 146}
Data
Stats
Input:
Calculated
results:
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Data
Stats
Drawn
results:
2-SampTTest
2-SampTTest (two-sample t test; item 4) tests the equality of the means of two
populations (m and m ) based on independent samples when neither population
1
2
standard deviation (s or s ) is known. The null hypothesis H : m =m is tested against
1
2
0
1
2
one of the alternatives below.
•
•
•
H : m ƒm (m1:ƒm2)
a
1
2
H : m <m (m1:<m2)
a
1
2
H : m >m (m1:>m2)
a
1
2
In the example:
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SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Data
Stats
Input:
Calculated
results:
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Data
Stats
Drawn
results:
1-PropZTest
1-PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of
successes (prop). It takes as input the count of successes in the sample x and the count
of observations in the sample n. 1-PropZTest tests the null hypothesis H : prop=p
0
0
against one of the alternatives below.
•
•
•
H : propƒp (prop:ƒp0)
a
0
H : prop<p (prop:<p0)
a
0
H : prop>p (prop:>p0)
a
0
Input:
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Calculated
results:
Drawn
results:
2-PropZTest
2-PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of
successes (p and p ) from two populations. It takes as input the count of successes in
1
2
each sample (x and x ) and the count of observations in each sample (n and n ).
1
2
1
2
2-PropZTest tests the null hypothesis H : p =p (using the pooled sample proportion Ç)
0
1
2
against one of the alternatives below.
•
•
H : p ƒp (p1:ƒp2)
a
1
2
H : p <p (p1:<p2)
a
1
2
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•
H : p >p (p1:>p2)
a
1
2
Input:
Calculated
results:
Drawn
results:
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ZInterval
ZInterval (one-sample z confidence interval; item 7) computes a confidence interval for
an unknown population mean m when the population standard deviation s is known. The
computed confidence interval depends on the user-specified confidence level.
In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data
Stats
Input:
Calculated
results:
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TInterval
TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an
unknown population mean m when the population standard deviation s is unknown. The
computed confidence interval depends on the user-specified confidence level.
In the example:
L6={1.6 1.7 1.8 1.9}
Data
Stats
Input:
Calculated
results:
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2-SampZInt
2-SampZInt (two-sample z confidence interval; item 9) computes a confidence interval for
the difference between two population means (m Nm ) when both population standard
1
2
deviations (s and s ) are known. The computed confidence interval depends on the
1
2
user-specified confidence level.
In the example:
LISTC={154 109 137 115 140}
LISTD={108 115 126 92 146}
Data
Stats
Input:
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Data
Stats
Calculated
results:
2-SampTInt
2-SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for
the difference between two population means (m Nm ) when both population standard
1
2
deviations (s and s ) are unknown. The computed confidence interval depends on the
1
2
user-specified confidence level.
In the example:
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SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
Data
Stats
Input:
Calculated
results:
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1-PropZInt
1-PropZInt (one-proportion z confidence interval; item A) computes a confidence interval
for an unknown proportion of successes. It takes as input the count of successes in the
sample x and the count of observations in the sample n. The computed confidence
interval depends on the user-specified confidence level.
Input:
Calculated
results:
2-PropZInt
2-PropZInt (two-proportion z confidence interval; item B) computes a confidence interval
for the difference between the proportion of successes in two populations (p Np ). It
1
2
takes as input the count of successes in each sample (x and x ) and the count of
1
2
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observations in each sample (n and n ). The computed confidence interval depends on
1
2
the user-specified confidence level.
Input:
Calculated
results:
2
c -Test
2
c -Test (chi-square test; item C) computes a chi-square test for association on the two-
way table of counts in the specified Observed matrix. The null hypothesis H for a two-way
0
table is: no association exists between row variables and column variables. The
alternative hypothesis is: the variables are related.
2
Before computing a c -Test, enter the observed counts in a matrix. Enter that matrix
2
variable name at the Observed: prompt in the c .Test editor; default=[A]. At the
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Expected: prompt, enter the matrix variable name to which you want the computed
expected counts to be stored; default=[B].
Matrix
editor:
Note: Press y ú ~ ~ 1 to
select 1:[A] from the MATRX EDIT
menu.
Input:
Note: Press y ú †] Í to
display matrix [B].
Calculated
results:
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Drawn results:
2
c GOF-Test
2
c GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample
2
data is from a population that conforms to a specified distribution. For example, c GOF
can confirm that the sample data came from a normal distribution.
In the example:
list 1={16,25,22,8,10}
list 2={16.2,21.6,16.2,14.4,12.6}
The Chi-square
Goodness of Fit
Note: Press … ~ ~ to
select TESTS. Press †
input screen:
several times to select
2
D:X GOF-Test... Press
Í. To enter data for
df (degree of freedom),
press † † †. Type 4.
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Calculated
results:
Drawn results:
2-SampFTest
2-SampÜTest (two-sample Ü-test; item E) computes an Ü-test to compare two normal
population standard deviations (s and s ). The population means and standard
1
2
deviations are all unknown. 2-SampÜTest, which uses the ratio of sample variances
2
2
Sx1 /Sx2 , tests the null hypothesis H : s =s against one of the alternatives below.
0
1
2
•
•
•
H : s s (s1:ƒs2)
ƒ
a
1
2
H : s <s (s1:<s2)
a
1
2
H : s >s (s1:>s2)
a
1
2
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In the example:
SAMP4={
SAMP5={
7
L1
18 17
L1 L3
1
5
10 11
L4
12
L3 L5
L2}
L1
2
L11
L3}
3
L5
Data
Stats
Input:
Calculated
results:
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Data
Stats
Drawn results:
LinRegTTest
LinRegTTest (linear regression t test; item F) computes a linear regression on the given
data and a t test on the value of slope b and the correlation coefficient r for the equation
y=a+bx. It tests the null hypothesis H : b=0 (equivalently, r=0) against one of the
0
alternatives below.
•
•
•
H : bƒ0 and rƒ0 (b & r:ă0)
a
H : b<0 and r<0 (b & r:<0)
a
H : b>0 and r>0 (b & r:>0)
a
The regression equation is automatically stored to RegEQ (VARS Statistics EQ secondary
menu). If you enter a Y= variable name at the RegEQ: prompt, the calculated regression
equation is automatically stored to the specified Y= equation. In the example below, the
regression equation is stored to Y1, which is then selected (turned on).
In the example:
L3={
L4={
38
41
56
63
59
70
64
72
74}
84}
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Input:
Calculated
results:
When LinRegTTest is executed, the list of residuals is created and stored to the list name
RESID automatically. RESID is placed on the LIST NAMES menu.
Note: For the regression equation, you can use the fix-decimal mode setting to control
the number of digits stored after the decimal point (Chapter 1). However, limiting the
number of digits to a small number could affect the accuracy of the fit.
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LinRegTInt
LinRegTInt computes a linear regression T confidence interval for the slope coefficient b.
If the confidence interval contains 0, this is insufficient evidence to indicate that the data
exhibits a linear relationship.
In the example:
list 1={4, 5, 6, 7, 8}
list 2={1, 2, 3, 3.5, 4.5}
LinRegTInt input
Note: Press … ~ ~ to
select TESTS. Press †
screen:
several times to select
G:LinRegTint... Press
Í. Press † several
times to select Calculate.
Press Í.
Calculated
results:
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Xlist, Ylist is the list of independent and dependent variables. The list containing the Freq
(frequency) values for the data is stored in List. The default is 1. All elements must be
real numbers. Each element in the Freq list is the frequency of occurence for each
corresponding data point in the input list specified in the List fields. RegEQ (optional) is
the designated Yn variable for storing the regression equation. StoreRegEqn (optional)
is the designated variable for storing the regression equation. The C level is the
Confidence level probability with default = .95.
ANOVA(
ANOVA( (one-way analysis of variance; item H) computes a one-way analysis of variance
for comparing the means of two to 20 populations. The ANOVA procedure for comparing
these means involves analysis of the variation in the sample data. The null hypothesis
H : m =m =...=m is tested against the alternative H : not all m ...m are equal.
0
1
2
k
a
1
k
ANOVA(list1,list2[,...,list20])
In the example:
L1={7 4 6 6 5}
L2={6 5 5 8 7}
L3={4 7 6 7 6}
Input:
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Calculated
results:
Note: SS is sum of squares and MS is mean square.
Inferential Statistics Input Descriptions
The tables in this section describe the inferential statistics inputs discussed in this
chapter. You enter values for these inputs in the inferential stat editors. The tables
present the inputs in the same order that they appear in this chapter.
Input
Description
Hypothesized value of the population mean that you are testing.
m
s
0
The known population standard deviation; must be a real number
> 0.
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Input
List
Description
The name of the list containing the data you are testing.
Freq
The name of the list containing the frequency values for the data
in List. Default=1. All elements must be integers | 0.
Calculate/Draw
Determines the type of output to generate for tests and intervals.
Calculate displays the output on the home screen. In tests, Draw
draws a graph of the results.
Summary statistics (mean, standard deviation, and sample size)
for the one-sample tests and intervals.
v, Sx, n
s1
The known population standard deviation from the first population
for the two-sample tests and intervals. Must be a real number > 0.
The known population standard deviation from the second
population for the two-sample tests and intervals. Must be a real
number > 0.
s2
List1, List2
The names of the lists containing the data you are testing for the
two-sample tests and intervals. Defaults are L1 and L2,
respectively.
Freq1, Freq2
The names of the lists containing the frequencies for the data in
List1 and List2 for the two-sample tests and intervals.
Defaults=1. All elements must be integers | 0.
Summary statistics (mean, standard deviation, and sample size)
for sample one and sample two in the two-sample tests and
intervals.
v1, Sx1, n1, v2, Sx2, n2
Pooled
Specifies whether variances are to be pooled for 2-SampTTest
and 2-SampTInt. No instructs the TI-84 Plus not to pool the
variances. Yes instructs the TI-84 Plus to pool the variances.
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Input
Description
p
The expected sample proportion for 1-PropZTest. Must be a real
0
number, such that 0 < p < 1.
0
x
The count of successes in the sample for the 1-PropZTest and
1-PropZInt. Must be an integer | 0.
n
The count of observations in the sample for the 1-PropZTest and
1-PropZInt. Must be an integer > 0.
x1
The count of successes from sample one for the 2-PropZTest
and 2-PropZInt. Must be an integer | 0.
x2
The count of successes from sample two for the 2-PropZTest
and 2-PropZInt. Must be an integer | 0.
n1
The count of observations in sample one for the 2-PropZTest and
2-PropZInt. Must be an integer > 0.
n2
The count of observations in sample two for the 2-PropZTest and
2-PropZInt. Must be an integer > 0.
C-Level
The confidence level for the interval instructions. Must be ‚ 0 and
< 100. If it is ‚ 1, it is assumed to be given as a percent and is
divided by 100. Default=0.95.
Observed (Matrix)
Expected (Matrix)
The matrix name that represents the columns and rows for the
2
observed values of a two-way table of counts for the c -Test and
2
c GOF-Test. Observed must contain all integers | 0. Matrix
dimensions must be at least 2×2.
The matrix name that specifies where the expected values should
be stored. Expected is created upon successful completion of
2
2
the c -Test and c GOF-Test.
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Input
df
Description
df (degree of freedom) represents (number of sample categories)
- (number of estimated parameters for the selected distribution +
1).
Xlist, Ylist
The names of the lists containing the data for LinRegTTest and
LinRegTInt. Defaults are L1 and L2, respectively. The
dimensions of Xlist and Ylist must be the same.
RegEQ
The prompt for the name of the Y= variable where the calculated
regression equation is to be stored. If a Y= variable is specified,
that equation is automatically selected (turned on). The default is
to store the regression equation to the RegEQ variable only.
Test and Interval Output Variables
The inferential statistics variables are calculated as indicated below. To access these
variables for use in expressions, press 5 (5:Statistics), and then select the VARS
menu listed in the last column below.
LinRegTTest,
ANOVA
VARS
Menu
Variables
p-value
Tests
p
Intervals
p
TEST
TEST
2
test statistics
t, Ü
z, t, c , Ü
degrees of freedom
df
df
df
TEST
TEST
sample mean of x values for
sample 1 and sample 2
v1, v2
v1, v2
sample standard deviation of x for
sample 1 and sample 2
Sx1,
Sx2
Sx1,
Sx2
TEST
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LinRegTTest,
ANOVA
VARS
Menu
Variables
Tests
Intervals
n1, n2
number of data points for sample 1
and sample 2
n1, n2
TEST
pooled standard deviation
SxP
‚Ç
SxP
‚Ç
SxP
TEST
TEST
TEST
estimated sample proportion
estimated sample proportion for
population 1
‚Ç1
‚Ç1
estimated sample proportion for
population 2
TEST
TEST
‚Ç2
‚Ç2
confidence interval pair
lower,
upper
mean of x values
XY
XY
v
Sx
n
v
Sx
n
sample standard deviation of x
number of data points
standard error about the line
regression/fit coefficients
correlation coefficient
XY
s
a, b
r
TEST
EQ
EQ
coefficient of determination
regression equation
r2
EQ
RegEQ
EQ
Note: The variables listed above cannot be archived.
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Distribution Functions
DISTR menu
To display the DISTR menu, press y =.
DISTR DRAW
nn probability density function
1: normalpdf(
2: normalcdf(
3: invNorm(
4: invT(
5: tpdf(
6: tcdf(
2
nn cumulative distribution function
Inverse cumulative normal distribution
Inverse cumulative Student-t distribution
Student-t probability density
Student-t distribution probability
Chi-square probability density
7:
8:
c pdf(
2
Chi-square distribution probability
c cdf
9: Üpdf(
wÜprobability density
wÜdistribution probability
Binomial probability
0: Ücdf(
A: binompdf(
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DISTR DRAW
Binomial cumulative density
Poisson probability
B: binomcdf(
C: poissonpdf(
D: poissoncdf(
E: geometpdf(
F: geometcdf(
Poisson cumulative density
Geometric probability
Geometric cumulative density
Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for
example, specify lowerbound= L1â99.
normalpdf(
normalpdf( computes the probability density function (pdf) for the normal distribution at a
specified x value. The defaults are mean m=0 and standard deviation s=1. To plot the
normal distribution, paste normalpdf( to the Y= editor. The probability density function
(pdf) is:
(x – µ)2
–
–------------------
1
--------------
2σ2
f(x) =
e
,σ > 0
2πσ
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normalpdf(x[,m,s])
Note: For this example,
Xmin = 28
Xmax = 42
Ymin = 0
Ymax = .2
Xscl = 1
Yscl = .1
Note: For plotting the normal distribution, you can set window variables Xmin and Xmax
so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu.
normalcdf(
normalcdf( computes the normal distribution probability between lowerbound and
upperbound for the specified mean m and standard deviation s. The defaults are m=0 and
s=1.
normalcdf(lowerbound,upperbound[,m,s])
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invNorm(
invNorm( computes the inverse cumulative normal distribution function for a given area
under the normal distribution curve specified by mean m and standard deviation s. It
calculates the x value associated with an area to the left of the x value. 0 area 1 must
be true. The defaults are m=0 and s=1.
invNorm(area[,m,s])
invT(
invT( computes the inverse cumulative Student-t probability function specified by Degree
of Freedom, df for a given Area under the curve.
invT(area,df)
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tpdf(
tpdf( computes the probability density function (pdf) for the Student-t distribution at a
specified x value. df (degrees of freedom) must be > 0. To plot the Student-t distribution,
paste tpdf( to the Y= editor. The probability density function (pdf) is:
–(df + 1)/2
2
(1 + x /df)
Γ[(df + 1)/2]
------------------------------------------------
f(x) = --------------------------------
Γ(df ⁄ 2)
πdf
tpdf(x,df)
Note: For this example,
Xmin = L4.5
Xmax = 4.5
Ymin = 0
Ymax = .4
tcdf(
tcdf( computes the Student-t distribution probability between lowerbound and upperbound for
the specified df (degrees of freedom), which must be > 0.
tcdf(lowerbound,upperbound,df)
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2
c pdf(
2
2
c pdf( computes the probability density function (pdf) for the c (chi-square) distribution
2
at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c
2
distribution, paste c pdf( to the Y= editor. The probability density function (pdf) is:
1
df/2 df ⁄ 2 – 1 –x/2
--------------------
f(x) =
(1/2)
x
e
,x ≥ 0
Γ(df ⁄ 2)
2
c pdf(x,df)
Note: For this example,
Xmin = 0
Xmax = 30
Ymin = L.02
Ymax = .132
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2
c cdf(
2
2
c cdf( computes the c (chi-square) distribution probability between lowerbound and
upperbound for the specified df (degrees of freedom), which must be an integer > 0.
2
c cdf(lowerbound,upperbound,df)
Fpdf(
Üpdf( computes the probability density function (pdf) for the Ü distribution at a specified x
value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot
the Ü distribution, paste Üpdf( to the Y= editor. The probability density function (pdf) is:
n/2
Γ[(n + d)/2] n
⎛ ⎞
--------------------------------- --
n/2 – 1
–(n + d)/2
f(x) =
x
(1 + nx/d)
,x ≥ 0
⎝ ⎠
Γ(n/2)Γ(d/2) d
where
n = numerator degrees of freedom
d = denominator degrees of freedom
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Üpdf(x,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = 0
Ymax = 1
Fcdf(
Ücdf( computes the Ü distribution probability between lowerbound and upperbound for the
specified numerator df (degrees of freedom) and denominator df. numerator df and denominator
df must be integers > 0.
Ücdf(lowerbound,upperbound,numerator df,denominator df)
binompdf
binompdf( computes a probability at x for the discrete binomial distribution with the
specified numtrials and probability of success (p) on each trial. x can be an integer or a list
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of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a
list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is:
x
n – x
n
x
⎛ ⎞
f(x) =
p (1 – p)
,x = 0,1,...,n
⎝ ⎠
where n = numtrials
binompdf(numtrials,p[,x])
binomcdf(
binomcdf( computes a cumulative probability at x for the discrete binomial distribution
with the specified numtrials and probability of success (p) on each trial. x can be a real
number or a list of real numbers. 0p1 must be true. numtrials must be an integer > 0. If
you do not specify x, a list of cumulative probabilities is returned.
binomcdf(numtrials,p[,x])
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poissonpdf(
poissonpdf( computes a probability at x for the discrete Poisson distribution with the
specified mean m, which must be a real number > 0. x can be an integer or a list of
integers. The probability density function (pdf) is:
–µ
x
f(x) = e µ ⁄ x!,x = 0,1,2,...
poissonpdf(m,x)
poissoncdf(
poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution
with the specified mean m, which must be a real number > 0. x can be a real number or a
list of real numbers.
poissoncdf(m,x)
geometpdf(
geometpdf( computes a probability at x, the number of the trial on which the first success
occurs, for the discrete geometric distribution with the specified probability of success p.
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0p1 must be true. x can be an integer or a list of integers. The probability density
function (pdf) is:
x – 1
f(x) = p(1 – p)
,x = 1,2,...
geometpdf(p,x)
geometcdf(
geometcdf( computes a cumulative probability at x, the number of the trial on which the
first success occurs, for the discrete geometric distribution with the specified probability
of success p. 0p1 must be true. x can be a real number or a list of real numbers.
geometcdf(p,x)
Distribution Shading
DISTR DRAW Menu
To display the DISTR DRAW menu, press y = ~. DISTR DRAW instructions draw
various types of density functions, shade the area specified by lowerbound and upperbound,
and display the computed area value.
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To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8).
Note: Before you execute a DISTR DRAW instruction, you must set the window variables
so that the desired distribution fits the screen.
DISTR DRAW
Shades normal distribution.
1: ShadeNorm(
2: Shade_t(
2
Shades Student-t distribution.
2
3:
Shadec (
Shades c distribution.
4: ShadeÜ(
Shades Üdistribution.
Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for
example, specify lowerbound=L1â99.
ShadeNorm(
ShadeNorm( draws the normal density function specified by mean m and standard
deviation s and shades the area between lowerbound and upperbound. The defaults are m=0
and s=1.
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ShadeNorm(lowerbound,upperbound[,m,s])
Note: For this example,
Xmin = 55
Xmax = 72
Ymin = L.05
Ymax = .2
Shade_t(
Shade_t( draws the density function for the Student-t distribution specified by df (degrees
of freedom) and shades the area between lowerbound and upperbound.
Shade_t(lowerbound,upperbound,df)
Note: For this example,
Xmin = L3
Xmax = 3
Ymin = L.15
Ymax = .5
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2
Shadec (
2
2
Shadec ( draws the density function for the c (chi-square) distribution specified by df
(degrees of freedom) and shades the area between lowerbound and upperbound.
2
Shadec (lowerbound,upperbound,df)
Note: For this example,
Xmin = 0
Xmax = 35
Ymin = L.025
Ymax = .1
ShadeF(
ShadeÜ( draws the density function for the Ü distribution specified by numerator df
(degrees of freedom) and denominator df and shades the area between lowerbound and
upperbound.
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ShadeÜ(lowerbound,upperbound,numerator df,denominator df)
Note: For this example,
Xmin = 0
Xmax = 5
Ymin = L.25
Ymax = .9
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Chapter 14:
Applications
The Applications Menu
The TI-84 Plus comes with Finance and EasyData App and several other applications
already listed on the APPLICATIONS menu. Except for the Finance application, you can
add and remove applications as space permits. The Finance application is built into the
TI-84 Plus code and cannot be deleted.
You can buy additional TI-84 Plus software applications that allow you to customize
further your calculator’s functionality. The calculator reserves 1.54 M of space within
ROM memory specifically for applications.
Your TI-84 Plus includes Flash applications in addition to the ones mentioned above.
Press ŒÎ to see the complete list of applications that came with your calculator.
Documentation for applications are on the Texas Instruments Web site at:
Steps for Running the Finance Application
Follow these basic steps when using the Finance application.
1. Press Œ Í to select the Finance application.
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2. Select from list of functions.
Getting Started: Financing a Car
Getting Started is a fast-paced introduction. Read the chapter for details.
You have found a car you would like to buy. The car costs 9,000. You can afford
payments of 250 per month for four years. What annual percentage rate (APR) will make
it possible for you to afford the car?
1. Press z † ~ ~ ~ Í to set the fixed-decimal
mode setting to 2. The TI-84 Plus will display all
numbers with two decimal places).
2. Press Œ Í to select 1:Finance from the
APPLICATIONS menu.
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3. Press Í to select 1:TVM Solver from the
CALC VARS menu. The TVM Solver is displayed.
Press 48 Í to store 48 months to Ú. Press † 9000
Í to store 9,000 to PV. Press Ì 250 Í to store
L250 to PMT. (Negation indicates cash outflow.) Press 0
Í to store 0 to FV.
Press 12 Í to store 12 payments per year to P/Y
and 12 compounding periods per year to C/Y. Setting
P/Y to 12 will compute an annual percentage rate
(compounded monthly) for æ. Press † Í to select
PMT:END, which indicates that payments are due at the
end of each period.
4. Press } } } } } } to move the cursor to the æ
prompt. Press ƒ \ to solve for æ. What APR
should you look for?
Getting Started: Computing Compound Interest
At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7
years?
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Note: Because there are no payments when you solve compound interest problems,
PMT must be set to 0 and P/Y must be set to 1.
1. Press Œ Í to select 1:Finance from the
APPLICATIONS menu.
2. Press Í to select 1:TVM Solver from the CALC
VARS menu. The TVM Solver is displayed. Press 7 to
enter the number of periods in years. Press † †
Ì 1250 to enter the present value as a cash outflow
(investment). Press † 0 to specify no payments. Press
† 2000 to enter the future value as a cash inflow
(return). Press † 1 to enter payment periods per year.
Press † 12 to set compounding periods per year to 12.
3. Press } } } } } to place the cursor on the æ
prompt.
4. Press ƒ \ to solve for æ, the annual interest
rate.
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Using the TVM Solver
Using the TVM Solver
The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable
values, the TVM Solver solves for the fifth variable.
The FINANCE VARS menu section describes the five TVM variables (Ú, æ, PV, PMT, and
FV) and P/Y and C/Y.
PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items
Pmt_End (payment at the end of each period) and Pmt_Bgn (payment at the beginning of
each period).
To solve for an unknown TVM variable, follow these steps.
1. Press Œ Í Í to display the TVM Solver. The screen below shows the
default values with the fixed-decimal mode set to two decimal places.
2. Enter the known values for four TVM variables.
Note: Enter cash inflows as positive numbers and cash outflows as negative
numbers.
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3. Enter a value for P/Y, which automatically enters the same value for C/Y; if P/Y ƒ C/Y,
enter a unique value for C/Y.
4. Select END or BEGIN to specify the payment method.
5. Place the cursor on the TVM variable for which you want to solve.
6. Press ƒ \. The answer is computed, displayed in the TVM Solver, and
stored to the appropriate TVM variable. An indicator square in the left column
designates the solution variable.
Using the Financial Functions
Entering Cash Inflows and Cash Outflows
When using the TI-84 Plus financial functions, you must enter cash inflows (cash
received) as positive numbers and cash outflows (cash paid) as negative numbers. The
TI-84 Plus follows this convention when computing and displaying answers.
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FINANCE CALC Menu
To display the FINANCE CALC menu, press ÎŒ Í.
CALC VARS
Displays the TVM Solver.
1: TVM Solver...
2: tvm_Pmt
3: tvm_¾æ
4: tvm_PV
5: tvm_òÚ
6: tvm_FV
7: npv(
Computes the amount of each payment.
Computes the interest rate per year.
Computes the present value.
Computes the number of payment periods.
Computes the future value.
Computes the net present value.
Computes the internal rate of return.
Computes the amortization sched. balance.
Computes the amort. sched. princ. sum.
Computes the amort. sched. interest sum.
Computes the nominal interest rate.
Computes the effective interest rate.
Calculates the days between two dates.
Selects ordinary annuity (end of period).
Selects annuity due (beginning of period).
8: irr(
9: bal(
0: GPrn(
A: GInt(
B: 4Nom(
C: 4Eff(
D: dbd(
E: Pmt_End
F: Pmt_Bgn
Use these functions to set up and perform financial calculations on the home screen.
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TVM Solver
TVM Solver displays the TVM Solver.
Calculating Time Value of Money (TVM)
Calculating Time Value of Money
Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial
instruments such as annuities, loans, mortgages, leases, and savings.
Each TVM function takes zero to six arguments, which must be real numbers. The values
that you specify as arguments for TVM functions are not stored to the TVM variables.
Note: To store a value to a TVM variable, use the TVM Solver or use ¿ and any TVM
variable on the FINANCE VARS menu.
If you enter less than six arguments, the TI-84 Plus substitutes a previously stored TVM
variable value for each unspecified argument.
If you enter any arguments with a TVM function, you must place the argument or
arguments in parentheses.
tvm_Pmt
tvm_Pmt computes the amount of each payment.
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tvm_Pmt[(òÚ,¾æ,PV,FV,P/Y,C/Y)]
Note: In the example above, the values are stored to the TVM variables in the
TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the
values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect
on the payment amount.
tvm_I%
tvm_æ computes the annual interest rate.
tvm_¾æ [(Ú,PV,PMT,FV,P/Y,C/Y)]
tvm_PV
tvm_PV computes the present value.
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Calculating Cash Flows
Calculating a Cash Flow
Use the cash flow functions (menu items 7 and 8) to analyze the value of money over
equal time periods. You can enter unequal cash flows, which can be cash inflows or
outflows. The syntax descriptions for npv( and irr( use these arguments.
•
interest rate is the rate by which to discount the cash flows (the cost of money) over
one period.
•
•
•
CF0 is the initial cash flow at time 0; it must be a real number.
CFList is a list of cash flow amounts after the initial cash flow CF0.
CFFreq is a list in which each element specifies the frequency of occurrence for a
grouped (consecutive) cash flow amount, which is the corresponding element of
CFList. The default is 1; if you enter values, they must be positive integers < 10,000.
For example, express this uneven cash flow in lists.
2000
2000
2000
4000
4000
-3000
CF0 = 2000
CFList = {2000,L3000,4000}
CFFreq = {2,1,2}
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npv(, irr(
npv( (net present value) is the sum of the present values for the cash inflows and
outflows. A positive result for npv indicates a profitable investment.
npv(interest rate,CF0,CFList[,CFFreq])
irr( (internal rate of return) is the interest rate at which the net present value of the cash
flows is equal to zero.
irr(CF0,CFList[,CFFreq])
1000
0
5000
3000
-2500
-2000
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Calculating Amortization
Calculating an Amortization Schedule
Use the amortization functions (menu items 9, 0, and A) to calculate balance, sum of
principal, and sum of interest for an amortization schedule.
bal(
bal( computes the balance for an amortization schedule using stored values for æ, PV,
and PMT. npmt is the number of the payment at which you want to calculate a balance. It
must be a positive integer < 10,000. roundvalue specifies the internal precision the
calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-84
Plus uses the current Float/Fix decimal-mode setting.
bal(npmt[,roundvalue])
GPrn(, GInt(
GPrn( computes the sum of the principal during a specified period for an amortization
schedule using stored values for ¾æ, PV, and PMT. pmt1 is the starting payment. pmt2 is the
ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000. roundvalue
specifies the internal precision the calculator uses to calculate the principal; if you do not
specify roundvalue, the TI-84 Plus uses the current Float/Fix decimal-mode setting.
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Note: You must enter values for æ, PV, PMT, and before computing the principal.
GPrn(pmt1,pmt2[,roundvalue])
GInt( computes the sum of the interest during a specified period for an amortization
schedule using stored values for ¾æ, PV, and PMT. pmt1 is the starting payment. pmt2 is
the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.
roundvalue specifies the internal precision the calculator uses to calculate the interest; if
you do not specify roundvalue, the TI-84 Plus uses the current Float/Fix decimal-mode
setting.
GInt(pmt1,pmt2[,roundvalue])
Amortization Example: Calculating an Outstanding Loan Balance
You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments
are 800. Calculate the outstanding loan balance after each payment and display the
results in a graph and in the table.
1. Press z. Press † ~ ~ ~ Í to set the
fixed-decimal mode setting to 2. Press † † ~ Í to
select Par graphing mode.
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2. Press Î Œ Í Í to display the TVM Solver.
3. Press 360 to enter number of payments. Press † 8 to
enter the interest rate. Press † † Ì 800 to enter the
payment amount. Press † 0 to enter the future value
of the mortgage. Press † 12 to enter the payments per
year, which also sets the compounding periods per
year to 12. Press † † Í to select PMT:END.
4. Press } } } } } to place the cursor on the PV prompt.
Press ƒ \ to solve for the present value.
5. Press o to display the parametric Y= editor. Turn off
all stat plots. Press „ to define X1T as T. Press †
Œ Í 9 „ ¤ to define Y1T as bal(T).
6. Press p to display the window variables. Enter the
values below.
Tmin=0
Tmax=360 Xmax=360 Ymax=125000
Tstep=12 Xscl=50 Yscl=10000
Xmin=0
Ymin=0
7. Press r to draw the graph and activate the trace
cursor. Press ~ and | to explore the graph of the
outstanding balance over time. Press a number and
then press Í to view the balance at a specific
time T.
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8. Press y - and enter the values below.
TblStart=0
@Tbl=12
9. Press y 0 to display the table of outstanding
balances (Y1T).
10. Press z † † † † † † † ~ ~ Í to select
G-T split-screen mode, in which the graph and table are
displayed simultaneously.
Press r to display X1T (time) and Y1T (balance) in
the table.
Calculating Interest Conversion
Calculating an Interest Conversion
Use the interest conversion functions (menu items B and C) to convert interest rates
from an annual effective rate to a nominal rate (4Nom( ) or from a nominal rate to an
annual effective rate (4Eff( ).
4Nom(
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4Nom( computes the nominal interest rate. effective rate and compounding periods must be
real numbers. compounding periods must be >0.
4Nom(effective rate,compounding periods)
4Eff(
4Eff( computes the effective interest rate. nominal rate and compounding periods must be real
numbers. compounding periods must be >0.
4Eff(nominal rate,compounding periods)
Finding Days between Dates/Defining Payment
Method
dbd(
Use the date function dbd( (menu item D) to calculate the number of days between two
dates using the actual-day-count method. date1 and date2 can be numbers or lists of
numbers within the range of the dates on the standard calendar.
Note: Dates must be between the years 1950 through 2049.
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dbd(date1,date2)
You can enter date1 and date2 in either of two formats.
•
•
MM.DDYY (United States)
DDMM.YY (Europe)
The decimal placement differentiates the date formats.
Defining the Payment Method
Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary
annuity or an annuity due. When you execute either command, the TVM Solver is
updated.
Pmt_End
Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end
of each payment period. Most loans are in this category. Pmt_End is the default.
Pmt_End
On the TVM Solver’s PMT:END BEGIN line, select END to set PMT to ordinary annuity.
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Pmt_Bgn
Pmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the
beginning of each payment period. Most leases are in this category.
Pmt_Bgn
On the TVM Solver’s PMT:END BEGIN line, select BEGIN to set PMT to annuity due.
Using the TVM Variables
FINANCE VARS Menu
To display the FINANCE VARS menu, press Î Œ Í ~. You can use TVM variables
in TVM functions and store values to them on the home screen.
CALC VARS
Total number of payment periods
1: Ú
Annual interest rate
2: æ
Present value
3: PV
Payment amount
4: PMT
5: FV
Future value
Number of payment periods per year
Number of compounding periods/year
6: P/Y
7: C/Y
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N, I%, PV, PMT, FV
Ú, æ, PV, PMT, and FV are the five TVM variables. They represent the elements of
common financial transactions, as described in the table above. æ is an annual interest
rate that is converted to a per-period rate based on the values of P/Y and C/Y.
P/Y and C/Y
P/Y is the number of payment periods per year in a financial transaction.
C/Y is the number of compounding periods per year in the same transaction.
When you store a value to P/Y, the value for C/Y automatically changes to the same
value. To store a unique value to C/Y, you must store the value to C/Y after you have
stored a value to P/Y.
The EasyData App
The EasyData App by Vernier Software and Technology allows you to view and analyze
real-world data when the TI-84 Plus is connected to data collection devices such as
Texas Instruments CBR 2é, CBL 2é, Vernier LabProê, Vernier USB sensors, Vernier
Go!éMotion, or Vernier Motion Detector Unit. The TI-84 Plus comes with the EasyData
App already installed.
Note: The App will only work with Vernier auto-ID sensors when using CBL 2é and
Vernier LabProê.
The EasyData app will autolaunch on your TI-84 Plus if you plug in a USB sensor such
as the CBR 2é or Vernier USB Temperature sensor.
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Steps for Running the EasyData App
Follow these basic steps when using the EasyData App.
Starting EasyData
1. Attach your data collection device to your TI-84 Plus.
Make sure the cables are firmly connected.
2. If the EasyData app has not auto-launched, press Œ
and the } or † to select the EasyData App.
3. Press Í. The EasyData information screen is
displayed for about three seconds followed by the main
screen.
Quitting EasyData
1. To quit EasyData, select Quit (press s).
The Ready to quit? screen is displayed, which indicates that the collected data has
been transferred to lists L1 through L4 on the TI-84 Plus.
2. Press OK (press s) to quit.
EasyData Settings
Changing EasyData settings
EasyData displays the most commonly used settings before data collection begins.
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To change a predefined setting:
1. From the main screen in the EasyData App, choose Setup and select 2: Time Graph.
The current settings are displayed on the calculator.
Note: If using a motion detector, settings for 3: Distance Match and 4: Ball Bounce in
the Setup menu are preset and cannot be changed.
2. Select Next (press q) to move to the setting you want to change. Press ‘ to
clear a setting.
3. Repeat to cycle through the available options. When the option is correct, select
Next to move to the next option.
4. To change a setting, enter 1 or 2 digits, and then select Next (press q).
5. When all the settings are correct, select OK (press s) to return to the main
menu.
6. Select Start (press q) to begin collecting data.
Restoring EasyData to the default settings
The default settings are appropriate for a wide variety of sampling situations. If you are
unsure of the best settings, begin with the default settings, and then adjust the settings
for your specific activity.
To restore the default settings in EasyData while a data collection device is connected to
the TI-84 Plus, choose File and select 1:New.
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Starting and Stopping Data Collection
Starting Data Collection
To start sampling, select Start (press q). Sampling will automatically stop when the
number of samples set in the Time Graph Settings menu is reached. The TI-84 Plus will
then display a graph of the sampled data.
Stopping Data Collection
To stop sampling before it automatically stops, select Stop (press and hold q) at any
time during the sampling process. When sampling stops, a graph of the sampled data is
displayed.
Saving Collected Data
Collected data is automatically transferred to the TI-84 Plus and stored in lists L1 through
L4 when data collection is complete. When you exit the EasyData App, a prompt reminds
you of the lists in which time, distance, velocity, and acceleration are stored.
For more information about the EasyData app, refer to the Texas Instrument Web site at:
education.ti.com/guides.
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Chapter 15:
CATALOG, Strings, Hyperbolic
Functions
Browsing the TI-84 Plus CATALOG
What Is the CATALOG?
The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus.
You also can access each CATALOG item from a menu or the keyboard, except:
•
•
•
•
The six string functions
The six hyperbolic functions
The solve( instruction without the equation solver editor (Chapter 2)
The inferential stat functions without the inferential stat editors (Chapter 13)
Note: The only CATALOG programming commands you can execute from the home
screen are GetCalc(, Get(, and Send(.
Selecting an Item from the CATALOG
To select a CATALOG item, follow these steps.
1. Press y N to display the CATALOG.
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The 4 in the first column is the selection cursor.
2. Press † or } to scroll the CATALOG until the selection cursor points to the item you
want.
•
•
To jump to the first item beginning with a particular letter, press that letter; alpha-
lock is on.
Items that begin with a number are in alphabetical order according to the first
letter after the number. For example, 2-PropZTest( is among the items that begin
with the letter P.
L1
•
Functions that appear as symbols, such as +, , <, and ‡(, follow the last item
that begins with Z. To jump to the first symbol, !, press [q].
3. Press Í to paste the item to the current screen.
Note: From the top of the CATALOG menu, press } to move to the bottom. From the
bottom, press † to move to the top.
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Entering and Using Strings
What Is a String?
A string is a sequence of characters that you enclose within quotation marks. On the
TI-84 Plus, a string has two primary applications.
•
•
It defines text to be displayed in a program.
It accepts input from the keyboard in a program.
Characters are the units that you combine to form a string.
•
•
Count each number, letter, and space as one character.
Count each instruction or function name, such as sin( or cos(, as one character; the
TI-84 Plus interprets each instruction or function name as one character.
Entering a String
To enter a string on a blank line on the home screen or in a program, follow these steps.
1. Press ƒ [ã] to indicate the beginning of the string.
2. Enter the characters that comprise the string.
•
Use any combination of numbers, letters, function names, or instruction names
to create the string.
•
•
To enter a blank space, press ƒ O.
To enter several alpha characters in a row, press y 7 to activate alpha-
lock.
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3. Press ƒ [ã] to indicate the end of the string.
ãstringã
4. Press Í. On the home screen, the string is displayed on the next line without
quotations. An ellipsis (...) indicates that the string continues beyond the screen. To
scroll the entire string, press ~ and |.
Note: Quotation marks do not count as string characters.
Storing Strings to String Variables
String Variables
The TI-84 Plus has 10 variables to which you can store strings. You can use string
variables with string functions and instructions.
To display the VARS STRING menu, follow these steps.
1. Press to display the VARS menu. Move the cursor to 7:String.
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2. Press Í to display the STRING secondary menu.
Storing a String to a String Variable
To store a string to a string variable, follow these steps.
1. Press ƒ [ã], enter the string, and press ƒ [ã].
2. Press ¿.
3. Press 7 to display the VARS STRING menu.
4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the
string.
The string variable is pasted to the current cursor location, next to the store symbol
(!).
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5. Press Í to store the string to the string variable. On the home screen, the stored
string is displayed on the next line without quotation marks.
Displaying the Contents of a String Variable
To display the contents of a string variable on the home screen, select the string variable
from the VARS STRING menu, and then press Í. The string is displayed.
String Functions and Instructions in the CATALOG
Displaying String Functions and Instructions in the CATALOG
String functions and instructions are available only from the CATALOG. The table below
lists the string functions and instructions in the order in which they appear among the
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other CATALOG menu items. The ellipses in the table indicate the presence of additional
CATALOG items.
CATALOG
...
Converts an equation to a string.
Converts a string to an expression.
Equ4String(
expr(
...
Returns a character’s place number.
Returns a string’s character length.
inString(
...
length(
...
Converts a string to an equation.
Returns a string subset as a string.
String4Equ(
sub(
...
Concatenation
To concatenate two or more strings, follow these steps.
1. Enter string1, which can be a string or string name.
2. Press Ã.
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3. Enter string2, which can be a string or string name. If necessary, press à and enter
string3, and so on.
string1+string2+string3...
4. Press Í to display the strings as a single string.
Selecting a String Function from the CATALOG
To select a string function or instruction and paste it to the current screen, follow the
steps for selecting an item from the CATALOG.
Equ4String(
Equ4String( converts to a string an equation that is stored to any VARS Y-VARS variable.
Yn contains the equation. Strn (from Str1 to Str9, or Str0) is the string variable to which
you want the equation to be stored as a string.
Equ4String(Yn,Strn)
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expr(
expr( converts the character string contained in string to an expression and executes it.
string can be a string or a string variable.
expr(string)
inString(
inString( returns the character position in string of the first character of substring. string can
be a string or a string variable. start is an optional character position at which to start the
search; the default is 1.
inString(string,substring[,start])
Note: If string does not contain substring, or start is greater than the length of string, inString(
returns 0.
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length(
length( returns the number of characters in string. string can be a string or string variable.
Note: An instruction or function name, such as sin( or cos(, counts as one character.
length(string)
String4Equ(
String4Equ( converts string into an equation and stores the equation to Yn. string can be a
string or string variable. String4Equ( is the inverse of Equ4String(.
String4Equ(string,Yn)
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sub(
sub( returns a string that is a subset of an existing string. string can be a string or a string
variable. begin is the position number of the first character of the subset. length is the
number of characters in the subset.
sub(string,begin,length)
Entering a Function to Graph during Program Execution
In a program, you can enter a function to graph during program execution using these
commands.
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Note: When you execute this program, enter a function to store to Y3 at the ENTRY=
prompt.
Hyperbolic Functions in the CATALOG
Hyperbolic Functions
The hyperbolic functions are available only from the CATALOG. The table below lists the
hyperbolic functions in the order in which they appear among the other CATALOG menu
items. The ellipses in the table indicate the presence of additional CATALOG items.
CATALOG
...
Hyperbolic cosine
cosh(
-1
Hyperbolic arccosine
cosh (
...
Hyperbolic sine
sinh(
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CATALOG
-1
Hyperbolic arcsine
sinh (
...
Hyperbolic tangent
tanh(
-1
Hyperbolic arctangent
tanh (
...
sinh(, cosh(, tanh(
sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers,
expressions, and lists.
sinh(value)
cosh(value)
tanh(value)
-1
-1
-1
sinh (, cosh (, tanh (
-1
-1
sinh ( is the hyperbolic arcsine function. cosh ( is the hyperbolic arccosine function.
-1
tanh ( is the hyperbolic arctangent function. Each is valid for real numbers, expressions,
and lists.
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-1
sinh (value)
-1
cosh (value)
-1
sinh (value)
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Chapter 16:
Programming
Getting Started: Volume of a Cylinder
Getting Started is a fast-paced introduction. Read the chapter for details.
A program is a set of commands that the TI-84 Plus executes sequentially, as if you had
entered them from the keyboard. Create a program that prompts for the radius R and the
height H of a cylinder and then computes its volume.
1. Press ~ ~ to display the PRGM NEW menu.
2. Press Í to select 1:Create New. The Name=
prompt is displayed, and alpha-lock is on. Press [C]
[Y] [L] [I] [N] [D] [E] [R], and then press Í to
name the program CYLINDER.
You are now in the program editor. The colon ( : )
in the first column of the second line indicates the
beginning of a command line.
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3. Press ~ 2 to select 2:Prompt from the
PRGM I/O menu. Prompt is copied to the command
line. Press ƒ [R] ¢ ƒ [H] to enter the
variable names for radius and height. Press
Í.
4. Press y B ƒ [R] ¡ ƒ [H] ¿ ƒ
2
[V] Í to enter the expression pR H and store
it to the variable V.
5. Press ~ 3 to select 3:Disp from the
PRGM I/O menu. Disp is pasted to the command
line. Press y 7 [ã] [V] [O] [L] [U] [M] [E] O [I]
[S] [ã] ƒ ¢ ƒ [V] Í to set up the
program to display the text VOLUME ISon one line
and the calculated value of Von the next.
6. Press y 5 to display the home screen.
7. Press to display the PRGM EXEC menu. The
items on this menu are the names of stored
programs.
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8. Press Í to paste prgmCYLINDERto the current
cursor location. (If CYLINDER is not item 1 on your
PRGM EXEC menu, move the cursor to CYLINDER
before you press Í.)
9. Press Í to execute the program. Enter 1.5for
the radius, and then press Í. Enter 3for the
height, and then press Í. The text VOLUME IS,
the value of V, and Doneare displayed.
Repeat steps 7 through 9 and enter different
values for R and H.
Creating and Deleting Programs
What Is a Program?
A program is a set of one or more command lines. Each line contains one or more
instructions. When you execute a program, the TI-84 Plus performs each instruction on
each command line in the same order in which you entered them. The number and size
of programs that the TI-84 Plus can store is limited only by available memory.
Creating a New Program
To create a new program, follow these steps.
1. Press | to display the PRGM NEW menu.
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2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock
is on.
3. Press a letter from A to Z or q to enter the first character of the new program name.
Note: A program name can be one to eight characters long. The first character must
be a letter from A to Z or q. The second through eighth characters can be letters,
numbers, or q.
4. Enter zero to seven letters, numbers, or q to complete the new program name.
5. Press Í. The program editor is displayed.
6. Enter one or more program commands.
7. Press y 5 to leave the program editor and return to the home screen.
Managing Memory and Deleting a Program
To check whether adequate memory is available for a program you want to enter:
1. Press y L to display the MEMORY menu.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu
(Chapter 18).
3. Select 7:Prgm to display the PRGM editor.
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The TI-84 Plus expresses memory quantities in bytes.
You can increase available memory in one of two ways. You can delete one or more
programs or you can archive some programs.
To increase available memory by deleting a specific program:
1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu.
2. Select 7:Prgm to display the PRGM editor (Chapter 18).
3. Press } and † to move the selection cursor (4) next to the program you want to
delete, and then press {. The program is deleted from memory.
Note: You will receive a message asking you to confirm this delete action. Select
2:yes to continue.
To leave the PRGM editor screen without deleting anything, press y 5, which
displays the home screen.
To increase available memory by archiving a program:
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4. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu.
5. Select 2:Mem Mgmt/Del to display the MEM MGMT/DEL menu.
6. Select 7:Prgm... to display the PRGM menu.
7. Press Í to archive the program. An asterisk will appear to the left of the program
to indicate it is an archived program.
To unarchive a program in this screen, put the cursor next to the archived program
and press Í. The asterisk will disappear.
Note: Archive programs cannot be edited or executed. In order to edit or execute an
archived program, you must first unarchive it.
Entering Command Lines and Executing Programs
Entering a Program Command Line
You can enter on a command line any instruction or expression that you could execute
from the home screen. In the program editor, each new command line begins with a colon.
To enter more than one instruction or expression on a single command line, separate each
with a colon.
Note: A command line can be longer than the screen is wide; long command lines wrap
to the next screen line.
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While in the program editor, you can display and select from menus. You can return to
the program editor from a menu in either of two ways.
•
•
Select a menu item, which pastes the item to the current command line.
Press ‘.
When you complete a command line, press Í. The cursor moves to the next
command line.
Programs can access variables, lists, matrices, and strings saved in memory. If a
program stores a new value to a variable, list, matrix, or string, the program changes the
value in memory during execution.
You can call another program as a subroutine.
Executing a Program
To execute a program, begin on a blank line on the home screen and follow these steps.
1. Press to display the PRGM EXEC menu.
2. Select a program name from the PRGM EXEC menu. prgmname is pasted to the home
screen (for example, prgmCYLINDER).
3. Press Í to execute the program. While the program is executing, the busy
indicator is on.
Last Answer (Ans) is updated during program execution. Last Entry is not updated as
each command is executed (Chapter 1).
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The TI-84 Plus checks for errors during program execution. It does not check for errors
as you enter a program.
Breaking a Program
To stop program execution, press É. The ERR:BREAK menu is displayed.
•
•
To return to the home screen, select 1:Quit.
To go where the interruption occurred, select 2:Goto.
Editing Programs
Editing a Program
To edit a stored program, follow these steps.
1. Press ~ to display the PRGM EDIT menu.
2. Select a program name from the PRGM EDIT menu. Up to the first seven lines of the
program are displayed.
Note: The program editor does not display a $ to indicate that a program continues
beyond the screen.
3. Edit the program command lines.
•
•
Move the cursor to the appropriate location, and then delete, overwrite, or insert.
Press ‘ to clear all program commands on the command line (the leading
colon remains), and then enter a new program command.
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Note: To move the cursor to the beginning of a command line, press y |; to move to
the end, press y ~. To scroll the cursor down seven command lines, press ƒ †.
To scroll the cursor up seven command lines, press ƒ }.
Inserting and Deleting Command Lines
To insert a new command line anywhere in the program, place the cursor where you
want the new line, press y 6, and then press Í. A colon indicates a new line.
To delete a command line, place the cursor on the line, press ‘ to clear all
instructions and expressions on the line, and then press { to delete the command line,
including the colon.
Copying and Renaming Programs
Copying and Renaming a Program
To copy all command lines from one program into a new program, follow steps 1 through
5 for Creating a New Program, and then follow these steps.
1. Press y K. Rcl is displayed on the bottom line of the program editor in the new
program (Chapter 1).
2. Press | to display the PRGM EXEC menu.
3. Select a name from the menu. prgmname is pasted to the bottom line of the program
editor.
4. Press Í. All command lines from the selected program are copied into the new
program.
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Copying programs has at least two convenient applications.
•
•
You can create a template for groups of instructions that you use frequently.
You can rename a program by copying its contents into a new program.
Note: You also can copy all the command lines from one existing program to another
existing program using RCL.
Scrolling the PRGM EXEC and PRGM EDIT Menus
The TI-84 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically into
alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0.
To jump to the first program name that begins with a particular alpha character or q,
press ƒ [letter from A to Z or q].
Note: From the top of either the PRGM EXEC or PRGM EDIT menu, press } to move to
the bottom. From the bottom, press † to move to the top. To scroll the cursor down the
menu seven items, press ƒ †. To scroll the cursor up the menu seven items, press
ƒ }.
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PRGM CTL (Control) Instructions
PRGM CTL Menu
To display the PRGM CTL (program control) menu, press from the program editor
only.
CTL
I/O EXEC
Creates a conditional test.
1: If
Executes commands when If is true.
Executes commands when If is false.
Creates an incrementing loop.
Creates a conditional loop.
Creates a conditional loop.
Signifies the end of a block.
Pauses program execution.
Defines a label.
2: Then
3: Else
4: For(
5: While
6: Repeat
7: End
8: Pause
9: Lbl
Goes to a label.
0: Goto
A: IS>(
B: DS<(
C: Menu(
Increments and skips if greater than.
Decrements and skips if less than.
Defines menu items and branches.
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CTL
I/O EXEC
Executes a program as a subroutine.
Returns from a subroutine.
D: prgm
E: Return
F: Stop
Stops execution.
Deletes a variable from within program.
Designates the graph style to be drawn.
G: DelVar
H: GraphStyle(
These menu items direct the flow of an executing program. They make it easy to repeat
or skip a group of commands during program execution. When you select an item from
the menu, the name is pasted to the cursor location on a command line in the program.
To return to the program editor without selecting an item, press ‘.
Controlling Program Flow
Program control instructions tell the TI-84 Plus which command to execute next in a
program. If, While, and Repeat check a defined condition to determine which command
to execute next. Conditions frequently use relational or Boolean tests (Chapter 2), as in:
If A<7:A+1!A
or
If N=1 and M=1:Goto Z
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If
Use If for testing and branching. If condition is false (zero), then the command immediately
following If is skipped. If condition is true (nonzero), then the next command is executed. If
instructions can be nested.
:If condition
:command (if true)
:command
Program
Output
If-Then
Then following an If executes a group of commands if condition is true (nonzero). End
identifies the end of the group of commands.
:If condition
:Then
:command (if true)
:command (if true)
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:End
:command
Program
Output
If-Then-Else
Else following If-Then executes a group of commands if condition is false (zero). End
identifies the end of the group of commands.
:If condition
:Then
:command (if true)
:command (if true)
:Else
:command (if false)
:command (if false)
:End
:command
Program
Output
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For(
For( loops and increments. It increments variable from begin to end by increment. increment is
optional (default is 1) and can be negative (end<begin). end is a maximum or minimum
value not to be exceeded. End identifies the end of the loop. For( loops can be nested.
:For(variable,begin,end[,increment])
:command (while end not exceeded)
:command (while end not exceeded)
:End
:command
Program
Output
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While
While performs a group of commands while condition is true. condition is frequently a
relational test (Chapter 2). condition is tested when While is encountered. If condition is true
(nonzero), the program executes a group of commands. End signifies the end of the group.
When condition is false (zero), the program executes each command following End. While
instructions can be nested.
:While condition
:command (while condition is true)
:command (while condition is true)
:End
:command
Program
Output
Repeat
Repeat repeats a group of commands until condition is true (nonzero). It is similar to While,
but condition is tested when End is encountered; therefore, the group of commands is
always executed at least once. Repeat instructions can be nested.
:Repeat condition
:command (until condition is true)
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:command (until condition is true)
:End
:command
Program
Output
End
End identifies the end of a group of commands. You must include an End instruction at the
end of each For(, While, or Repeat loop. Also, you must paste an End instruction at the
end of each If-Then group and each If-Then-Else group.
Pause
Pause suspends execution of the program so that you can see answers or graphs.
During the pause, the pause indicator is on in the top-right corner. Press Í to
resume execution.
•
•
Pause without a value temporarily pauses the program. If the DispGraph or Disp
instruction has been executed, the appropriate screen is displayed.
Pause with value displays value on the current home screen. value can be scrolled.
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Pause [value]
Program
Output
Lbl, Goto
Lbl (label) and Goto (go to) are used together for branching.
Lbl specifies the label for a command. label can be one or two characters (A through Z, 0
through 99, or q).
Lbl label
Goto causes the program to branch to label when Goto is encountered.
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Goto label
Program
Output
IS>(
IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an
expression), the next command is skipped; if the answer is { value, the next command is
executed. variable cannot be a system variable.
:IS>(variable,value)
:command (if answer value)
:command (if answer > value)
Program
Output
Note: IS>( is not a looping instruction.
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DS<(
DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be
an expression), the next command is skipped; if the answer is | value, the next command is
executed. variable cannot be a system variable.
:DS<(variable,value)
:command (if answer ‚ value)
:command (if answer < value)
Program
Output
Note: DS<( is not a looping instruction.
Menu(
Menu( sets up branching within a program. If Menu( is encountered during program
execution, the menu screen is displayed with the specified menu items, the pause
indicator is on, and execution pauses until you select a menu item.
The menu title is enclosed in quotation marks ( " ). Up to seven pairs of menu items
follow. Each pair comprises a text item (also enclosed in quotation marks) to be displayed
as a menu selection, and a label item to which to branch if you select the corresponding
menu selection.
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Menu("title","text1",label1,"text2",label2, . . .)
Program Output
The program above pauses until you select 1 or 2. If you select 2, for example, the menu
disappears and the program continues execution at Lbl B.
prgm
Use prgm to execute other programs as subroutines. When you select prgm, it is pasted
to the cursor location. Enter characters to spell a program name. Using prgm is equivalent
to selecting existing programs from the PRGM EXEC menu; however, it allows you to
enter the name of a program that you have not yet created.
prgmname
Note: You cannot directly enter the subroutine name when using RCL. You must paste
the name from the PRGM EXEC menu.
Return
Return quits the subroutine and returns execution to the calling program, even if
encountered within nested loops. Any loops are ended. An implied Return exists at the
end of any program that is called as a subroutine. Within the main program, Return stops
execution and returns to the home screen.
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Stop
Stop stops execution of a program and returns to the home screen. Stop is optional at
the end of a program.
DelVar
DelVar deletes from memory the contents of variable.
DelVar variable
GraphStyle(
GraphStyle( designates the style of the graph to be drawn. function# is the number of the
Y= function name in the current graphing mode. graphstyle is a number from 1 to 7 that
corresponds to the graph style, as shown below.
1 = ç (line)
5 = ë (path)
6 = ì (animate)
7 = í (dot)
2 = è (thick)
3 = é (shade above)
4 = ê (shade below)
GraphStyle(function#,graphstyle)
For example, GraphStyle(1,5) in Func mode sets the graph style for Y1 to ë (path; 5).
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Not all graph styles are available in all graphing modes. For a detailed description of
each graph style, see the Graph Styles table in Chapter 3.
PRGM I/O (Input/Output) Instructions
PRGM I/O Menu
To display the PRGM I/O (program input/output) menu, press ~ from within the
program editor only.
CTL I/O EXEC
Enters a value or uses the cursor.
Prompts for entry of variable values.
Displays text, value, or the home screen.
Displays the current graph.
1: Input
2: Prompt
3: Disp
4: DispGraph
5: DispTable
6: Output(
7: getKey
8: ClrHome
9: ClrTable
0: GetCalc(
A: Get(
Displays the current table.
Displays text at a specified position.
Checks the keyboard for a keystroke.
Clears the display.
Clears the current table.
Gets a variable from another TI-84 Plus.
Gets a variable from CBL 2™ or CBR™.
Sends a variable to CBL 2 or CBR.
B: Send(
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These instructions control input to and output from a program during execution. They
allow you to enter values and display answers during program execution.
To return to the program editor without selecting an item, press ‘.
Displaying a Graph with Input
Input without a variable displays the current graph. You can move the free-moving
cursor, which updates X and Y (and R and q for PolarGC format). The pause indicator is
on. Press Í to resume program execution.
Input
Program
Output
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Storing a Variable Value with Input
Input with variable displays a ?(question mark) prompt during execution. variable may be a
real number, complex number, list, matrix, string, or Y= function. During program
execution, enter a value, which can be an expression, and then press Í. The value
is evaluated and stored to variable, and the program resumes execution.
Input [variable]
You can display text or the contents of Strn (a string variable) of up to 16 characters as a
prompt. During program execution, enter a value after the prompt and then press Í.
The value is stored to variable, and the program resumes execution.
Input ["text",variable]
Input [Strn,variable]
Program
Output
Note: When a program prompts for input of lists and Yn functions during execution, you
must include the braces ( { } ) around the list elements and quotation marks ( " ) around
the expressions.
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Prompt
During program execution, Prompt displays each variable, one at a time, followed by =?.
At each prompt, enter a value or expression for each variable, and then press Í. The
values are stored, and the program resumes execution.
Prompt variableA[,variableB,...,variable n]
Program
Output
Note: Y= functions are not valid with Prompt.
Displaying the Home Screen
Disp (display) without a value displays the home screen. To view the home screen during
program execution, follow the Disp instruction with a Pause instruction.
Disp
Displaying Values and Messages
Disp with one or more values displays the value of each.
Disp [valueA,valueB,valueC,...,value n]
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•
•
If value is a variable, the current value is displayed.
If value is an expression, it is evaluated and the result is displayed on the right side of
the next line.
•
If value is text within quotation marks, it is displayed on the left side of the current
display line. ! is not valid as text.
Program
Output
If Pause is encountered after Disp, the program halts temporarily so you can examine the
screen. To resume execution, press Í.
Note: If a matrix or list is too large to display in its entirety, ellipses (...) are displayed in
the last column, but the matrix or list cannot be scrolled. To scroll, use Pause value.
DispGraph
DispGraph (display graph) displays the current graph. If Pause is encountered after
DispGraph, the program halts temporarily so you can examine the screen. Press Í
to resume execution.
DispTable
DispTable (display table) displays the current table. The program halts temporarily so you
can examine the screen. Press Í to resume execution.
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Output(
Output( displays text or value on the current home screen beginning at row (1 through 8)
and column (1 through 16), overwriting any existing characters.
Note: You may want to precede Output( with ClrHome.
Expressions are evaluated and values are displayed according to the current mode
settings. Matrices are displayed in entry format and wrap to the next line. ! is not valid
as text.
Output(row,column,"text")
Output(row,column,value)
Program
Output
For Output( on a Horiz split screen, the maximum value for row is 4.
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getKey
getKey returns a number corresponding to the last key pressed, according to the key
code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside
loops to transfer control, for example, when creating video games.
Program
Output
Note: , Œ, , and Í were pressed
during program execution.
Note: You can press É at any time during execution to break the program.
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TI-84 Plus Key Code Diagram
ClrHome, ClrTable
ClrHome (clear home screen) clears the home screen during program execution.
ClrTable (clear table) clears the values in the table during program execution.
GetCalc(
GetCalc( gets the contents of variable on another TI-84 Plus and stores it to variable on the
receiving TI-84 Plus. variable can be a real or complex number, list element, list name,
matrix element, matrix name, string, Y= variable, graph database, or picture.
GetCalc(variable[,portflag])
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By default, the TI-84 Plus uses the USB port if it is connected. If the USB cable is not
connected, it uses the I/O port. If you want to specify either the USB or I/O port, use the
following portflag numbers:
portflag=0 use USB port if connected;
portflag=1 use USB port;
portflag=2 use I/O port
Note: GetCalc( does not work between TI.82 and TI-83 Plus or a TI.82 and TI-84 Plus
calculators.
Get(, Send(
Get( gets data from the CBL 2™ or CBR™ and stores it to variable on the receiving TI-84
Plus. variable can be a real number, list element, list name, matrix element, matrix name,
string, Y= variable, graph database, or picture.
Get(variable)
Note: If you transfer a program that references the Get( command to the TI-84 Plus from
a TI.82, the TI-84 Plus will interpret it as the Get( described above. Use GetCalc( to get
data from another TI-84 Plus.
Send( sends the contents of variable to the CBL 2™ or CBR™. You cannot use it to send
to another TI-84 Plus. variable can be a real number, list element, list name, matrix
element, matrix name, string, Y= variable, graph database, or picture. variable can be a
list of elements.
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Send(variable)
Note: This program gets sound data and time in
seconds from CBL 2™.
Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them
from the home screen (Chapter 15).
Calling Other Programs as Subroutines
Calling a Program from Another Program
On the TI-84 Plus, any stored program can be called from another program as a
subroutine. Enter the name of the program to use as a subroutine on a line by itself.
You can enter a program name on a command line in either of two ways.
•
Press | to display the PRGM EXEC menu and select the name of the program
prgmname is pasted to the current cursor location on a command line.
•
Select prgm from the PRGM CTL menu, and then enter the program name.
prgmname
When prgmname is encountered during execution, the next command that the program
executes is the first command in the second program. It returns to the subsequent
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command in the first program when it encounters either Return or the implied Return at
the end of the second program.
Program
Output
Subroutine ( '
Notes about Calling Programs
Variables are global.
label used with Goto and Lbl is local to the program where it is located. label in one
program is not recognized by another program. You cannot use Goto to branch to a label
in another program.
Return exits a subroutine and returns to the calling program, even if it is encountered
within nested loops.
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Running an Assembly Language Program
You can run programs written for the TI-84 Plus in assembly language. Typically,
assembly language programs run much faster and provide greater control than than the
keystroke programs that you write with the built-in program editor.
Note: Because an assembly langauge program has greater control over the calculator, if
your assembly language program has error(s), it may cause your calculator to reset and
lose all data, programs, and applications stored in memory.
When you download an assembly language program, it is stored among the other
programs as a PRGM menu item. You can:
•
•
Transmit it using the TI-84 Plus communication link (Chapter 19).
Delete it using the MEM MGMT DEL screen (Chapter 18).
To run an assembly Program, the syntax is: Asm(assemblyprgmname)
If you write an assembly language program, use the two instructions below from the
CATALOG to identify and compile the program.
Instructions
Comments
AsmComp(prgmASM1,
prgmASM2)
Compiles an assembly language program written in
ASCII and stores the hex version
AsmPrgm
Identifies an assembly language program; must be
entered as the first line of an assembly language
program
To compile an assembly program that you have written:
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1. Follow the steps for writing a program (16-4) but be sure to include AsmPrgm as the
first line of your program.
2. From the home screen, press y N and then select AsmComp( to paste it to
the screen.
3. Press to display the PRGM EXEC menu.
4. Select the program you want to compile. It will be pasted to the home screen.
5. Press ¢ and then select prgm from the CATALOG.
6. Key in the name you have chosen for the output program.
Note: This name must be unique — not a copy of an existing program name.
7. Press ¤ to complete the sequence.
The sequence of the arguments should be as follows:
AsmComp(prgmASM1, prgmASM2)
8. Press Í to compile your program and generate the output program.
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Chapter 17:
Activities
The Quadratic Formula
Entering a Calculation
2
Use the quadratic formula to solve the quadratic equations 3x + 5x + 2 = 0 and
2
2
2x N x + 3 = 0. Begin with the equation 3x + 5x + 2 = 0.
1. Press 3 ¿ ƒ [A] (above ) to
2
store the coefficient of the x term.
2. Press ƒ [:] (above Ë). The colon
allows you to enter more than one
instruction on a line.
3. Press 5 ¿ ƒ [B] (above Œ) to
store the coefficient of the X term. Press
ƒ [:] to enter a new instruction on
the same line. Press 2 ¿ ƒ [C]
(above ) to store the constant.
4. Press Í to store the values to the
variables A, B, and C.
The last value you stored is shown on
the right side of the display. The cursor
moves to the next line, ready for your
next entry.
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5. Press £ Ì ƒ [B] Ã y C ƒ
[B] ¡ ¹ 4 ƒ [A] ƒ [C] ¤ ¤ ¥
£ 2 ƒ [A] ¤ to enter the expression
for one of the solutions for the quadratic
formula,
– b ± b2 – 4ac
--------------------------------------
2a
6. Press Í to find one solution for the
2
equation 3x + 5x + 2 = 0.
The answer is shown on the right side of
the display. The cursor moves to the next
line, ready for you to enter the next
expression.
Converting to a Fraction
You can show the solution as a fraction.
1. Press to display the MATH menu.
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2. Press 1 to select 1:4Frac from the MATH
menu.
When you press 1, Ans4Frac is displayed
on the home screen. Ans is a variable
that contains the last calculated answer.
3. Press Í to convert the result to a
fraction.
To save keystrokes, you can recall the last expression you entered, and then edit it for a
new calculation.
4. Press y [ (above Í) to recall
the fraction conversion entry, and then
press y [ again to recall the
quadratic-formula expression,
– b + b2 – 4ac
--------------------------------------
2a
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5. Press } to move the cursor onto the +
sign in the formula. Press ¹ to edit the
quadratic-formula expression to become:
– b – b2 – 4ac
--------------------------------------
2a
6. Press Í to find the other solution for
2
the quadratic equation 3x + 5x + 2 = 0.
Displaying Complex Results
2
Now solve the equation 2x N x + 3 = 0. When you set a+bi complex number mode, the
TI-84 Plus displays complex results.
1. Press z † † † † † † (6 times),
and then press ~ to position the cursor
over a+bi. Press Í to select a+bi
complex-number mode.
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2. Press y 5 (above z) to return to
the home screen, and then press ‘
to clear it.
3. Press 2 ¿ ƒ [A] ƒ [:] Ì 1
¿ ƒ [B] ƒ [:] 3 ¿ ƒ
[C] Í.
2
The coefficient of the x term, the
coefficient of the X term, and the
constant for the new equation are stored
to A, B, and C, respectively.
4. Press y [ to recall the store
instruction, and then press y [
again to recall the quadratic-formula
expression,
– b – b2 – 4ac
--------------------------------------
2a
5. Press Í to find one solution for the
2
equation 2x N x + 3 = 0.
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6. Press y [ repeatedly until this
quadratic-formula expression is
displayed:
– b + b2 – 4ac
--------------------------------------
2a
7. Press Í to find the other solution for
2
the quadratic equation: 2x N x + 3 = 0.
Note: An alternative for solving equations for real numbers is to use the built-in Equation
Solver.
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Box with Lid
Defining a Function
Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut
X × 12½ cm rectangles from the other two corners as shown in the diagram below. Fold
the paper into a box with a lid. What value of X would give your box the maximum
volume V? Use the table and graphs to determine the solution.
Begin by defining a function that describes
the volume of the box.
X
20 A
X
From the diagram:
2X + A = 20
2X + 2B = 25
V = A…B…X
X
B
B
25
1. Press o to display the Y= editor, which
is where you define functions for tables
and graphing.
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2. Press £ 20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹
„ ¤ „ Í to define the
volume function as Y1 in terms of X.
„ lets you enter X quickly, without
having to press ƒ. The highlighted =
sign indicates that Y1 is selected.
Defining a Table of Values
The table feature of the TI-84 Plus displays numeric information about a function. You
can use a table of values from the function you just defined to estimate an answer to the
problem.
1. Press y - (above p) to
display the TABLE SETUP menu.
2. Press Í to accept TblStart=0.
3. Press 1 Í to define the table
increment @Tbl=1. Leave Indpnt: Auto
and Depend: Auto so that the table will be
generated automatically.
4. Press y 0 (above s) to
display the table.
Notice that the maximum value for Y1
(box’s volume) occurs when X is about 4,
between 3 and 5.
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5. Press and hold † to scroll the table until
a negative result for Y1 is displayed.
Notice that the maximum length of X for
this problem occurs where the sign of Y1
(box’s volume) changes from positive to
negative, between 10 and 11.
6. Press y -.
Notice that TblStart has changed to 6 to
reflect the first line of the table as it was
last displayed. (In step 5, the first value
of X displayed in the table is 6.)
Zooming In on the Table
You can adjust the way a table is displayed to get more information about a defined
function. With smaller values for @Tbl, you can zoom in on the table.
1. Press 3 Í to set TblStart. Press Ë 1
Í to set @Tbl.
This adjusts the table setup to get a more
accurate estimate of X for maximum
volume Y1.
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2. Press y 0.
3. Press † and } to scroll the table.
Notice that the maximum value for Y1 is
410.26, which occurs at X=3.7. Therefore,
the maximum occurs where 3.6<X<3.8.
4. Press y -. Press 3 Ë 6 Í to
set TblStart. Press Ë 01 Í to set
@Tbl.
5. Press y 0, and then press † and
} to scroll the table.
Four equivalent maximum values are
shown, 410.26 at X=3.67, 3.68, 3.69, and
3.70.
6. Press † or } to move the cursor to 3.67.
Press ~ to move the cursor into the Y1
column.
The value of Y1 at X=3.67 is displayed on
the bottom line in full precision as
410.261226.
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7. Press † to display the other maximum.
The value of Y1 at X=3.68 in full precision
is 410.264064, at X=3.69 is 410.262318 and
at X=3.7 is 410.256.
The maximum volume of the box would
occur at 3.68 if you could measure and
cut the paper at .01-centimeter
increments.
Setting the Viewing Window
You also can use the graphing features of the TI-84 Plus to find the maximum value of a
previously defined function. When the graph is activated, the viewing window defines the
displayed portion of the coordinate plane. The values of the window variables determine
the size of the viewing window.
1. Press p to display the window
editor, where you can view and edit the
values of the window variables.
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The standard window variables define
the viewing window as shown. Xmin,
Xmax, Ymin, and Ymax define the
boundaries of the display. Xscl and Yscl
define the distance between tick marks
on the X and Y axes. Xres controls
resolution.
2. Press 0 Í to define Xmin.
3. Press 20 ¥ 2 to define Xmax using an
expression.
4. Press Í. The expression is
evaluated, and 10 is stored in Xmax.
Press Í to accept Xscl as 1.
5. Press 0 Í 500 Í 100 Í 1
Í to define the remaining window
variables.
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Displaying and Tracing the Graph
Now that you have defined the function to be graphed and the window in which to graph
it, you can display and explore the graph. You can trace along a function using the
TRACE feature.
1. Press s to graph the selected
function in the viewing window.
The graph of Y1=(20N2X)(25à2NX)X is
displayed.
2. Press ~ to activate the free-moving
graph cursor.
The X and Y coordinate values for the
position of the graph cursor are
displayed on the bottom line.
3. Press |, ~, }, and † to move the free-
moving cursor to the apparent maximum
of the function.
As you move the cursor, the X and Y
coordinate values are updated
continually.
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4. Press r. The trace cursor is
displayed on the Y1 function.
The function that you are tracing is
displayed in the top-left corner.
5. Press | and ~ to trace along Y1, one X
dot at a time, evaluating Y1 at each X.
You also can enter your estimate for the
maximum value of X.
6. Press 3 Ë 8. When you press a number
key while in TRACE, the X= prompt is
displayed in the bottom-left corner.
7. Press Í.
The trace cursor jumps to the point on
the Y1 function evaluated at X=3.8.
8. Press | and ~ until you are on the
maximum Y value.
This is the maximum of Y1(X) for the X
pixel values. The actual, precise
maximum may lie between pixel values.
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Zooming In on the Graph
To help identify maximums, minimums, roots, and intersections of functions, you can
magnify the viewing window at a specific location using the ZOOM instructions.
1. Press q to display the ZOOM menu.
This menu is a typical TI-84 Plus menu.
To select an item, you can either press
the number or letter next to the item, or
you can press † until the item number or
letter is highlighted, and then press
Í.
2. Press 2 to select 2:Zoom In.
The graph is displayed again. The cursor
has changed to indicate that you are
using a ZOOM instruction.
3. With the cursor near the maximum value
of the function, press Í.
The new viewing window is displayed.
Both XmaxNXmin and YmaxNYmin have
been adjusted by factors of 4, the default
values for the zoom factors.
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4. Press p to display the new window
settings.
Finding the Calculated Maximum
You can use a CALCULATE menu operation to calculate a local maximum of a function.
1. Press y / (above r) to display
the CALCULATE menu. Press 4 to select
4:maximum.
The graph is displayed again with a
Left Bound? prompt.
2. Press | to trace along the curve to a
point to the left of the maximum, and
then press Í.
A 4 at the top of the screen indicates the
selected bound.
A Right Bound? prompt is displayed.
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3. Press ~ to trace along the curve to a
point to the right of the maximum, and
then press Í.
A 3 at the top of the screen indicates the
selected bound.
A Guess? prompt is displayed.
4. Press | to trace to a point near the
maximum, and then press Í.
Or, press 3 Ë 8, and then press Í to
enter a guess for the maximum.
When you press a number key in TRACE,
the X= prompt is displayed in the bottom-
left corner.
Notice how the values for the calculated
maximum compare with the maximums
found with the free-moving cursor, the
trace cursor, and the table.
Note: In steps 2 and 3 above, you can
enter values directly for Left Bound and
Right Bound, in the same way as
described in step 4.
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Comparing Test Results Using Box Plots
Problem
An experiment found a significant difference between boys and girls pertaining to their
ability to identify objects held in their left hands, which are controlled by the right side of
their brains, versus their right hands, which are controlled by the left side of their brains.
The TI Graphics team conducted a similar test for adult men and women.
The test involved 30 small objects, which participants were not allowed to see. First, they
held 15 of the objects one by one in their left hands and guessed what they were. Then
they held the other 15 objects one by one in their right hands and guessed what they
were. Use box plots to compare visually the correct-guess data from this table.
Each row in the table represents the results observed for one subject. Note that 10
women and 12 men were tested.
Correct Guesses
Women
Left
Women
Right
Men
Left
Men
Right
8
9
4
1
7
8
12
6
12
11
10
8
8
7
12
12
7
12
11
11
13
5
7
8
11
12
12
11
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Correct Guesses
Women
Left
Women
Right
Men
Left
Men
Right
7
9
12
4
8
12
11
9
11
10
14
13
5
11
12
9
Procedure
1. Press … 5 to select 5:SetUpEditor. Enter list names WLEFT, WRGHT, MLEFT, and
MRGHT, separated by commas. Press Í. The stat list editor now contains only
these four lists.
2. Press … 1 to select 1:Edit.
3. Enter into WLEFT the number of correct guesses each woman made using her left
hand (Women Left). Press ~ to move to WRGHT and enter the number of correct
guesses each woman made using her right hand (Women Right).
4. Likewise, enter each man’s correct guesses in MLEFT (Men Left) and MRGHT (Men
Right).
5. Press y ,. Select 1:Plot1. Turn on plot 1; define it as a modified box plot Õ
that uses WLEFT. Move the cursor to the top line and select Plot2. Turn on plot 2;
define it as a modified box plot that uses WRGHT.
6. Press o. Turn off all functions.
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7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This
adjusts the viewing window and displays the box plots for the women’s results.
8. Press r.
Women’s left-hand data
Women’s right-hand data
Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the
outlier to the women’s right-hand data. What is the median for the left hand? For the
right hand? With which hand were the women more accurate guessers, according to
the box plots?
9. Examine the men’s results. Redefine plot 1 to use MLEFT, redefine plot 2 to use
MRGHT. Press r.
Men’s left-hand data
Men’s right-hand data
Press | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. What
difference do you see between the plots?
10. Compare the left-hand results. Redefine plot 1 to use WLEFT, redefine plot 2 to use
MLEFT, and then press r to examine minX, Q1, Med, Q3, and maxX for each
plot. Who were the better left-hand guessers, men or women?
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11. Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use
MRGHT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot.
Who were the better right-hand guessers?
In the original experiment boys did not guess as well with right hands, while girls
guessed equally well with either hand. This is not what our box plots show for adults.
Do you think that this is because adults have learned to adapt or because our
sample was not large enough?
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Graphing Piecewise Functions
Problem
The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50;
plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for
each kph from 66 kph and above. Graph the piecewise function that describes the cost
of the ticket.
The fine (Y) as a function of kilometers per hour (X) is:
Y = 0
Y = 50 + 5 (X N 45)
Y = 50 + 5 … 10 + 10 (X N 55)
Y = 50 + 5 … 10 + 10 … 10 + 20 (X N 65)
0 < X 45
45 < X 55
55 < X 65
65 < X
Procedure
1. Press z. Select Func and the default settings.
2. Press o. Turn off all functions and stat plots. Enter the Y= function to describe the
fine. Use the TEST menu operations to define the piecewise function. Set the graph
style for Y1 to í (dot).
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3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore Xmax and
Ymax; they are set by @X and @Y in step 4.
4. Press y 5 to return to the home screen. Store 1 to @X, and then store 5 to @Y.
@X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the
horizontal and vertical distance between the centers of adjacent pixels. Integer
values for @X and @Y produce nice values for tracing.
5. Press r to plot the function. At what speed does the ticket exceed 250?
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Graphing Inequalities
Problem
3
Graph the inequality 0.4x N 3x + 5 < 0.2x + 4. Use the TEST menu operations to explore
the values of X where the inequality is true and where it is false.
Procedure
1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes
all graph style icons to í (dot) in the Y= editor.
2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4
and the right side as Y5.
3. Enter the statement of the inequality as Y6. This function evaluates to 1 if true or 0 if
false.
4. Press q 6 to graph the inequality in the standard window.
5. Press r † † to move to Y6. Then press | and ~ to trace the inequality,
observing the value of Y.
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6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality.
7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is
false.
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Solving a System of Nonlinear Equations
Problem
3
Using a graph, solve the equation x N2x=2cos(x). Stated another way, solve the system
3
of two equations and two unknowns: y = x N2x and y = 2cos(x). Use ZOOM factors to
control the decimal places displayed on the graph.
Procedure
1. Press z. Select the default mode settings. Press o. Turn off all functions and stat
plots. Enter the functions.
2. Press q 4 to select 4:ZDecimal. The display shows that two solutions may exist
(points where the two functions appear to intersect).
3. Press q ~ 4 to select 4:SetFactors from the ZOOM MEMORY menu. Set XFact=10
and YFact=10.
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4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the free-moving
cursor onto the apparent intersection of the functions on the right side of the display.
As you move the cursor, notice that the X and Y values have one decimal place.
5. Press Í to zoom in. Move the cursor over the intersection. As you move the
cursor, notice that now the X and Y values have two decimal places.
6. Press Í to zoom in again. Move the free-moving cursor onto a point exactly on
the intersection. Notice the number of decimal places.
7. Press y / 5 to select 5:intersect. Press Í to select the first curve and Í
to select the second curve. To guess, move the trace cursor near the intersection.
Press Í. What are the coordinates of the intersection point?
8. Press q 4 to select 4:ZDecimal to redisplay the original graph.
9. Press q. Select 2:Zoom In and repeat steps 4 through 8 to explore the apparent
function intersection on the left side of the display.
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Using a Program to Create the Sierpinski Triangle
Setting up the Program
This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores
the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and
then press Í. The program editor is displayed.
Program
PROGRAM:SIERPINS
:FnOff :ClrDraw
:PlotsOff
:AxesOff
Set viewing window.
:0!Xmin:1!Xmax
:0!Ymin:1!Ymax
:rand!X:rand!Y
Beginning of For group.
:For(K,1,3000)
:rand!N
:If N1à3
:Then
:.5X!X
:.5Y!Y
:End
If/Then group
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:If 1à3<N and N2à3
:Then
:.5(.5+X)!X
:.5(1+Y)!Y
:End
If/Then group.
:If 2à3<N
:Then
If/Then group.
:.5(1+X)!X
:.5Y!Y
:End
Draw point.
End of For group.
Store picture.
:Pt-On(X,Y)
:End
:StorePic 6
After you execute the program above, you can recall and display the picture with the
instruction RecallPic 6.
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Graphing Cobweb Attractors
Problem
Using Web format, you can identify points with attracting and repelling behavior in
sequence graphing.
Procedure
1. Press z. Select Seq and the default mode settings. Press y .. Select
Web format and the default format settings.
2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that
corresponds to the expression Y = K X(1NX).
u(n)=Ku(nN1)(1Nu(nN1))
u(nMin)=.01
3. Press y 5 to return to the home screen, and then store 2.9 to K.
4. Press p. Set the window variables.
nMin=0
Xmin=0
Xmax=1
Xscl=1
Ymin=M.26
Ymax=1.1
Yscl=1
nMax=10
PlotStart=1
PlotStep=1
5. Press r to display the graph, and then press ~ to trace the cobweb. This is a
cobweb with one attractor.
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6. Change K to 3.44 and trace the graph to show a cobweb with two attractors.
7. Change K to 3.54 and trace the graph to show a cobweb with four attractors.
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Using a Program to Guess the Coefficients
Setting Up the Program
This program graphs the function A sin(BX) with random integer coefficients between 1
and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program
continues until your guess is correct.
Program
PROGRAM:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
Define equations.
:"Asin(BX)"!Y1
:"Csin(DX)"!Y2
Set line and path graph styles.
:GraphStyle(1,1)
:GraphStyle(2,5)
:FnOff 2
:randInt(1,10)!A
:randInt(1,10)!B
:0!C:0!D
Initialize coefficients.
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:L2p!Xmin
:2p!Xmax
:pà2!Xscl
:L10!Ymin
:10!Ymax
:1!Yscl
Set viewing window.
Display graph.
:DispGraph
:Pause
:FnOn 2
:Lbl Z
Prompt for guess.
Display graph.
:Prompt C,D
:DispGraph
:Pause
:If C=A
:Text(1,1,"C IS OK")
:If CƒA
:Text(1,1,"C IS
WRONG")
Display results.
:If D=B
:Text(1,50,"D IS OK")
:If DƒB
:Text(1,50,"D IS
WRONG")
:DispGraph
:Pause
Display graph.
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:If C=A and D=B
:Stop
Quit if guesses are correct.
:Goto Z
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Graphing the Unit Circle and Trigonometric Curves
Problem
Using parametric graphing mode, graph the unit circle and the sine curve to show the
relationship between them.
Any function that can be plotted in Func mode can be plotted in Par mode by defining the
X component as T and the Y component as F(T).
Procedure
1. Press z. Select Par, Simul, and the default settings.
2. Press p. Set the viewing window.
Tmin=0
Tmax=2p
Tstep=.1
Xmin=L2
Xmax=7.4
Xscl=pà2
Ymin=L3
Ymax=3
Yscl=1
3. Press o. Turn off all functions and stat plots. Enter the expressions to define the
unit circle centered on (0,0).
4. Enter the expressions to define the sine curve.
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5. Press r. As the graph is plotting, you may press Í to pause and Í
again to resume graphing as you watch the sine function “unwrap” from the unit
circle.
Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig
function to unwrap that function.
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Finding the Area between Curves
Problem
Find the area of the region bounded by:
2
f(x)
g(x)
x
=
=
=
300x/(x + 625)
3cos(.1x)
75
Procedure
1. Press z. Select the default mode settings.
2. Press p. Set the viewing window.
Xmin=0
Xmax=100
Xscl=10
Xres=1
Ymin=L5
Ymax=10
Yscl=1
3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions.
2
Y1=300Xà(X +625)
Y2=3cos(.1X)
4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve,
second curve, and guess for the intersection toward the left side of the display. The
solution is displayed, and the value of X at the intersection, which is the lower limit of
the integral, is stored in Ans and X.
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5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see
the area graphically.
Shade(Y2,Y1,Ans,75)
6. Press y 5 to return to the home screen. Enter the expression to evaluate the
integral for the shaded region.
fnInt(Y1NY2,X,Ans,75)
The area is 325.839962.
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Using Parametric Equations: Ferris Wheel Problem
Problem
Using two pairs of parametric equations, determine when two objects in motion are
closest to each other in the same plane.
A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate
(s) of one revolution every 12 seconds. The parametric equations below describe the
location of a ferris wheel passenger at time T, where a is the angle of rotation, (0,0) is the
bottom center of the ferris wheel, and (10,10) is the passenger’s location at the rightmost
point, when T=0.
X(T) = r cos a
where a = 2pTs and r = dà2
Y(T) = r + r sin a
A person standing on the ground throws a ball to the ferris wheel passenger. The
thrower’s arm is at the same height as the bottom of the ferris wheel, but 25 meters (b) to
the right of the ferris wheel’s lowest point (25,0). The person throws the ball with velocity
(v ) of 22 meters per second at an angle (q) of 66¡ from the horizontal. The parametric
0
equations below describe the location of the ball at time T.
X(T) = b N Tv cosq
0
2
2
where g = 9.8 m/sec
Y(T) = Tv sinq N (gà2) T
0
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Procedure
1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode
simulates the two objects in motion over time.
2. Press p. Set the viewing window.
Tmin=0
Tmax=12
Tstep=.1
Ymin=0
Ymax=31
Yscl=10
Xmin=L13
Xmax=34
Xscl=10
3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path
of the ferris wheel and the path of the ball. Set the graph style for X2T to ë (path).
Note: Try setting the graph styles to ë X1T and ì X2T, which simulates a chair on the
ferris wheel and the ball flying through the air when you press s.
4. Press s to graph the equations. Watch closely as they are plotted. Notice that
the ball and the ferris wheel passenger appear to be closest where the paths cross
in the top-right quadrant of the ferris wheel.
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5. Press p. Change the viewing window to concentrate on this portion of the
graph.
Tmin=1
Tmax=3
Tstep=.03
Xmin=0
Xmax=23.5
Xscl=10
Ymin=10
Ymax=25.5
Yscl=10
6. Press r. After the graph is plotted, press ~ to move near the point on the ferris
wheel where the paths cross. Notice the values of X, Y, and T.
7. Press † to move to the path of the ball. Notice the values of X and Y (T is
unchanged). Notice where the cursor is located. This is the position of the ball when
the ferris wheel passenger passes the intersection. Did the ball or the passenger
reach the intersection first?
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You can use r to, in effect, take snapshots in time and explore the relative
behavior of two objects in motion.
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Demonstrating the Fundamental Theorem of
Calculus
Problem 1
Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by
integrals and derivatives demonstrates graphically that:
x
F(x) = dt = ln(x), x > 0 and that
∫
1
x
1
--
1
x
Dx
dt = --
∫
t
1
Procedure 1
1. Press z. Select the default settings.
2. Press p. Set the viewing window.
Xmin=.01
Xmax=10
Xscl=1
Xres=3
Ymin=L1.5
Ymax=2.5
Yscl=1
3. Press o. Turn off all functions and stat plots. Enter the numerical integral of 1àT
from 1 to X and the function ln(X). Set the graph style for Y1 to ç (line) and Y2 to
ë (path).
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4. Press r. Press |, }, ~, and † to compare the values of Y1 and Y2.
5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral
of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick).
6. Press r. Again, use the cursor keys to compare the values of the two graphed
functions, Y3 and Y4.
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Problem 2
Explore the functions defined by
x
x
x
2
2
2
y = t dt ,
t dt , and
t dt
∫
∫
∫
2
2
0
Procedure 2
1. Press o. Turn off all functions and stat plots. Use a list to define these three
functions simultaneously. Store the function in Y5.
2. Press q 6 to select 6:ZStandard.
3. Press r. Notice that the functions appear identical, only shifted vertically by a
constant.
4. Press o. Enter the numerical derivative of Y5 in Y6.
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5. Press r. Notice that although the three graphs defined by Y5 are different, they
share the same derivative.
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Computing Areas of Regular N-Sided Polygons
Problem
Use the equation solver to store a formula for the area of a regular N-sided polygon, and
then solve for each variable, given the other variables. Explore the fact that the limiting
2
case is the area of a circle, pr .
2
Consider the formula A = NB sin(pàN) cos(pàN) for the area of a regular polygon with N
sides of equal length and B distance from the center to a vertex.
N = 8 sides
N = 4 sides
N = 12 sides
Procedure
1. Press 0 to select 0:Solver from the MATH menu. Either the equation editor or
the interactive solver editor is displayed. If the interactive solver editor is displayed,
press } to display the equation editor.
2
2. Enter the formula as 0=ANNB sin(p / N)cos(p / N), and then press Í. The
interactive solver editor is displayed.
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3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to
vertex of 6 centimeters.
4. Press } } to move the cursor onto A, and then press ă \. The solution for
A is displayed on the interactive solver editor.
5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6.
To find the distance B, move the cursor onto B, and then press ƒ \.
6. Enter N=8. To find the distance B, move the cursor onto B, and then press ƒ
\. Find B for N=9, and then for N=10.
Find the area given B=6, and N=10, 100, 150, 1000, and 10000. Compare your results with
2
p6 (the area of a circle with radius 6), which is approximately 113.097.
7. Enter B=6. To find the area A, move the cursor onto A, and then press ƒ \.
Find A for N=10, then N=100, then N=150, then N=1000, and finally N=10000. Notice
2
that as N gets large, the area A approaches pB .
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Now graph the equation to see visually how the area changes as the number of sides
gets large.
8. Press z. Select the default mode settings.
9. Press p. Set the viewing window.
Xmin=0
Ymin=0
Xres=1
Xmax=200
Xscl=10
Ymax=150
Yscl=10
10. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X
in place of N. Set the graph styles as shown.
11. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150
2
Í. Press 188 Í. Notice that as X increases, the value of Y converges to p6 ,
2
which is approximately 113.097. Y2=pB (the area of the circle) is a horizontal
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asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from
2
the center to a vertex, approaches the area of a circle with radius r (pr ) as N gets
large.
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Computing and Graphing Mortgage Payments
Problem
You are a loan officer at a mortgage company, and you recently closed on a 30-year
home mortgage at 8 percent interest with monthly payments of 800. The new home
owners want to know how much will be applied to the interest and how much will be
applied to the principal when they make the 240th payment 20 years from now.
Procedure
1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode
settings to the defaults.
2. Press Œ Í Í to display the TVM Solver. Enter these values.
Note: Enter a positive number (800) to show PMT as a cash inflow. Payment values
will be displayed as positive numbers on the graph. Enter 0 for FV, since the future
value of a loan is 0 once it is paid in full. Enter PMT: END, since payment is due at the
end of a period.
3. Move the cursor onto the PV= prompt, and then press ƒ \. The present
value, or mortgage amount, of the house is displayed at the PV= prompt.
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Now compare the graph of the amount of interest with the graph of the amount of
principal for each payment.
4. Press z. Set Par and Simul.
5. Press o. Turn off all functions and stat plots. Enter these equations and set the
graph styles as shown.
Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE).
6. Press p. Set these window variables.
Tmin=1
Xmin=0
Ymin=0
Tmax=360
Tstep=12
Xmax=360
Xscl=10
Ymax=1000
Yscl=100
Note: To increase the graph speed, change Tstep to 24.
7. Press r. After the graph is drawn, press 240 Í to move the trace cursor to
T=240, which is equivalent to 20 years of payments.
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The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is
applied to principal (Y=358.03).
Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800.
8. Press † to move the cursor onto the function for interest defined by X2T and Y2T.
Enter 240.
The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is
interest (Y=441.97).
9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen. Check the figures
from the graph.
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At which monthly payment will the principal allocation surpass the interest allocation?
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Chapter 18:
Memory and Variable Management
Checking Available Memory
MEMORY Menu
At any time you can check available memory or manage existing memory by selecting
items from the MEMORY menu. To access this menu, press y L.
MEMORY
Displays information about the graphing
calculator including current OS version number.
1: About...
Reports memory availability and variable usage.
Clears ENTRY (last-entry storage).
Clears all lists in memory.
2: Mem Mgmt/Del...
3: Clear Entries
4: ClrAllLists
5: Archive...
Archives a selected variable.
UnArchives a selected variable.
6: UnArchive...
7: Reset...
Displays the RAM, ARCHIVE, and ALL menus
Displays GROUP and UNGROUP menus.
8: Group...
To check memory availability, first press y L and then select 2:Mem Mgmt/Del.
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RAM FREE displays the
amount of available RAM.
ARC FREE displays the
amount of available Archive.
Available RAM, Archive, and App Slots
The TI-84 Plus / TI-84 Plus Silver Edition has Archive, RAM, and Application (App) slot
memory for you to use and manage. The available RAM stores computations, lists,
variables, and data. The available Archive lets you store programs, Apps, groups, and
other variables. The App slots are actually individual sectors of Flash ROM where Apps
are stored.
Graphing
calculator
Available RAM
Available
Archive
App
Slots
TI-84 Plus
24 Kilobytes
24 Kilobytes
491 Kilobytes
1.5 Megabytes
30
94
TI-84 Plus Silver
Edition
Note: Some Apps take up several App slots.
Displaying the About Screen
About displays information about the TI-84 Plus Operating System (OS) Version,
Product Number, Product Identification (ID), and Flash Application (App) Certificate
Revision Number. To display the About screen, press y L and then select 1:About.
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Displays the type of
graphing calculator.
Displays the Product
ID. Each Flash-based
graphing calculator has
a unique product ID,
which you may need if
you contact technical
support. You can also
use this 14 digit ID to
register your calculator
at education.ti.com, or
identify your calculator
in the event that it is
lost or stolen.
Displays the OS
version. As new
software upgrades
become available,
you can
electronically
upgrade your unit.
Displaying the MEMORY MANAGEMENT/DELETE Menu
Mem Mgmt/Del displays the MEMORY MANAGEMENT/DELETE menu. The two lines at the
top report the total amount of available RAM (RAM FREE) and Archive (ARC FREE)
memory. By selecting menu items on this screen, you can see the amount of memory
each variable type is using. This information can help you determine if you need to
delete variables from memory to make room for new data, such as programs or Apps.
To check memory usage, follow these steps.
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1. Press y L to display the MEMORY menu.
Note: The # and $ in the top or bottom of
the left column indicate that you can scroll
up or down to view more variable types.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. The
TI-84 Plus expresses memory quantities in bytes.
3. Select variable types from the list to display memory usage.
Notes: Real, List, Y-Vars, and Prgm variable types never reset to zero, even after
memory is cleared.
Apps are independent applications which are stored in Flash ROM. AppVars is a
variable holder used to store variables created by Apps. You cannot edit or change
variables in AppVars unless you do so through the application which created them.
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To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or ‘.
Both options display the home screen.
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Deleting Items from Memory
Deleting an Item
To increase available memory by deleting the contents of any variable (real or complex
number, list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or
string), follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu.
3. Select the type of data you want to delete, or select 1:All for a list of all variables of
all types. A screen is displayed listing each variable of the type you selected and the
number of bytes each variable is using.
For example, if you select 4:List, the LIST editor screen is displayed.
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4. Press } and † to move the selection cursor (4) next to the item you want to delete,
and then press {. The variable is deleted from memory. You can delete individual
variables one by one from this screen. No warning will be given to verify the deletion.
Note: If you are deleting programs or Apps, you will receive a message asking you to
confirm this delete action. Select 2:Yes to continue.
To leave any variable screen without deleting anything, press y 5, which
displays the home screen.
You cannot delete some system variables, such as the last-answer variable Ans and
the statistical variable RegEQ.
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Clearing Entries and List Elements
Clear Entries
Clear Entries clears the contents of the ENTRY (last entry on home screen) storage area.
To clear the ENTRY storage area, follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 3:Clear Entries to paste the instruction to the home screen.
3. Press Í to clear the ENTRY storage area.
To cancel Clear Entries, press ‘.
Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is
pasted to the program editor, and the Entry (last entry) is cleared when the program is
executed.
ClrAllLists
ClrAllLists sets the dimension of each list in RAM to 0.
To clear all elements from all lists, follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 4:ClrAllLists to paste the instruction to the home screen.
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3. Press Í to set the dimension of each list in memory to 0.
To cancel ClrAllLists, press ‘.
ClrAllLists does not delete list names from memory, from the LIST NAMES menu, or from
the stat list editor.
Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction is pasted
to the program editor. The lists are cleared when the program is executed.
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Archiving and UnArchiving Variables
Archiving and UnArchiving Variables
Archiving lets you store data, programs, or other variables to the user data archive
(ARC) where they cannot be edited or deleted inadvertently. Archiving also allows you to
free up RAM for variables that may require additional memory.
Archived variables cannot be edited or executed. They can only be seen and
unarchived. For example, if you archive list L1, you will see that L1 exists in memory but
if you select it and paste the name L1 to the home screen, you won’t be able to see its
contents or edit it.
Note: Not all variables may be archived. Not all archived variables may be unarchived.
For example, system variables including r, t, x, y, and q cannot be archived. Apps and
Groups always exist in Flash ROM so there is no need to archive them. Groups cannot
be unarchived. However, you can ungroup or delete them.
Archive?
(yes/no)
UnArchive?
(yes/no)
Variable Type
Names
Real numbers
A, B, ... , Z
A, B, ... , Z
yes
yes
yes
yes
Complex
numbers
Matrices
Lists
[A], [B], [C], ... , [J]
yes
yes
yes
yes
L1, L2, L3, L4, L5, L6,
and user-defined names
Programs
yes
yes
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Archive?
(yes/no)
UnArchive?
(yes/no)
Variable Type
Names
Functions
Y1, Y2, . . . , Y9, Y0
no
no
no
no
no
not
applicable
Parametric
equations
X1T and Y1T, ... , X6T
and Y6T
not
applicable
Polar functions
r1, r2, r3, r4, r5, r6
not
applicable
Sequence
functions
u, v, w
not
applicable
Stat plots
Plot1, Plot2, Plot3
not
applicable
Graph databases GDB1, GDB2,...
yes
yes
yes
yes
Graph pictures
Pic1, Pic2, ... , Pic9,
Pic0
Strings
Tables
Str1, Str2, . . . Str9, Str0 yes
yes
TblStart, Tb1, TblInput no
not
applicable
Apps
Applications
see Note
no
above
AppVars
Groups
Application variables
yes
yes
no
see Note
above
Variables with
minX, maxX, RegEQ,
no
not
reserved names
and others
applicable
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Archive?
(yes/no)
UnArchive?
(yes/no)
Variable Type
Names
System variables Xmin, Xmax, and others no
not
applicable
Archiving and unarchiving can be done in two ways:
•
•
Use the 5:Archive or 6:UnArchive commands from the MEMORY menu or CATALOG.
Use a Memory Management editor screen.
Before archiving or unarchiving variables, particularly those with a large byte size (such
as large programs) use the MEMORY menu to:
•
•
Find the size of the variable.
See if there is enough free space.
For:
Sizes must be such that:
Archive
Archive free size > variable size
RAM free size > variable size
UnArchive
Note: If there is not enough space, unarchive or delete variables as necessary. Be aware
that when you unarchive a variable, not all the memory associated with that variable in
user data archive will be released since the system keeps track of where the variable
has been and where it is now in RAM.
Even if there appears to be enough free space, you may see a Garbage Collection
message when you attempt to archive a variable. Depending on the usability of empty
blocks in the user data archive, you may need to unarchive existing variables to create
more free space.
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To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the
MEMORY menu:
1. Press y L to display the MEMORY menu.
2. Select 5:Archive or 6:UnArchive to place the command in the Home screen.
3. Press y d to place the L1 variable in the Home screen.
4. Press Í to complete the archive process.
Note: An asterisk will be displayed to the left of the Archived variable name to indicate it
is archived.
To archive or unarchive a list variable (L1) using a Memory Management editor:
1. Press y L to display the MEMORY menu.
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2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu.
3. Select 4:List to display the LIST menu.
4. Press Í to archive L1. An asterisk will appear to the left of L1 to indicate it is an
archived variable. To unarchive a variable in this screen, put the cursor next to the
archived variable and press Í. The asterisk will disappear.
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5. Press y 5 to leave the LIST menu.
Note: You can access an archived variable for the purpose of linking, deleting, or
unarchiving it, but you cannot edit it.
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Resetting the TI-84 Plus
RAM ARCHIVE ALL Menu
Reset displays the RAM ARCHIVE ALL menu. This menu gives you the option of resetting
all memory (including default settings) or resetting selected portions of memory while
preserving other data stored in memory, such as programs and Y= functions. For
instance, you can choose to reset all of RAM or just restore the default settings. Be
aware that if you choose to reset RAM, all data and programs in RAM will be erased. For
archive memory, you can reset variables (Vars), applications (Apps), or both of these. Be
aware that if you choose to reset Vars, all data and programs in archive memory will be
erased. If you choose to reset Apps, all applications in archive memory will be erased.
When you reset defaults on the TI-84 Plus, all defaults in RAM are restored to the factory
settings. Stored data and programs are not changed.
These are some examples of TI-84 Plus defaults that are restored by resetting the
defaults.
•
Mode settings such as Normal (notation); Func (graphing); Real (numbers); and Full
(screen)
•
•
•
•
Y= functions off
Window variable values such as Xmin=L10, Xmax=10, Xscl=1, Yscl=1, and Xres=1
STAT PLOTS off
Format settings such as CoordOn (graphing coordinates on); AxesOn; and ExprOn
(expression on)
•
rand seed value to 0
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Displaying the RAM ARCHIVE ALL Menu
To display the RAM ARCHIVE ALL menu on the TI-84 Plus, follow these steps.
1. Press y L to display the MEMORY menu.
2. Select 7:Reset to display the RAM ARCHIVE ALL menu.
Resetting RAM Memory
Resetting all RAM restores RAM system variables to factory settings and deletes all
nonsystem variables and all programs. Resetting RAM defaults restores all system
variables to default settings without deleting variables and programs in RAM. Resetting
all RAM or resetting defaults does not affect variables and applications in user data
archive.
Note: Before you reset all RAM memory, consider restoring sufficient available memory
by deleting only selected data.
To reset all RAM memory or RAM defaults on the TI-84 Plus, follow these steps.
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1. From the RAM ARCHIVE ALL menu, select 1:All RAM to display the RESET RAM
menu or 2:Defaults to display the RESET DEFAULTS menu.
2. If you are resetting RAM, read the message below the RESET RAM menu.
•
•
To cancel the reset and return to the HOME screen, press Í.
To erase RAM memory or reset defaults, select 2:Reset. Depending on your
choice, the message RAM cleared or Defaults set is displayed on the home
screen.
Resetting Archive Memory
When resetting archive memory on the TI-84 Plus, you can choose to delete from user
data archive all variables, all applications, or both variables and applications.
To reset all or part of user data archive memory, follow these steps.
1. From the RAM ARCHIVE ALL menu, press ~ to display the ARCHIVE menu.
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2. Select one of the following:
1:Vars to display the RESET ARC VARS menu.
2:Apps to display the RESET ARC APPS menu.
3:Both to display the RESET ARC BOTH menu.
3. Read the message below the menu.
•
To cancel the reset and return to the HOME screen, press Í.
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•
To continue with the reset, select 2:Reset. A message indicating the type of
archive memory cleared will be displayed on the HOME screen.
Resetting All Memory
When resetting all memory on the TI-84 Plus, RAM and user data archive memory is
restored to factory settings. All nonsystem variables, applications, and programs are
deleted. All system variables are reset to default settings.
Before you reset all memory, consider restoring sufficient available memory by deleting
only selected data.
To reset all memory on the TI-84 Plus, follow these steps.
1. From the RAM ARCHIVE ALL menu, press ~ ~ to display the ALL menu.
2. Select 1:All Memory to display the RESET MEMORY menu.
3. Read the message below the RESET MEMORY menu.
•
To cancel the reset and return to the HOME screen, press Í.
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•
To continue with the reset, select 2:Reset. The message MEM cleared is
displayed on the HOME screen.
When you clear memory, the contrast sometimes changes. If the screen is faded or
blank, adjust the contrast by pressing y } or †.
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Grouping and Ungrouping Variables
Grouping Variables
Grouping allows you to make a copy of two or more variables residing in RAM and then
store them as a group in user data archive. The variables in RAM are not erased. The
variables must exist in RAM before they can be grouped. In other words, archived data
cannot be included in a group. Once grouped, the variables can be deleted from RAM to
open memory. When the variables are needed later, they can be ungrouped for use.
To create a group of variables:
1. Press y L to display the MEMORY menu.
2. Select 8:Group to display GROUP UNGROUP menu.
3. Press Í to display the GROUP menu.
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4. Enter a name for the new group and press Í.
Note: A group name can be one to eight characters long. The first character must be
a letter from A to Z or q. The second through eighth characters can be letters,
numbers, or q.
5. Select the type of data you want to group. You can select 1:All+ which shows all
variables of all types available and selected. You can also select 2:All- which shows
all variables of all types available but not selected. A screen is displayed listing each
variable of the type you selected.
For example, suppose some variables have been created in RAM, and selecting
2:All- displays the following screen.
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6. Press } and † to move the selection cursor (4) next to the first item you want to
copy into a group, and then press Í. A small square will remain to the left of all
variables selected for grouping.
Repeat the selection process until all variables for the new group are selected and
then press ~ to display the DONE menu.
7. Press Í to complete the grouping process.
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Note: You can only group variables in RAM. You cannot group some system variables,
such as the last-answer variable Ans and the statistical variable RegEQ.
Ungrouping Variables
Ungrouping allows you to make a copy of variables in a group stored in user data archive
and place them ungrouped in RAM.
DuplicateName Menu
During the ungrouping action, if a duplicate variable name is detected in RAM, the
DUPLICATE NAME menu is displayed.
DuplicateName
Prompts to rename receiving variable.
1: Rename
Overwrites data in receiving duplicate variable.
2: Overwrite
3: Overwrite All
Overwrites data in all receiving duplicate
variables.
Skips ungrouping of sending variable.
Stops ungrouping at duplicate variable.
4: Omit
5: Quit
Notes about Menu Items:
•
When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on.
Enter a new variable name, and then press Í. Ungrouping resumes.
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•
•
•
•
When you select 2:Overwrite, the unit overwrites the data of the duplicate variable
name found in RAM. Ungrouping resumes.
When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable
names found in RAM. Ungrouping resumes.
When you select 4:Omit, the unit does not ungroup the variable in conflict with the
duplicated variable name found in RAM. Ungrouping resumes with the next item.
When you select 5:Quit, ungrouping stops, and no further changes are made.
To ungroup a group of variables:
1. Press y L to display the MEMORY menu.
2. Select 8:Group to display the GROUP UNGROUP menu.
3. Press ~ to display the UNGROUP menu.
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4. Press } and † to move the selection cursor (4) next to the group variable you want
to ungroup, and then press Í.
The ungroup action is completed.
Note: Ungrouping does not remove the group from user data archive. You must delete
the group in user data archive to remove it.
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Garbage Collection
Garbage Collection Message
If you use the user data archive extensively, you may see a Garbage Collect? message.
This occurs if you try to archive a variable when there is not enough free contiguous
archive memory.
The Garbage Collect? message lets you know an archive will take longer than usual. It
also alerts you that the archive will fail if there is not enough memory.
The message can also alert you when a program is caught in a loop that repetitively fills
the user data archive. Select No to cancel the garbage collection process, and then find
and correct the errors in your program.
When YES is selected, the TI-84 Plus will attempt to rearrange the archived variables to
make additional room.
Responding to the Garbage Collection Message
•
•
To cancel, select 1:No.
If you select 1:No, the message
ERR:ARCHIVE FULL will be displayed.
•
•
To continue archiving, select 2:Yes.
If you select 2:Yes, the process message
Garbage Collecting... or Defragmenting...
will be displayed.
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Note: The process message Defragmenting... is displayed whenever an application
marked for deletion is encountered. Garbage collection may take up to 20 minutes,
depending on how much of archive memory has been used to store variables.
After garbage collection, depending on how much additional space is freed, the variable
may or may not be archived. If not, you can unarchive some variables and try again.
Why Is Garbage Collection Necessary?
The user data archive is divided into sectors. When you first begin archiving, variables
are stored consecutively in sector 1. This continues to the end of the sector.
An archived variable is stored in a continuous block within a single sector. Unlike an
application stored in user data archive, an archived variable cannot cross a sector
boundary. If there is not enough space left in the sector, the next variable is stored at the
beginning of the next sector. Typically, this leaves an empty block at the end of the
previous sector.
Sector 1
variable A
variable B
Empty
block
variable C
variable D
Sector 2
Sector 3
Depending on its size,
variable D is stored in
one of these locations.
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Each variable that you archive is stored in the first empty block large enough to hold it.
This process continues to the end of the last sector. Depending on the size of individual
variables, the empty blocks may account for a significant amount of space. Garbage
collection occurs when the variable you are archiving is larger than any empty block.
How Unarchiving a Variable Affects the Process
When you unarchive a variable, it is copied to RAM but it is not actually deleted from
user data archive memory. Unarchived variables are “marked for deletion,” meaning they
will be deleted during the next garbage collection.
Sector 1
v
a
r
i a
b
l e
A
After you unarchive
variables B and C,
they continue to take
up space.
Sector 2
Sector 3
v
a
r
i a
b
l e
D
If the MEMORY Screen Shows Enough Free Space
Even if the MEMORY screen shows enough free space to archive a variable or store an
application, you may still get a Garbage Collect? message or an ERR: ARCHIVE FULL
message.
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When you unarchive a variable, the Archive free amount increases immediately, but the
space is not actually available until after the next garbage collection.
If the Archive free amount shows enough available space for your variable, there
probably will be enough space to archive it after garbage collection (depending on the
usability of any empty blocks).
The Garbage Collection Process
The garbage collection process:
•
Deletes unarchived variables
from the user data archive.
Sector 1
Sector 2
va ria b le
va ria b le
A
D
•
Rearranges the remaining
variables into consecutive
blocks.
Note: Power loss during garbage collection may cause all memory (RAM and Archive) to
be deleted.
Using the GarbageCollect Command
You can reduce the number of automatic garbage collections by periodically optimizing
memory. This is done by using the GarbageCollect command.
To use the GarbageCollect command, follow these steps.
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1. From the HOME screen, press y N to display the CATALOG.
2. Press † or } to scroll the CATALOG until the selection cursor points to the
GarbageCollect command or press G to skip to the commands starting with the letter
G.
3. Press Í to paste the command to the HOME screen.
4. Press Í to display the Garbage Collect? message.
5. Select 2:Yes to begin garbage collection.
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ERR:ARCHIVE FULL Message
Even if the MEMORY screen shows enough
free space to archive a variable or store an
application, you may still get an ERR:
ARCHIVE FULL message.
An ERR:ARCHIVE FULL message may be displayed:
•
•
When there is insufficient space to archive a variable within a continuous block and
within a single sector.
When there is insufficient space to store an application within a continuous block of
memory.
When the message is displayed, it will indicate the largest single space of memory
available for storing a variable and an application.
To resolve the problem, use the GarbageCollect command to optimize memory. If
memory is still insufficient, you must delete variables or applications to increase space.
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Chapter 19:
Communication Link
Getting Started: Sending Variables
Getting Started is a fast-paced introduction. Read the chapter for details.
Create and store a variable and a matrix, and then transfer them to another TI-84 Plus.
1. On the home screen of the sending unit,
press 5 Ë 5 ¿ ƒ Q. Press Í
to store 5.5 to Q.
2. Press y H y H 1 ¢ 2 y I y H
3 ¢ 4 y I y I ¿ y > 1.
Press Í to store the matrix to [A].
3. On the sending unit, press y L to
display the MEMORY menu.
4. On the sending unit, press 2 to select
2:Mem Mgmt/Del. The MEMORY
MANAGEMENT menu is displayed.
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5. On the sending unit, press 5 to select
5:Matrix. The MATRIX editor screen is
displayed.
6. On the sending unit, press Í to
archive [A]. An asterisk (ä) will appear,
signifying that [A] is now archived.
7. Connect the graphing calculators with
the USB unit-to-unit cable. Push both
ends in firmly.
8. On the receiving unit, press y 8 ~
to display the RECEIVE menu. Press 1 to
select 1:Receive. The message Waiting...
is displayed and the busy indicator is on.
9. On the sending unit, press y 8 to
display the SEND menu.
10. Press 2 to select 2:AllN. The AllN SELECT
screen is displayed.
11. Press † until the selection cursor ( 4 ) is
next to [A] MATRX. Press Í.
12. Press † until the selection cursor is next
to Q REAL. Press Í. A square dot
next to [A] and Q indicates that each is
selected to send.
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13. On the sending unit, press ~ to display
the TRANSMIT menu.
14. On the sending unit, press 1 to select
1:Transmit and begin transmission. The
receiving unit displays the message
Receiving....When the items are
transmitted, both units display the name
and type of each transmitted variable.
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TI-84 Plus LINK
This chapter describes how to communicate with compatible TI units. The TI-84 Plus
has a USB port to connect and communicate with another TI-84 Plus or TI-84 Plus Silver
Edition. A USB unit-to-unit cable is included with the TI-84 Plus.
The TI-84 Plus also has an I/O port using a I/O unit-to-unit cable to communicate with:
•
•
•
TI-83 Plus Silver Edition
TI-83 Plus
•
•
•
TI-82
TI-73
TI-83
CBL 2™ or a CBR™
Connecting Two Graphing Calculators with a USB Unit-to-Unit Cable or
an I/O Unit-to-Unit Cable
USB Unit-to-Unit Cable
The TI-84 Plus USB link port is located at the
top right edge of the graphing calculator.
1. Firmly insert either end of the USB
unit-to-unit cable into the USB port.
2. Insert the other end of the cable into the
other graphing calculator’s USB port.
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I/O Unit-to-Unit Cable
The TI-84 Plus I/O link port is located at the
top left edge of the graphing calculator.
1. Firmly insert either end of the I/O
unit-to-unit cable into the port.
2. Insert the other end of the cable into the
other graphing calculator’s I/O port.
TI-84 Plus to a TI-83 Plus using I/O Unit-to-Unit Cable
The TI-84 Plus I/O link port is located at the
top left edge of the graphing calculator. The
TI-83 Plus I/O link port is located at the
bottom edge of the graphing calculator.
3. Firmly insert either end of the I/O
unit-to-unit cable into the port.
4. Insert the other end of the cable into the
other graphing calculator’s I/O port.
Linking to the CBL/CBR System
The CBL 2™ and the CBR™ are optional accessories that also connect to a TI-84 Plus
with the I/O unit-to-unit cable. With a CBL 2 or CBR and a TI-84 Plus, you can collect
and analyze real-world data.
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Selecting Items to Send
LINK SEND Menu
To display the LINK SEND menu, press y 8.
SEND RECEIVE
Displays all items as selected, including RAM
and Flash applications.
1: All+...
Displays all items as deselected.
Displays all program names.
Displays all list names.
2: AllN...
3: Prgm...
4: List...
Displays list names L1 through L6.
5: Lists to
TI82...
Displays all graph databases.
Displays all picture data types.
Displays all matrix data types.
Displays all real variables.
6: GDB...
7: Pic...
8: Matrix...
9: Real...
Displays all complex variables.
Displays all Y= variables.
0: Complex...
A: Y-Vars...
B: String...
C: Apps...
Displays all string variables.
Displays all software applications.
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SEND RECEIVE
D: AppVars...
E: Group...
Displays all software application variables.
Displays all grouped variables.
Sends the Calculator ID number immediately.
(You do not need to select SEND.)
F: SendId
Sends operating system updates to another
TI-84 Plus Silver Edition or TI-84 Plus. You can
not send the operating system to the TI-83 Plus
product family.
G: SendOS
Selects all RAM and mode settings (no Flash
applications or archived items) for backup to
another TI-84 Plus, TI-84 Plus Silver Edition,
TI-83 Plus Silver Edition, or to a TI-83 Plus.
H: Back Up...
When you select an item on the LINK SEND menu, the corresponding SELECT screen is
displayed.
Note: Each SELECT screen, except All+…, is initially displayed with nothing pre-selected.
All+… is displayed with everything pre-selected.
To select items to send:
1. Press y 8 on the sending unit to display the LINK SEND menu.
2. Select the menu item that describes the data type to send. The corresponding
SELECT screen is displayed.
3. Press } and † to move the selection cursor ( 4 ) to an item you want to select or
deselect.
4. Press Í to select or deselect the item. Selected names are marked with a 0.
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Note: An asterisk (ä) to the left of an item indicates the item is archived.
5. Repeat steps 3 and 4 to select or deselect additional items.
Sending the Selected Items
After you have selected items to send on the sending unit and set the receiving unit to
receive, follow these steps to transmit the items. To set the receiving unit, see Receiving
Items.
1. Press ~ on the sending unit to display the TRANSMIT menu.
2. Confirm that Waiting... is displayed on the receiving unit, which indicates it is set to
receive.
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3. Press Í to select 1:Transmit. The name and type of each item are displayed
line-by-line on the sending unit as the item is queued for transmission, and then on
the receiving unit as each item is accepted.
Note: Items sent from the RAM of the sending unit are transmitted to the RAM of the
receiving unit. Items sent from user data archive (flash) of the sending unit are
transmitted to user data archive (flash) of the receiving unit.
After all selected items have been transmitted, the message Done is displayed on both
calculators. Press } and † to scroll through the names.
Sending to a TI-84 Plus Silver Edition or TI-84 Plus
You can transfer variables (all types), programs, and Flash applications to another TI-84
Plus Silver Edition or TI-84 Plus. You can also backup the RAM memory of one unit to
another.
Note: Keep in mind that the TI-84 Plus has less Flash memory than the TI-84 Plus Silver
Edition.
•
Variables stored in RAM on the sending TI-84 Plus Silver Edition will be sent to the
RAM of the receiving TI-84 Plus Silver Edition or TI-84 Plus.
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•
Variables and applications stored in the user data archive of the sending TI-84 Plus
Silver Edition will be sent to the user data archive of the receiving TI-84 Plus Silver
Edition or TI-84 Plus.
After sending or receiving data, you can repeat the same transmission to additional
TI-84 Plus Silver Edition or TI-84 Plus units—from either the sending unit or the receiving
unit—without having to reselect data to send. The current items remain selected.
However, you cannot repeat transmission if you selected All+ or All..
To send data to an additional TI-84 Plus Silver Edition or a TI-84 Plus:
1. Use a USB unit-to-unit cable to link two units together.
2. On the sending unit press y 8 and select a data type and items to SEND.
3. Press ~ on the sending unit to display the TRANSMIT menu.
4. On the other unit, press y 8 ~ to display the RECEIVE menu.
5. Press Í on the receiving unit.
6. Press Í on the sending unit. A copy of the selected item(s) is sent to the
receiving unit.
7. Disconnect the link cable only from the receiving unit and connect it to another unit.
8. Press y 8 on the sending unit.
9. Select only the data type. For example, if the unit just sent a list, select 4:LIST.
Note: The item(s) you want to send are pre-selected from the last transmission. Do
not select or deselect any items. If you select or deselect an item, all selections or
deselections from the last transmission are cleared.
10. Press ~ on the sending unit to display the TRANSMIT menu.
11. On the new receiving unit, press y 8 ~ to display the RECEIVE menu.
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12. Press Í on the receiving unit.
13. Press Í on the sending unit. A copy of the selected item(s) is sent to the
receiving unit.
14. Repeat steps 7 through 13 until the items are sent to all additional units.
Sending to a TI-83 Plus or TI-83 Plus Silver Edition
You can send all variables from a TI-84 Plus to a TI-83 Plus or TI-83 Plus Silver Edition
except Flash applications with new features, or programs with new features in them.
If archived variables on the TI-84 Plus are variable types recognized and used on the
TI-83 Plus or TI-83 Plus Silver Edition, you can send these variables to the TI-83 Plus or
TI-83 Plus Silver Edition. They will be automatically sent to the RAM of the TI-83 Plus or
TI-83 Plus Silver Edition during the transfer process. It will send to archive if the item is
from archive.
To send data to a TI-83 Plus or TI-83 Plus Silver Edition:
1. Use an I/O unit-to-unit cable to link the two units together.
2. Set the TI-83 Plus or TI-83 Plus Silver Edition to receive.
3. Press y 8 on the sending TI-84 Plus to display the LINK SEND menu.
4. Select the menu of the items you want to transmit.
5. Press ~ on the sending TI-84 Plus to display the LINK TRANSMIT menu.
6. Confirm that the receiving unit is set to receive.
7. Press Í on the sending TI-84 Plus to select 1:Transmit and begin transmitting.
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Receiving Items
LINK RECEIVE Menu
To display the LINK RECEIVE menu, press y 8 ~.
SEND RECEIVE
Sets unit to receive data transmission.
1: Receive
Receiving Unit
When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the
message Waiting... and the busy indicator are displayed. The receiving unit is ready to
receive transmitted items. To exit the receive mode without receiving items, press É,
and then select 1:Quit from the Error in Xmit menu.
When transmission is complete, the unit exits the receive mode. You can select
1:Receive again to receive more items. The receiving unit then displays a list of items
received. Press y 5 to exit the receive mode.
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DuplicateName Menu
During transmission, if a variable name is duplicated, the DuplicateName menu is
displayed on the receiving unit.
DuplicateName
Prompts to rename receiving variable.
Overwrites data in receiving variable.
Skips transmission of sending variable.
Stops transmission at duplicate variable.
1: Rename
2: Overwrite
3: Omit
4: Quit
When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a
new variable name, and then press Í. Transmission resumes.
When you select 2:Overwrite, the sending unit’s data overwrites the existing data stored
on the receiving unit. Transmission resumes.
When you select 3:Omit, the sending unit does not send the data in the duplicated
variable name. Transmission resumes with the next item.
When you select 4:Quit, transmission stops, and the receiving unit exits receive mode.
Receiving from a TI-84 Plus Silver Edition or TI-84 Plus
The TI-84 Plus Silver Edition and the TI-84 Plus are totally compatible. Keep in mind,
however that the TI-84 Plus has less Flash memory than a TI-84 Plus Silver Edition.
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You cannot send memory backups between the TI-84 Plus product family and the TI-83
Plus product family.
Receiving from a TI-83 Plus Silver Edition or TI-83 Plus
The TI-84 Plus product family and the TI-83 Plus product family are compatible with a
few exceptions.
Receiving from a TI-83
You can transfer all variables and programs from a TI-83 to a TI-84 Plus if they fit in the
RAM of the TI-84 Plus. The RAM of the TI-84 Plus is slightly less than the RAM of the
TI-83.
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Backing Up RAM Memory
Warning: H:Back Up overwrites the RAM memory and mode settings in the receiving unit.
All information in the RAM memory of the receiving unit is lost.
Note: Archived items on the receiving unit are not overwritten.
You can backup the contents of RAM memory and mode settings (no Flash applications
or archived items) to another TI-84 Plus Silver Edition. You can also backup RAM
memory and mode settings to a TI-84 Plus.
To perform a RAM memory backup:
1. Use a USB unit-to-unit cable to link two TI-84 Plus units, or a TI-84 Plus and a TI-84
Plus Silver Edition together.
2. On the sending unit press y 8 and select H:Back Up. The MEMORYBACKUP
screen displays.
3. On the receiving unit, press y 8 ~ to display the RECEIVE menu.
4. Press Í on the receiving unit.
5. Press Í on the sending unit. A WARNING — Backup message displays on the
receiving unit.
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6. Press Í on the receiving unit to continue the backup.
— or —
Press 2:Quit on the receiving unit to cancel the backup and return to the LINK SEND
menu
Note: If a transmission error is returned during a backup, the receiving unit is reset.
Memory Backup Complete
When the backup is complete, both the sending graphing calculator and receiving
graphing calculator display a confirmation screen.
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Error Conditions
A transmission error occurs after one or two seconds if:
•
•
A cable is not attached to the sending unit.
A cable is not attached to the receiving unit.
Note: If the cable is attached, push it in firmly and try again.
The receiving unit is not set to receive transmission.
•
•
You attempt a backup between a TI-73, TI-82, TI-83, TI-83 Plus, or TI-83 Plus Silver
Edition.
•
You attempt a data transfer from a TI-84 Plus to a TI-83 Plus, TI-83 Plus Silver
Edition, TI-83, TI-82, or TI-73 with variables or features not recognized by the TI-83
Plus, TI-83 Plus Silver Edition, TI-83, TI-82, or TI-73.
New variable types and features not recognized by the TI-83, TI-83 Plus, TI-82, or
TI-73 include applications, application variables, grouped variables, new variable
types, or programs with new features in them such as Archive, UnArchive, SendID,
SendOS, Asm(, AsmComp(, AsmPrgm, checkTmr(, ClockOff, ClockOn, dayOfWk(,
getDate, getDtFmt, getDtStr(, getTime, getTmFmt, getTmStr, isClockOn, setDate(,
setDtFmt(, setTime(, setTmFmt(, startTmr, and timeCnv.
•
•
•
•
You attempt a data transfer from a TI-84 Plus to a TI-82 with data other than real lists
L1 through L6 or without using menu item 5:Lists to TI82.
You attempt a data transfer from a TI-84 Plus to a TI-73 with data other than real
numbers, pics, real lists L1 through L6 or named lists with q as part of the name.
Although a transmission error does not occur, these two conditions may prevent
successful transmission.
You try to use Get( with a graphing calculator instead of a CBL 2™ or CBR™.
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•
You try to use GetCalc( with a TI-83 instead of a TI-84 Plus or TI-84 Plus Silver
Edition.
Insufficient Memory in Receiving Unit
•
•
•
During transmission, if the receiving unit does not have sufficient memory to receive
an item, the Memory Full menu is displayed on the receiving unit.
To skip this item for the current transmission, select 1:Omit. Transmission resumes
with the next item.
To cancel the transmission and exit receive mode, select 2:Quit.
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Appendix A:
Functions and Instructions
Functions return a value, list, or matrix. You can use functions in an expression.
Instructions initiate an action. Some functions and instructions have arguments. Optional
arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about
an item, including argument descriptions and restrictions, turn to the page listed on the
right side of the table.
From the CATALOG, you can paste any function or instruction to the home screen or to a
command line in the program editor. However, some functions and instructions are not
valid on the home screen. The items in this table appear in the same order as they
appear in the CATALOG.
† indicates either keystrokes that are valid in the program editor only or ones that paste
certain instructions when you are in the program editor. Some keystrokes display menus
that are available only in the program editor. Others paste mode, format, or table-set
instructions only when you are in the program editor.
Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
abs(value)
Returns the absolute value
of a real number,
NUM
expression, list, or matrix.
1:abs(
abs(complex value)
Returns the magnitude of a
complex number or list.
CPX
5:abs(
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
valueA and valueB
Returns 1 if both valueA
and valueB are ƒ 0. valueA
and valueB can be real
numbers, expressions, or
lists.
y :
LOGIC
1:and
angle(value)
Returns the polar angle of
a complex number or list of
complex numbers.
CPX
4:angle(
ANOVA(list1,list2
[,list3,...,list20])
Performs a one-way
…
analysis of variance for
comparing the means of
two to 20 populations.
TESTS
H:ANOVA(
Ans
Returns the last answer.
y Z
Archive
Moves the specified
variables from RAM to the
user data archive memory.
y L
5:Archive
Asm(assemblyprgmname) Executes an assembly
y N
language program.
Asm(
AsmComp(prgmASM1,
prgmASM2)
Compiles an assembly
language program written
in ASCII and stores the hex
version.
y N
AsmComp(
AsmPrgm
Must be used as the first
line of an assembly
language program.
y N
AsmPrgm
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
augment(matrixA,
matrixB)
Returns a matrix, which is
matrixB appended to
y >
MATH
matrixA as new columns.
7:augment(
augment(listA,listB)
Returns a list, which is listB
concatenated to the end of
listA.
y 9
OPS
9:augment(
AxesOff
AxesOn
a+bi
Turns off the graph axes.
† y .
AxesOff
Turns on the graph axes.
† y .
AxesOn
Sets the mode to
rectangular complex
number mode (a+bi).
† z
a+bi
bal(npmt[,roundvalue])
Computes the balance at
npmt for an amortization
schedule using stored
values for PV, æ, and PMT
and rounds the
Π1:Finance
CALC
9:bal(
computation to roundvalue.
binomcdf(numtrials,p
[,x])
Computes a cumulative
probability at x for the
discrete binomial
y =
DISTR
B:binomcdf(
distribution with the
specified numtrials and
probability p of success on
each trial.
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
binompdf(numtrials,p
[,x])
Computes a probability at x
for the discrete binomial
distribution with the
y =
DISTR
A:binompdf(
specified numtrials and
probability p of success on
each trial.
2
2
y =
c cdf(lowerbound,
Computes the c
DISTR
upperbound,df)
distribution probability
between lowerbound and
upperbound for the specified
degrees of freedom df.
2
8:c cdf(
2
Computes the probability
density function (pdf) for
y =
c pdf(x,df)
DISTR
2
2
the c distribution at a
7:c pdf(
specified x value for the
specified degrees of
freedom df.
2
Performs a chi-square test.
drawflag=1 draws results;
drawflag=0 calculates
results.
† …
c LTest(observedmatrix,
TESTS
expectedmatrix
[,drawflag])
2
C:c LTest(
2
Performs a test to confirm
that sample data is from a
population that conforms to
a specified distribution.
† …
c GOF-Test(observedlist,
TESTS
expectedlist,df)
2
D:c GOFLTest(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
checkTmr(starttime)
Returns the number of
seconds since you used
startTmr to start the timer.
The starttime is the value
displayed by startTmr.
y N
checkTmr(
Circle(X,Y,radius)
Draws a circle with center
(X,Y) and radius.
y <
DRAW
9:Circle(
Clear Entries
Clears the contents of the
Last Entry storage area.
y L
MEMORY
3:Clear Entries
ClockOff
ClockOn
ClrAllLists
Turns off the clock display
in the mode screen.
y N
ClockOff
Turns on the clock display
in the mode screen.
y N
ClockOn
Sets to 0 the dimension of
all lists in memory.
y L
MEMORY
4:ClrAllLists
ClrDraw
ClrHome
Clears all drawn elements
from a graph or drawing.
y <
DRAW
1:ClrDraw
Clears the home screen.
†
I/O
8:ClrHome
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
ClrList listname1
[,listname2, ...,
listname n]
Sets to 0 the dimension of
one or more listnames.
…
EDIT
4:ClrList
ClrTable
Clears all values from the
table.
†
I/O
9:ClrTable
conj(value)
Returns the complex
conjugate of a complex
number or list of complex
numbers.
CPX
1:conj(
Connected
Sets connected plotting
mode; resets all Y= editor
graph-style settings to ç .
† z
Connected
CoordOff
CoordOn
cos(value)
Turns off cursor coordinate
value display.
† y .
CoordOff
Turns on cursor coordinate
value display.
† y .
CoordOn
Returns cosine of a real
number, expression, or list.
™
L1
Returns arccosine of a real
number, expression, or list.
y @
cos (value)
cosh(value)
Returns hyperbolic cosine
of a real number,
y N
cosh(
expression, or list.
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
L1
Returns hyperbolic
arccosine of a real number,
expression, or list.
y N
cosh (
cosh (value)
L1
CubicReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a cubic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
6:CubicReg
cumSum(list)
Returns a list of the
y 9
OPS
6:cumSum(
cumulative sums of the
elements in list, starting
with the first element.
cumSum(matrix)
Returns a matrix of the
y >
MATH
0:cumSum(
cumulative sums of matrix
elements. Each element in
the returned matrix is a
cumulative sum of a matrix
column from top to bottom.
dayOfWk(year,month,
day)
Returns an integer from 1
to 7, with each integer
y N
dayOfWk(
1:Sunday
2:Monday
3:Tuesday...
representing a day of the
week. Use dayOfWk( to
determine on which day of
the week a particular date
would occur. The year must
be 4 digits; month and day
can be 1 or 2 digit.
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
dbd(date1,date2)
Calculates the number of
days between date1 and
date2 using the actual-day-
count method.
Π1:Finance
CALC
D:dbd(
Displays a real or complex
number, expression, list, or
matrix in decimal format.
value4Dec
MATH
2:4Dec
Degree
Sets degree angle mode.
† z
Degree
DelVar variable
Deletes from memory the
contents of variable.
†
CTL
G:DelVar
DependAsk
DependAuto
Sets table to ask for
dependent-variable values.
† y -
Depend: Ask
Sets table to generate
dependent-variable values
automatically.
† y -
Depend: Auto
det(matrix)
Returns determinant of
matrix.
y >
MATH
1:det(
DiagnosticOff
Sets diagnostics-off mode;
y N
2
2
DiagnosticOff
r, r , and R are not
displayed as regression
model results.
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
DiagnosticOn
Sets diagnostics-on mode;
y N
2
2
DiagnosticOn
r, r , and R are displayed
as regression model
results.
dim(listname)
Returns the dimension of
listname.
y 9
OPS
3:dim(
dim(matrixname)
length!dim(listname)
Returns the dimension of
matrixname as a list.
y >
MATH
3:dim(
Assigns a new dimension
(length) to a new or existing
listname.
y 9
OPS
3:dim(
Assigns new dimensions to
a new or existing
matrixname.
{rows,columns}!
y >
MATH
3:dim(
dim(matrixname)
Disp
Displays the home screen.
Displays each value.
Displays the graph.
†
I/O
3:Disp
Disp [valueA,valueB,
valueC,...,value n]
†
I/O
3:Disp
DispGraph
†
I/O
4:DispGraph
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
DispTable
Displays the table.
†
I/O
5:DispTable
Displays value in DMS
format.
value4DMS
y ;
ANGLE
4:4DMS
Dot
Sets dot plotting mode;
resets all Y= editor graph-
style settings to í .
† z
Dot
DrawF expression
DrawInv expression
Draws expression (in terms
of X) on the graph.
y <
DRAW
6:DrawF
Draws the inverse of
expression by plotting X
values on the y-axis and Y
values on the x-axis.
y <
DRAW
8:DrawInv
:DS<(variable,value)
:commandA
:commands
Decrements variable by 1;
skips commandA if variable
< value.
†
CTL
B:DS<(
e^(power)
Returns e raised to power.
y J
y J
e^(list)
Returns a list of e raised to
a list of powers.
Exponent:
valueâexponent
Returns value times 10 to
the exponent.
y D
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Exponent:
listâexponent
Returns list elements times
10 to the exponent.
y D
y D
Exponent:
matrixâexponent
Returns matrix elements
times 10 to the exponent.
Computes the effective
interest rate.
4Eff(nominal rate,
compounding periods)
Π1:Finance
CALC
C:4Eff(
Else
See If:Then:Else
End
Identifies end of For(,
If-Then-Else, Repeat, or
While loop.
†
CTL
7:End
Eng
Sets engineering display
mode.
† z
Eng
Converts the contents of a
Y= var to a string and
stores it in Strn.
Equ4String(Y= var,Strn)
y N
Equ4String(
expr(string)
Converts string to an
expression and executes it.
y N
expr(
ExpReg [Xlistname,
Ylistname,freqlist,regequ]
Fits an exponential
…
regression model to
Xlistname and Ylistname with
frequency freqlist, and
stores the regression
equation to regequ.
CALC
0:ExpReg
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
ExprOff
Turns off the expression
display during TRACE.
† y .
ExprOff
ExprOn
Turns on the expression
display during TRACE.
† y .
ExprOn
Ücdf(lowerbound,
upperbound,
numerator df,
Computes the Û
y =
DISTR
0:Ücdf(
distribution probability
between lowerbound and
upperbound for the specified
numerator df (degrees of
freedom) and denominator
df.
denominator df)
Fill(value,matrixname)
Fill(value,listname)
Fix #
Stores value to each
element in matrixname.
y >
MATH
4:Fill(
Stores value to each
element in listname.
y 9
OPS
4:Fill(
Sets fixed-decimal mode
for # of decimal places.
† z
0123456789
(select one)
Float
Sets floating decimal
mode.
† z
Float
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
fMax(expression,
variable,lower,upper
[,tolerance])
Returns the value of
variable where the local
maximum of expression
occurs, between lower and
upper, with specified
tolerance.
MATH
7:fMax(
fMin(expression,variable, Returns the value of
lower,upper[,tolerance])
variable where the local
minimum of expression
occurs, between lower and
upper, with specified
tolerance.
MATH
6:fMin(
fnInt(expression,variable, Returns the function
lower,upper[,tolerance])
integral of expression with
respect to variable,
MATH
9:fnInt(
between lower and upper,
with specified tolerance.
FnOff [function#,
function#,...,function n]
Deselects all Y= functions
or specified Y= functions.
Y-VARS
4:On/Off
2:FnOff
FnOn [function#,
function#,...,function n]
Selects all Y= functions or
specified Y= functions.
Y-VARS
4:On/Off
1:FnOn
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
:For(variable,begin,end
[,increment])
:commands
Executes commands
through End, incrementing
variable from begin by
increment until
†
CTL
4:For(
:End
:commands
variable>end.
fPart(value)
Returns the fractional part
or parts of a real or
NUM
complex number,
4:fPart(
expression, list, or matrix.
Üpdf(x,numerator df,
Computes the Û
y =
DISTR
9:Üpdf(
denominator df)
distribution probability
between lowerbound and
upperbound for the specified
numerator df (degrees of
freedom) and denominator
df.
Displays a real or complex
number, expression, list, or
matrix as a fraction
simplified to its simplest
terms.
value4Frac
MATH
1:4Frac
Full
Sets full screen mode.
† z
Full
Func
Sets function graphing
mode.
† z
Func
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
GarbageCollect
Displays the garbage
collection menu to allow
cleanup of unused archive
memory.
y N
GarbageCollect
gcd(valueA,valueB)
Returns the greatest
NUM
9:gcd(
common divisor of valueA
and valueB, which can be
real numbers or lists.
geometcdf(p,x)
Computes a cumulative
probability at x, the number
of the trial on which the first
success occurs, for the
discrete geometric
y =
DISTR
F:geometcdf(
distribution with the
specified probability of
success p.
geometpdf(p,x)
Computes a probability at x,
the number of the trial on
which the first success
occurs, for the discrete
geometric distribution with
the specified probability of
success p.
y =
DISTR
E:geometpdf(
Get(variable)
Gets data from the CBL 2™
or CBR™ System and
stores it in variable.
†
I/O
A:Get(
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
GetCalc(variable
[,portflag])
Gets contents of variable on
another TI-84 Plus and
stores it to variable on the
receiving TI-84 Plus. By
default, the TI-84 Plus uses
the USB port if it is
†
I/O
0:GetCalc(
connected. If the USB
cable is not connected, it
uses the I/O port.
portflag=0 use USB port if
connected;
portflag=1 use USB port;
portflag=2 use I/O port.
getDate
Returns a list giving the
date according to the
current value of the clock.
The list is in
y N
getDate
{year,month,day} format.
getDtFmt
Returns an integer
representing the date
format that is currently set
on the device.
y N
getDtFmt
1 = M/D/Y
2 = D/M/Y
3 = Y/M/D
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
getDtStr(integer)
Returns a string of the
current date in the format
specified by integer, where:
1 = M/D/Y
y N
getDtStr(
2 = D/M/Y
3 = Y/M/D
getKey
Returns the key code for
the current keystroke, or 0,
if no key is pressed.
†
I/O
7:getKey
getTime
Returns a list giving the
time according to the
current value of the clock.
The list is in
y N
getTime
{hour,minute,second} format.
The time is returned in the
24 hour format.
getTmFmt
Returns an integer
y N
representing the clock time
format that is currently set
on the device.
getTmFmt
12 = 12 hour format
24 = 24 hour format
getTmStr(integer)
Returns a string of the
current clock time in the
format specified by integer,
where:
y N
getTmStr(
12 = 12 hour format
24 = 24 hour format
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Goto label
Transfers control to label.
†
CTL
0:Goto
GraphStyle(function#,
graphstyle#)
Sets a graphstyle for
function#.
†
CTL
H:GraphStyle(
GridOff
GridOn
G-T
Turns off grid format.
Turns on grid format.
† y .
GridOff
† y .
GridOn
Sets graph-table vertical
split-screen mode.
† z
G-T
Horiz
Sets horizontal split-screen
mode.
† z
Horiz
Horizontal y
Draws a horizontal line at y.
y <
DRAW
3:Horizontal
identity(dimension)
Returns the identity matrix
of dimension rows x
y >
MATH
dimension columns.
5:identity(
:If condition
:commandA
:commands
If condition = 0 (false), skips
commandA.
†
CTL
1:If
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
:If condition
:Then
:commands
:End
Executes commands from
Then to End if condition = 1
(true).
†
CTL
2:Then
:commands
:If condition
:Then
Executes commands from
Then to Else if
†
CTL
:commands
:Else
:commands
:End
condition = 1 (true); from
Else to End if condition = 0
(false).
3:Else
:commands
imag(value)
Returns the imaginary
(nonreal) part of a complex
number or list of complex
numbers.
CPX
3:imag(
IndpntAsk
IndpntAuto
Input
Sets table to ask for
independent-variable
values.
† y -
Indpnt: Ask
Sets table to generate
independent-variable
values automatically.
† y -
Indpnt: Auto
Displays graph.
†
I/O
1:Input
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Input [variable]
Input ["text",variable]
Prompts for value to store
to variable.
†
I/O
1:Input
Input [Strn,variable]
Displays Strn and stores
entered value to variable.
†
I/O
1:Input
inString(string,substring
[,start])
Returns the character
position in string of the first
character of substring
beginning at start.
y N
inString(
int(value)
Returns the largest integer
a real or complex
NUM
number, expression, list, or 5:int(
matrix.
Computes the sum,
rounded to roundvalue, of
the interest amount
GInt(pmt1,pmt2
[,roundvalue])
Π1:Finance
CALC
A:GInt(
between pmt1 and pmt2 for
an amortization schedule.
Computes the inverse
cumulative normal
invNorm(area[,m,s])
y =
DISTR
distribution function for a
given area under the
normal distribution curve
specified by m and s.
3:invNorm(
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
invT(area,df)
Computes the inverse
cumulative student-t
probability function
y =
DISTR
4:invT(
specified by degree of
freedom, df for a given area
under the curve.
iPart(value)
Returns the integer part of
a real or complex number,
expression, list, or matrix.
NUM
3:iPart(
irr(CF0,CFList[,CFFreq]) Returns the interest rate at
which the net present value
of the cash flow is equal to
zero.
Π1:Finance
CALC
8:irr(
:IS>(variable,value)
:commandA
:commands
Increments variable by 1;
skips commandA if
variable>value.
†
CTL
A:IS>(
isClockOn
Identifies if clock is ON or
OFF. Returns 1 if the clock
is ON. Returns 0 if the
clock is OFF.
y N
isClockOn
Identifies the next one to
five characters as a user-
created list name.
Ùlistname
y 9
OPS
B:Ù
LabelOff
Turns off axes labels.
† y .
LabelOff
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
LabelOn
Turns on axes labels.
† y .
LabelOn
Lbl label
Creates a label of one or
two characters.
†
CTL
9:Lbl
lcm(valueA,valueB)
Returns the least common
multiple of valueA and
valueB, which can be real
numbers or lists.
NUM
8:lcm(
length(string)
Returns the number of
characters in string.
y N
length(
Line(X1,Y1,X2,Y2)
Draws a line from (X1,Y1) to
(X2,Y2).
y <
DRAW
2:Line(
Line(X1,Y1,X2,Y2,0)
Erases a line from (X1,Y1)
to (X2,Y2).
y <
DRAW
2:Line(
LinReg(a+bx) [Xlistname, Fits a linear regression
…
Ylistname,freqlist,
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
CALC
regequ]
8:LinReg(a+bx)
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
LinReg(ax+b) [Xlistname, Fits a linear regression
…
Ylistname,freqlist,
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
CALC
regequ]
4:LinReg(ax+b)
LinRegTTest [Xlistname, Performs a linear
† …
Ylistname,freqlist,
regression and a t-test.
TESTS
alternative,regequ]
alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
F:LinRegTTest
LinRegTInt [Xlistname,
Ylistname,freqlist,
confidence level, regequ]
Performs a linear
† …
regression and computes
the t confidence interval for
the slope coefficient b.
TESTS
G:LinRegTInt
Returns a list containing
the differences between
consecutive elements in
list.
@List(list)
y 9
OPS
7:@List(
Fills matrixname column by
column with the elements
from each specified
listname.
List 4 matr(listname1,...,
listname n,matrixname)
y 9
OPS
0:List 4 matr(
ln(value)
Returns the natural
logarithm of a real or
complex number,
expression, or list.
µ
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
LnReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a logarithmic
…
regression model to
Xlistname and Ylistname with
frequency freqlist, and
stores the regression
equation to regequ.
CALC
9:LnReg
log(value)
Returns logarithm of a real
or complex number,
expression, or list.
«
Logistic [Xlistname,
Ylistname,freqlist,
regequ]
Fits a logistic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
B:Logistic
Manual-Fit equname
Fits a linear equation to a
scatter plot.
…
CALC
D:Manual-Fit
Fills each listname with
elements from each
column in matrix.
Matr4list(matrix,
listnameA,...,listname n)
y 9
OPS
A:Matr4list(
Fills a listname with
elements from a specified
column# in matrix.
Matr4list(matrix,
column#,listname)
y 9
OPS
A:Matr4list(
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
max(valueA,valueB)
Returns the larger of valueA
and valueB.
NUM
7:max(
max(list)
Returns largest real or
complex element in list.
y 9
MATH
2:max(
max(listA,listB)
Returns a real or complex
list of the larger of each pair
of elements in listA and
listB.
y 9
MATH
2:max(
max(value,list)
Returns a real or complex
list of the larger of value or
each list element.
y 9
MATH
2:max(
mean(list[,freqlist])
median(list[,freqlist])
Returns the mean of list
with frequency freqlist.
y 9
MATH
3:mean(
Returns the median of list
with frequency freqlist.
y 9
MATH
4:median(
Med-Med [Xlistname,
Ylistname,freqlist,
regequ]
Fits a median-median
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
3:Med-Med
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Menu("title","text1",
label1[,...,"text7",label7])
Generates a menu of up to
seven items during
†
CTL
program execution.
C:Menu(
min(valueA,valueB)
min(list)
Returns smaller of valueA
and valueB.
NUM
6:min(
Returns smallest real or
complex element in list.
y 9
MATH
1:min(
min(listA,listB)
Returns real or complex list
of the smaller of each pair
of elements in listA and
listB.
y 9
MATH
1:min(
min(value,list)
valueA nCr valueB
value nCr list
Returns a real or complex
list of the smaller of value or
each list element.
y 9
MATH
1:min(
Returns the number of
combinations of valueA
taken valueB at a time.
PRB
3:nCr
Returns a list of the
combinations of value taken
each element in list at a
time.
PRB
3:nCr
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
list nCr value
Returns a list of the
combinations of each
element in list taken value
at a time.
PRB
3:nCr
listA nCr listB
Returns a list of the
PRB
3:nCr
combinations of each
element in listA taken each
element in listB at a time.
nDeriv(expression,
variable,value[,H])
Returns approximate
numerical derivative of
expression with respect to
variable at value, with
specified H.
MATH
8:nDeriv(
Computes the nominal
interest rate.
4Nom(effective rate,
compounding periods)
Π1:Finance
CALC
B:4Nom(
Normal
Sets normal display mode.
† z
Normal
normalcdf(lowerbound,
upperbound[,m,s])
Computes the normal
distribution probability
between lowerbound and
upperbound for the specified
m and s.
y =
DISTR
2:normalcdf(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Computes the probability
density function for the
normal distribution at a
specified x value for the
specified m and s.
normalpdf(x[,m,s])
y =
DISTR
1:normalpdf(
not(value)
Returns 0 if value is ƒ 0.
value can be a real number, LOGIC
y :
expression, or list.
4:not(
valueA nPr valueB
value nPr list
Returns the number of
permutations of valueA
taken valueB at a time.
PRB
2:nPr
Returns a list of the
permutations of value taken
each element in list at a
time.
PRB
2:nPr
list nPr value
Returns a list of the
permutations of each
element in list taken value
at a time.
PRB
2:nPr
listA nPr listB
Returns a list of the
PRB
2:nPr
permutations of each
element in listA taken each
element in listB at a time.
npv(interest rate,CF0,
CFList[,CFFreq])
Computes the sum of the
present values for cash
inflows and outflows.
Π1:Finance
CALC
7:npv(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
valueA or valueB
Returns 1 if valueA or
valueB is ƒ 0. valueA and
valueB can be real
numbers, expressions, or
lists.
y :
LOGIC
2:or
Output(row,column,
"text")
Displays text beginning at
specified row and column.
†
I/O
6:Output(
Output(row,column,
value)
Displays value beginning at
specified row and column.
†
I/O
6:Output(
Param
Pause
Sets parametric graphing
mode.
† z
Par
Suspends program
execution until you press
Í.
†
CTL
8:Pause
Pause [value]
Displays value; suspends
program execution until
you press Í.
†
CTL
8:Pause
Plot#(type,Xlistname,
Ylistname,mark)
Defines Plot# (1, 2, or 3) of
type Scatter or xyLine for
Xlistname and Ylistname
using mark.
† y ,
STAT PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Plot#(type,Xlistname,
freqlist)
Defines Plot# (1, 2, or 3) of
type Histogram or Boxplot
for Xlistname with frequency
freqlist.
† y ,
STAT PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
Plot#(type,Xlistname,
freqlist,mark)
Defines Plot# (1, 2, or 3) of
type ModBoxplot for
Xlistname with frequency
freqlist using mark.
† y ,
STAT PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
Plot#(type,datalistname,
data axis,mark)
Defines Plot# (1, 2, or 3) of
type NormProbPlot for
datalistname on data axis
using mark. data axis can be
X or Y.
† y ,
STAT PLOTS
1:Plot1-
2:Plot2-
3:Plot3-
PlotsOff [1,2,3]
PlotsOn [1,2,3]
Pmt_Bgn
Deselects all stat plots or
one or more specified stat
plots (1, 2, or 3).
y ,
STAT PLOTS
4:PlotsOff
Selects all stat plots or one
or more specified stat plots
(1, 2, or 3).
y ,
STAT PLOTS
5:PlotsOn
Specifies an annuity due,
where payments occur at
the beginning of each
payment period.
Π1:Finance
CALC
F:Pmt_Bgn
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Pmt_End
Specifies an ordinary
annuity, where payments
occur at the end of each
payment period.
Π1:Finance
CALC
E:Pmt_End
Computes a cumulative
probability at x for the
discrete Poisson
poissoncdf(m,x)
y =
DISTR
D:poissoncdf(
distribution with specified
mean m.
Computes a probability at x
for the discrete Poisson
distribution with the
poissonpdf(m,x)
y =
DISTR
C:poissonpdf(
specified mean m.
Polar
Sets polar graphing mode.
† z
Pol
Displays complex value in
polar format.
complex value 4Polar
CPX
7:4Polar
PolarGC
Sets polar graphing
coordinates format.
† y .
PolarGC
prgmname
Executes the program
name.
†
CTRL
D:prgm
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Computes the sum,
rounded to roundvalue, of
the principal amount
GPrn(pmt1,pmt2
[,roundvalue])
Π1:Finance
CALC
0:GPrn(
between pmt1 and pmt2 for
an amortization schedule.
prod(list[,start,end])
Returns product of list
elements between start and
end.
y 9
MATH
6:prod(
Prompt variableA
[,variableB,...,variable n]
Prompts for value for
variableA, then variableB,
and so on.
†
I/O
2:Prompt
1-PropZInt(x,n
[,confidence level])
Computes a one-proportion
z confidence interval.
† …
TESTS
A:1-PropZInt(
2-PropZInt(x1,n1,x2,n2
[,confidence level])
Computes a two-proportion
z confidence interval.
† …
TESTS
B:2-PropZInt(
1-PropZTest(p0,x,n
[,alternative,drawflag])
Computes a one-proportion
z test. alternative=L1 is <;
alternative=0 is ƒ;
† …
TESTS
5:1-PropZTest(
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
2-PropZTest(x1,n1,x2,n2 Computes a two-proportion
† …
[,alternative,drawflag])
z test. alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
TESTS
6:2-PropZTest(
Pt-Change(x,y)
Pt-Off(x,y[,mark])
Pt-On(x,y[,mark])
Reverses a point at (x,y).
y <
POINTS
3:Pt-Change(
Erases a point at (x,y) using
mark.
y <
POINTS
2:Pt-Off(
Draws a point at (x,y) using
mark.
y <
POINTS
1:Pt-On(
PwrReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a power regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
A:PwrReg
Pxl-Change(row,column) Reverses pixel at
(row,column); 0 row 62
and 0 column 94.
y <
POINTS
6:Pxl-Change(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Pxl-Off(row,column)
Erases pixel at
(row,column); 0 row 62
and 0 column 94.
y <
POINTS
5:Pxl-Off(
Pxl-On(row,column)
Draws pixel at (row,column);
0 row 62 and
y <
POINTS
4:Pxl-On(
0 column 94.
pxl-Test(row,column)
Returns 1 if pixel (row,
column) is on, 0 if it is off;
0 row 62 and
y <
POINTS
7:pxl-Test(
0 column 94.
Returns X, given polar
coordinates r and q or a list
of polar coordinates.
P4Rx(r,q)
y ;
ANGLE
7:P4Rx(
Returns Y, given polar
coordinates r and q or a list
of polar coordinates.
P4Ry(r,q)
y ;
ANGLE
8:P4Ry(
QuadReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a quadratic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
5:QuadReg
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
QuartReg [Xlistname,
Ylistname,freqlist,
regequ]
Fits a quartic regression
model to Xlistname and
Ylistname with frequency
freqlist, and stores the
regression equation to
regequ.
…
CALC
7:QuartReg
Radian
Sets radian angle mode.
† z
Radian
rand[(numtrials)]
Returns a random number
between 0 and 1 for a
specified number of trials
numtrials.
PRB
1:rand
randBin(numtrials,prob
[,numsimulations])
Generates and displays a
random real number from a
specified Binomial
PRB
7:randBin(
distribution.
randInt( lower,upper
[,numtrials])
Generates and displays a
random integer within a
range specified by lower
and upper integer bounds
for a specified number of
trials numtrials.
PRB
5:randInt(
randM(rows,columns)
Returns a random matrix of
rows (1-99) × columns
(1-99).
y >
MATH
6:randM(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Generates and displays a
random real number from a
specified Normal
randNorm(m,s
[,numtrials])
PRB
6:randNorm(
distribution specified by m
and s for a specified
number of trials numtrials.
Sets the mode to polar
complex number mode
(re^qi).
re^qi
† z
re^qi
Real
Sets mode to display
complex results only when
you enter complex
numbers.
† z
Real
real(value)
Returns the real part of a
complex number or list of
complex numbers.
CPX
2:real(
RecallGDB n
RecallPic n
Restores all settings stored
in the graph database
variable GDBn.
y <
STO
4:RecallGDB
Displays the graph and
adds the picture stored in
Picn.
y <
STO
2:RecallPic
Displays complex value or
list in rectangular format.
complex value 4Rect
CPX
6:4Rect
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
RectGC
Sets rectangular graphing
coordinates format.
† y .
RectGC
ref(matrix)
Returns the row-echelon
form of a matrix.
y >
MATH
A:ref(
:Repeat condition
:commands
:End
Executes commands until
condition is true.
†
CTL
6:Repeat
:commands
Return
Returns to the calling
program.
†
CTL
E:Return
round(value[,#decimals]) Returns a number,
expression, list, or matrix
NUM
rounded to #decimals ( 9).
2:round(
Returns a matrix with row
of matrix multiplied by value
and stored in row.
ärow(value,matrix,row)
y >
MATH
E:ärow(
row+(matrix,rowA,rowB)
Returns a matrix with rowA
of matrix added to rowB and
stored in rowB.
y >
MATH
D:row+(
Returns a matrix with rowA
of matrix multiplied by
value, added to rowB, and
stored in rowB.
ärow+(value,matrix,
y >
MATH
F:ärow+(
rowA,rowB)
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
rowSwap(matrix,rowA,
rowB)
Returns a matrix with rowA
of matrix swapped with
rowB.
y >
MATH
C:rowSwap(
rref(matrix)
Returns the reduced row-
echelon form of a matrix.
y >
MATH
B:rref(
Returns R, given
R4Pr(x,y)
y ;
ANGLE
5:R4Pr(
rectangular coordinates x
and y or a list of rectangular
coordinates.
R4Pq(x,y)
Returns q, given
y ;
ANGLE
6:R4Pq(
rectangular coordinates x
and y or a list of rectangular
coordinates.
Performs a two-sample
Û test. alternative=L1 is <;
alternative=0 is ƒ;
2-SampÜTest [listname1,
listname2,freqlist1,
freqlist2,alternative,
drawflag]
† …
TESTS
E:2-SampÜTest
alternative=1 is >.
(Data list input)
drawflag=1 draws results;
drawflag=0 calculates
results.
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Performs a two-sample
Û test. alternative=L1 is <;
alternative=0 is ƒ;
2-SampÜTest Sx1,n1,
Sx2,n2[,alternative,
drawflag]
† …
TESTS
E:2-SampÜTest
(Summary stats input)
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
2-SampTInt [listname1,
listname2,
freqlist1,freqlist2,
confidence level,pooled]
(Data list input)
Computes a two-sample t
confidence interval.
pooled=1 pools variances;
pooled=0 does not pool
variances.
† …
TESTS
0:2-SampTInt
Computes a two-sample t
confidence interval.
pooled=1 pools variances;
pooled=0 does not pool
variances.
2-SampTInt v1,Sx1,n1,
v2,Sx2,n2
[,confidence level,pooled]
(Summary stats input)
† …
TESTS
0:2-SampTInt
2-SampTTest [listname1, Computes a two-sample t
† …
listname2,freqlist1,
freqlist2,alternative,
pooled,drawflag]
(Data list input)
test. alternative=L1 is <;
alternative=0 is ƒ;
TESTS
4:2-SampTTest
alternative=1 is >. pooled=1
pools variances; pooled=0
does not pool variances.
drawflag=1 draws results;
drawflag=0 calculates
results.
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Computes a two-sample t
test. alternative=L1 is <;
alternative=0 is ƒ;
2-SampTTest v1,Sx1,n1,
v2,Sx2,n2[,alternative,
pooled,drawflag]
† …
TESTS
4:2-SampTTest
(Summary stats input)
alternative=1 is >. pooled=1
pools variances; pooled=0
does not pool variances.
drawflag=1 draws results;
drawflag=0 calculates
results.
Computes a two-sample z
confidence interval.
2-SampZInt(s ,s
† …
1
2
TESTS
[,listname1,listname2,
freqlist1,freqlist2,
confidence level])
(Data list input)
9:2-SampZInt(
Computes a two-sample z
confidence interval.
2-SampZInt(s ,s ,
† …
1
2
TESTS
v1,n1,v2,n2
[,confidence level])
9:2-SampZInt(
(Summary stats input)
Computes a two-sample z
test. alternative=L1 is <;
alternative=0 is ƒ;
2-SampZTest(s ,s
† …
1
2
TESTS
[,listname1,listname2,
freqlist1,freqlist2,
3:2-SampZTest(
alternative=1 is >.
alternative,drawflag])
(Data list input)
drawflag=1 draws results;
drawflag=0 calculates
results.
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments Result
Keys/Menu or
Screen/Item
Computes a two-sample z
2-SampZTest(s ,s ,
† …
1
2
test. alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
TESTS
v1,n1,v2,n2
[,alternative,drawflag])
(Summary stats input)
3:2-SampZTest(
Sci
Sets scientific notation
display mode.
† z
Sci
Select(Xlistname,
Ylistname)
Selects one or more
y 9
OPS
8:Select(
specific data points from a
scatter plot or xyLine plot
(only), and then store•s the
selected data points to two
new lists, Xlistname and
Ylistname.
Send(variable)
Sends contents of variable
to the CBL 2™ or CBR™
System.
†
I/O
B:Send(
seq(expression,variable,
begin,end[,increment])
Returns list created by
evaluating expression with
regard to variable, from
begin to end by increment.
y 9
OPS
5:seq(
Seq
Sets sequence graphing
mode.
† z
Seq
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Sequential
Sets mode to graph
functions sequentially.
† z
Sequential
setDate(year,month,day)
Sets the date using a year,
month, day format. The
y N
setDate(
year must be 4 digits; month
and day can be 1 or 2 digit.
setDtFmt(integer)
Sets the date format.
1 = M/D/Y
y N
setDtFmt(
2 = D/M/Y
3 = Y/M/D
setTime(hour,minute,
second)
Sets the time using an
hour, minute, second
format. The hour must be in
24 hour format, in which 13
= 1 p.m.
y N
setTime(
setTmFmt(integer)
Sets the time format.
12 = 12 hour format
24 = 24 hour format
y N
setTmFmt(
SetUpEditor
Removes all list names
from the stat list editor, and
then restores list names L1
through L6 to columns 1
through 6.
…
EDIT
5:SetUpEditor
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
SetUpEditor listname1
[,listname2,...,
listname20]
Removes all list names
from the stat list editor, then
sets it up to display one or
more listnames in the
specified order, starting
with column 1.
…
EDIT
5:SetUpEditor
Shade(lowerfunc,
upperfunc[,Xleft,Xright,
pattern,patres])
Draws lowerfunc and
upperfunc in terms of X on
the current graph and uses
pattern and patres to shade
the area bounded by
lowerfunc, upperfunc, Xleft,
and Xright.
y <
DRAW
7:Shade(
2
Draws the density function
y =
Shadec (lowerbound,
2
DRAW
for the c distribution
upperbound,df)
2
specified by degrees of
freedom df and shades the
area between lowerbound
and upperbound.
3:Shadec (
Draws the density function
for the Û distribution
ShadeÜ(lowerbound,
upperbound,
numerator df,
y =
DRAW
4:ShadeÜ(
specified by numerator df
and denominator df and
shades the area between
lowerbound and upperbound.
denominator df)
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
ShadeNorm(lowerbound, Draws the normal density
y =
DRAW
1:ShadeNorm(
upperbound[,m,s])
function specified by m and
s and shades the area
between lowerbound and
upperbound.
Shade_t(lowerbound,
upperbound,df)
Draws the density function
for the Student-t
y =
DRAW
distribution specified by
degrees of freedom df, and
shades the area between
lowerbound and upperbound.
2:Shade_t(
Simul
Sets mode to graph
functions simultaneously.
† z
Simul
sin(value)
Returns the sine of a real
number, expression, or list.
˜
L1
Returns the arcsine of a
real number, expression, or
list.
y ?
sin (value)
sinh(value)
Returns the hyperbolic sine
of a real number,
y N
sinh(
expression, or list.
L1
Returns the hyperbolic
arcsine of a real number,
expression, or list.
y N
sinh (
sinh (value)
L1
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
SinReg [iterations,
Xlistname,Ylistname,
period,regequ]
Attempts iterations times to
fit a sinusoidal regression
model to Xlistname and
Ylistname using a period
guess, and stores the
regression equation to
regequ.
…
CALC
C:SinReg
solve(expression,
variable,guess,
{lower,upper})
Solves expression for
variable, given an initial
guess and lower and upper
bounds within which the
solution is sought.
†
MATH
0:solve(
SortA(listname)
Sorts elements of listname
in ascending order.
y 9
OPS
1:SortA(
SortA(keylistname,
dependlist1[,dependlist2,
...,dependlist n])
Sorts elements of
keylistname in ascending
order, then sorts each
dependlist as a dependent
list.
y 9
OPS
1:SortA(
SortD(listname)
Sorts elements of listname
in descending order.
y 9
OPS
2:SortD(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
SortD(keylistname,dependl Sorts elements of
y 9
OPS
ist1[,dependlist2,
keylistname in descending
..., dependlist n])
order, then sorts each
dependlist as a dependent
list.
2:SortD(
startTmr
Starts the clock timer. Store
or note the displayed value,
and use it as the argument
for checkTmr( ) to check
the elapsed time.
y N
startTmr
stdDev(list[,freqlist])
Returns the standard
deviation of the elements in
list with frequency freqlist.
y 9
MATH
7:stdDev(
Stop
Ends program execution;
returns to home screen.
†
CTL
F:Stop
Stores value in variable.
Store: value!variable
¿
StoreGDB n
Stores current graph in
database GDBn.
y <
STO
3:StoreGDB
StorePic n
Stores current picture in
picture Picn.
y <
STO
1:StorePic
Converts string into an
equation and stores it in Y=
var.
String4Equ(string,Y= var)
y N
String4Equ(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
sub(string,begin,length)
Returns a string that is a
subset of another string,
from begin to length.
y N
sub(
sum(list[,start,end])
Returns the sum of
elements of list from start to
end.
y 9
MATH
5:sum(
tan(value)
Returns the tangent of a
real number, expression, or
list.
š
L1
Returns the arctangent of a
real number, expression, or
list.
y A
tan (value)
Tangent(expression,
value)
Draws a line tangent to
expression at X=value.
y <
DRAW
5:Tangent(
tanh(value)
Returns hyperbolic tangent
of a real number,
y N
tanh(
expression, or list.
L1
Returns the hyperbolic
arctangent of a real
number, expression, or list.
y N
tanh (
tanh (value)
L1
tcdf(lowerbound,
upperbound,df)
Computes the Student-t
distribution probability
between lowerbound and
upperbound for the specified
degrees of freedom df.
y =
DISTR
6:tcdf(
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Text(row,column,text1,
text2,...,text n)
Writes text on graph
beginning at pixel
(row,column), where
0 row 57 and
0 column 94.
y <
DRAW
0:Text(
Then
See If:Then
Time
Sets sequence graphs to
plot with respect to time.
† y .
Time
timeCnv(seconds)
Converts seconds to units
of time that can be more
easily understood for
evaluation. The list is in
{days,hours,minutes,seconds}
format.
y N
timeCnv
TInterval [listname,
freqlist,confidence level]
(Data list input)
Computes a t confidence
interval.
† …
TESTS
8:TInterval
Computes a t confidence
interval.
TInterval v,Sx,n
[,confidence level]
(Summary stats input)
† …
TESTS
8:TInterval
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
tpdf(x,df)
Computes the probability
density function (pdf) for
the Student-t distribution at
a specified x value with
specified degrees of
freedom df.
y =
DISTR
5:tpdf(
Trace
Displays the graph and
enters TRACE mode.
r
Performs a t test with
frequency freqlist.
alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
T-Test m0[,listname,
freqlist,alternative,
drawflag]
† …
TESTS
2:T-Test
(Data list input)
Performs a t test with
frequency freqlist.
alternative=L1 is < ;
alternative=0 is ă;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
T-Test m0, v,Sx,n
[,alternative,drawflag]
(Summary stats input)
† …
TESTS
2:T-Test
Computes the future value.
tvm_FV[(Ú,æ,PV,PMT,
Π1:Finance
CALC
P/Y,C/Y)]
6:tvm_FV
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Computes the annual
interest rate.
tvm_æ[(Ú,PV,PMT,FV,
Π1:Finance
CALC
P/Y,C/Y)]
3:tvm_æ
Computes the number of
payment periods.
tvm_Ú[(æ,PV,PMT,FV,
Π1:Finance
CALC
P/Y,C/Y)]
5:tvm_Ú
Computes the amount of
each payment.
tvm_Pmt[(Ú,æ,PV,FV,
Π1:Finance
CALC
P/Y,C/Y)]
2:tvm_Pmt
Computes the present
value.
tvm_PV[(Ú,æ,PMT,FV,
Π1:Finance
CALC
P/Y,C/Y)]
4:tvm_PV
UnArchive
Moves the specified
variables from the user
data archive memory to
RAM.
y L
6:UnArchive
To archive variables, use
Archive.
uvAxes
uwAxes
Sets sequence graphs to
plot u(n) on the x-axis and
v(n) on the y-axis.
† y .
uv
Sets sequence graphs to
plot u(n) on the x-axis and
w(n) on the y-axis.
† y .
uw
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
1-Var Stats [Xlistname,
freqlist]
Performs one-variable
analysis on the data in
Xlistname with frequency
freqlist.
…
CALC
1:1-Var Stats
2-Var Stats [Xlistname,
Ylistname,freqlist]
Performs two-variable
analysis on the data in
Xlistname and Ylistname with
frequency freqlist.
…
CALC
2:2-Var Stats
variance(list[,freqlist])
Vertical x
Returns the variance of the
elements in list with
frequency freqlist.
y 9
MATH
8:variance(
Draws a vertical line at x.
y <
DRAW
4:Vertical
vwAxes
Sets sequence graphs to
plot v(n) on the x-axis and
w(n) on the y-axis.
† y .
vw
Web
Sets sequence graphs to
trace as webs.
† y .
Web
:While condition
:commands
:End
Executes commands while
condition is true.
†
CTL
5:While
:command
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
valueA xor valueB
Returns 1 if only valueA or
valueB = 0. valueA and
valueB can be real
numbers, expressions, or
lists.
y :
LOGIC
3:xor
ZBox
Displays a graph, lets you
draw a box that defines a
new viewing window, and
updates the window.
† q
ZOOM
1:ZBox
ZDecimal
Adjusts the viewing window
so that @X=0.1 and
@Y=0.1, and displays the
graph screen with the
origin centered on the
screen.
† q
ZOOM
4:ZDecimal
ZInteger
Redefines the viewing
window using these
dimensions:
† q
ZOOM
8:ZInteger
@X=1
@Y=1
Xscl=10
Yscl=10
Computes a z confidence
interval.
ZInterval s[,listname,
freqlist,confidence level]
(Data list input)
† …
TESTS
7:ZInterval
Computes a z confidence
interval.
ZInterval s,v,n
[,confidence level]
(Summary stats input)
† …
TESTS
7:ZInterval
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Zoom In
Magnifies the part of the
graph that surrounds the
cursor location.
† q
ZOOM
2:Zoom In
Zoom Out
ZoomFit
Displays a greater portion
of the graph, centered on
the cursor location.
† q
ZOOM
3:Zoom Out
Recalculates Ymin and
Ymax to include the
minimum and maximum Y
values, between Xmin and
Xmax, of the selected
functions and replots the
functions.
† q
ZOOM
0:ZoomFit
ZoomRcl
ZoomStat
Graphs the selected
functions in a user-defined
viewing window.
† q
MEMORY
3:ZoomRcl
Redefines the viewing
window so that all
statistical data points are
displayed.
† q
ZOOM
9:ZoomStat
ZoomSto
Immediately stores the
current viewing window.
† q
MEMORY
2:ZoomSto
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
ZPrevious
Replots the graph using the
window variables of the
graph that was displayed
before you executed the
last ZOOM instruction.
† q
MEMORY
1:ZPrevious
ZSquare
Adjusts the X or Y window
settings so that each pixel
represents an equal width
and height in the
† q
ZOOM
5:ZSquare
coordinate system, and
updates the viewing
window.
ZStandard
Replots the functions
immediately, updating the
window variables to the
default values.
† q
ZOOM
6:ZStandard
Performs a z test with
frequency freqlist.
alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
Z-Test(m0,s[,listname,
freqlist,alternative,
drawflag])
† …
TESTS
1:Z-Test(
(Data list input)
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Performs a z test.
alternative=L1 is <;
alternative=0 is ƒ;
alternative=1 is >.
drawflag=1 draws results;
drawflag=0 calculates
results.
Z-Test(m0,s,v,n
[,alternative,drawflag])
(Summary stats input)
† …
TESTS
1:Z-Test(
ZTrig
Replots the functions
immediately, updating the
window variables to preset
values for plotting trig
functions.
† q
ZOOM
7:ZTrig
Factorial: value!
Returns factorial of value.
PRB
4:!
Factorial: list!
Returns factorial of list
elements.
PRB
4:!
Interprets value as degrees;
designates degrees in
DMS format.
Degrees notation: value¡
y ;
ANGLE
1:¡
r
Interprets angle as radians.
y ;
Radian: angle
ANGLE
r
3:
Appendix A: Functions and Instructions
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
T
Returns a matrix in which
each element (row, column)
is swapped with the
corresponding element
(column, row) of matrix.
y >
Transpose: matrix
MATH
T
2:
th
x
th
x root ‡value
Returns x root of value.
MATH
x
5: ‡
th
x
th
x root ‡list
Returns x root of list
MATH
elements.
x
5: ‡
x
Returns list roots of value.
list ‡value
MATH
x
5: ‡
x
Returns listA roots of listB.
listA ‡listB
MATH
x
5: ‡
3
Returns the cube of a real
or complex number,
expression, list, or square
matrix.
Cube: value
MATH
3
3:
3
Returns the cube root of a
real or complex number,
expression, or list.
Cube root: ‡(value)
MATH
3
4: ‡(
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Equal: valueA=valueB
Returns 1 if
y :
TEST
1:=
valueA = valueB. Returns 0
if valueA ƒ valueB. valueA
and valueB can be real or
complex numbers,
expressions, lists, or
matrices.
Not equal:
valueAƒvalueB
Returns 1 if
y :
TEST
2:ƒ
valueA ƒ valueB. Returns 0
if valueA = valueB. valueA
and valueB can be real or
complex numbers,
expressions, lists, or
matrices.
Less than:
valueA<valueB
Returns 1 if
y :
TEST
5:<
valueA < valueB. Returns 0
if valueA ‚ valueB. valueA
and valueB can be real or
complex numbers,
expressions, or lists.
Greater than:
valueA>valueB
Returns 1 if
y :
TEST
3:>
valueA > valueB. Returns 0
if valueA valueB. valueA
and valueB can be real or
complex numbers,
expressions, or lists.
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Less than or equal:
valueAvalueB
Returns 1 if
y :
TEST
6:
valueA valueB. Returns 0
if valueA > valueB. valueA
and valueB can be real or
complex numbers,
expressions, or lists.
Greater than or equal:
valueA‚valueB
Returns 1 if valueA ‚
valueB. Returns 0 if
y :
TEST
valueA < valueB. valueA and
valueB can be real or
complex numbers,
4:‚
expressions, or lists.
L1
Returns 1 divided by a real
or complex number or
expression.
—
—
Inverse: value
L1
Returns 1 divided by list
elements.
Inverse: list
L1
Returns matrix inverted.
—
¡
Inverse: matrix
2
Returns value multiplied by
itself. value can be a real or
complex number or
expression.
Square: value
2
Returns list elements
squared.
¡
¡
Square: list
2
Returns matrix multiplied by
itself.
Square: matrix
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Powers: value^power
Returns value raised to
power. value can be a real
or complex number or
expression.
›
Powers: list^power
Powers: value^list
Powers: matrix^power
Negation: Lvalue
Returns list elements
raised to power.
›
›
›
Ì
Returns value raised to list
elements.
Returns matrix elements
raised to power.
Returns the negative of a
real or complex number,
expression, list, or matrix.
Power of ten: 10^(value) Returns 10 raised to the
value power. value can be a
real or complex number or
y G
expression.
Power of ten: 10^(list)
Returns a list of 10 raised
to the list power.
y G
y C
Returns square root of a
real or complex number,
expression, or list.
Square root: ‡(value)
Multiplication:
valueAävalueB
Returns valueA times
valueB.
¯
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Multiplication:
valueälist
Returns value times each
list element.
¯
¯
¯
¯
¯
¥
¥
¥
¥
Multiplication:
listävalue
Returns each list element
times value.
Multiplication:
listAälistB
Returns listA elements
times listB elements.
Multiplication:
valueämatrix
Returns value times matrix
elements.
Multiplication:
matrixAämatrixB
Returns matrixA times
matrixB.
Returns valueA divided by
valueB.
Division: valueAàvalueB
Division: listàvalue
Division: valueàlist
Division: listAàlistB
Returns list elements
divided by value.
Returns value divided by
list elements.
Returns listA elements
divided by listB elements.
Addition: valueA+valueB
Returns valueA plus valueB.
Ã
Ã
Addition: list+value
Returns list in which value
is added to each list
element.
Addition: listA+listB
Returns listA elements plus
listB elements.
Ã
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Function or
Key or
Instruction/Arguments
Result
Keys/Menu or
Screen/Item
Addition:
matrixA+matrixB
Returns matrixA elements
plus matrixB elements.
Ã
Ã
¹
¹
¹
¹
¹
Concatenation:
string1+string2
Concatenates two or more
strings.
Subtraction:
valueANvalueB
Subtracts valueB from
valueA.
Subtraction:
valueNlist
Subtracts list elements
from value.
Subtraction:
listNvalue
Subtracts value from list
elements.
Subtraction:
listANlistB
Subtracts listB elements
from listA elements.
Subtraction:
matrixANmatrixB
Subtracts matrixB elements
from matrixA elements.
Minutes
notation:degrees¡minutes's
econds"
Interprets minutes angle
measurement as minutes.
y ;
ANGLE
2:'
Seconds notation:
degrees¡minutes'seconds"
Interprets seconds angle
measurement as seconds.
ƒ [ã]
626
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Appendix B:
Reference Information
Variables
User Variables
The TI-84 Plus uses the variables listed below in various ways. Some variables are
restricted to specific data types.
The variables A through Z and q are defined as real or complex numbers. You may store
to them. The TI-84 Plus can update X, Y, R, q, and T during graphing, so you may want to
avoid using these variables to store nongraphing data.
The variables (list names) L1 through L6 are restricted to lists; you cannot store another
type of data to them.
The variables (matrix names) [A] through [J] are restricted to matrices; you cannot store
another type of data to them.
The variables Pic1 through Pic9 and Pic0 are restricted to pictures; you cannot store
another type of data to them.
The variables GDB1 through GDB9 and GDB0 are restricted to graph databases; you
cannot store another type of data to them.
The variables Str1 through Str9 and Str0 are restricted to strings; you cannot store
another type of data to them.
Appendix B: Reference Information
627
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Except for system variables, you can store any string of characters, functions, instructions,
or variables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through
6), u(n), v(n), and w(n) directly or through the Y= editor. The validity of the string is
determined when the function is evaluated.
Archive Variables
You can store data, programs or any variable from RAM to user data archive memory
where they cannot be edited or deleted inadvertantly. Archiving also allows you to free up
RAM for variables that may require additional memory. The names of archived variables
are preceded by an asterisk “*” indicating they are in user data archive.
System Variables
The variables below must be real numbers. You may store to them. Since the TI-84 Plus
can update some of them, as the result of a ZOOM, for example, you may want to avoid
using these variables to store nongraphing data.
•
•
Xmin, Xmax, Xscl, @X, XFact, Tstep, PlotStart, nMin, and other window variables.
ZXmin, ZXmax, ZXscl, ZTstep, ZPlotStart, Zu(nMin), and other ZOOM variables.
The variables below are reserved for use by the TI-84 Plus. You cannot store to them.
2
2
n, v, Sx, sx, minX, maxX, Gy, Gy , Gxy, a, b, c, RegEQ, x1, x2, y1, z, t, F, c , Ç, v1, Sx1, n1,
2
2
lower, upper, r , R and other statistical variables.
Appendix B: Reference Information
628
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Statistics Formulas
This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA,
2-SampÜTest, and 2-SampTTest.
Logistic
The logistic regression algorithm applies nonlinear recursive least-squares techniques to
optimize the following cost function:
N
2
⎛
⎜
⎝
⎞
⎟
c
J =
----------------------- – y
i
∑
–bxi
⎠
1 + ae
i = 1
which is the sum of the squares of the residual errors,
x
y
N
where:
= the independent variable list
= the dependent variable list
= the dimension of the lists
This technique attempts to estimate the constants a, b, and c recursively to make J as
small as possible.
Appendix B: Reference Information
629
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SinReg
The sine regression algorithm applies nonlinear recursive least-squares techniques to
optimize the following cost function:
N
2
J =
[asin(bx + c) + d – y ]
i
i
∑
i = 1
which is the sum of the squares of the residual errors,
x
y
N
where:
= the independent variable list
= the dependent variable list
= the dimension of the lists
This technique attempts to recursively estimate the constants a, b, c, and d to make J as
small as possible.
ANOVA(
The ANOVA Ü statistic is:
FactorMS
ErrorMS
--------------------------
Ü =
Appendix B: Reference Information
630
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The mean squares (MS) that make up Ü are:
FactorSS
FactorMS = ------------------------
Factordf
ErrorSS
ErrorMS = ---------------------
Errordf
The sum of squares (SS) that make up the mean squares are:
I
2
FactorSS =
n (x –x)
i
i
∑
i = 1
I
2
ErrorSS =
(n –1)Sx
i
i
∑
i = 1
The degrees of freedom df that make up the mean squares are:
Factordf = I – 1 = numeratordf for Ü
I
Errordf =
(n – 1) = denominatordf for Ü
i
∑
i = 1
I
where:
= number of populations
= the mean of each list
x
i
= the standard deviation of each list
= the length of each list
= the mean of all lists
Sxi
ni
x
Appendix B: Reference Information
631
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2-SampFTest
Below is the definition for the 2-SampÜTest.
Sx1, Sx2
=
Sample standard deviations having n –1
1
and n –1 degrees of freedom df,
2
respectively.
2
Sx1
Sx2
⎛
⎝
⎞
⎠
--------
Û-statistic =
Ü
=
=
df(x, n –1 , n –1 )
Ûpdf( ) with degrees of freedom df, n –1 ,
1
2
1
and n –1
2
p
= reported p value
2-SampÜTest for the alternative hypothesis σ > σ .
1
2
α
p =
f(x,n – 1,n – 1)dx
1
2
∫
F
2-SampÜTest for the alternative hypothesis σ < σ .
1
2
F
p =
f(x,n – 1,n – 1)dx
1
2
∫
0
Appendix B: Reference Information
632
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2-SampÜTest for the alternative hypothesis s ƒ s . Limits must satisfy the following:
1
2
∞
Lbnd
p
2
-- =
f(x,n – 1,n – 1)dx =
f(x,n – 1,n – 1)dx
1
2
1
2
∫
∫
0
Ubnd
where: [Lbnd,Ubnd] = lower and upper limits
The Ü-statistic is used as the bound producing the smallest integral. The remaining
bound is selected to achieve the preceding integral’s equality relationship.
2-SampTTest
The following is the definition for the 2-SampTTest. The two-sample t statistic with
degrees of freedom df is:
x – x
1
2
t = ----------------
S
Appendix B: Reference Information
633
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where the computation of S and df are dependent on whether the variances are pooled. If
the variances are not pooled:
2
2
Sx
Sx
2
1
S = ---------- + ----------
n
n
2
1
2
2
2
⎛Sx
Sx ⎞
1
2
---------- + ----------
⎜
⎝
⎟
n
n
2
⎠
1
df = ---------------------------------------------------------------------------
2
2
2
2
Sx
Sx
⎛
⎞
⎟
⎠
⎛
⎞
⎟
⎠
1
1
1
2
-------------- ----------
-------------- ----------
+
⎜
⎜
n – 1
n
n – 1
n
2
⎝
⎝
1
1
2
otherwise:
2
2
(n – 1)Sx + (n – 1)Sx
1
1
2
2
Sx = --------------------------------------------------------------------
p
df
1
1
-----
S = ----- + Sx
p
n
n
2
1
df = n + n – 2
1
2
and Sxp is the pooled variance.
Appendix B: Reference Information
634
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Financial Formulas
This section contains financial formulas for computing time value of money, amortization,
cash flow, interest-rate conversions, and days between dates.
Time Value of Money
(y × ln(x + 1))
i = [e
]–1
PMT
y
x
C/Y
P/Y
I%
where
:
ƒ 0
= C/Y ÷ P/Y
= (.01 × I%) ÷ C/Y
= compounding periods per year
= payment periods per year
= interest rate per year
(1 ÷ N)
–
i = ( FV ÷ PV)
– 1
where: PMT = 0
Appendix B: Reference Information
635
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The iteration used to compute i:
–N
1 – (1 + i)
–N
------------------------------
0 = PV + PMT × G
+ FV × (1 + i)
i
i
(y × ln(x + 1))
I% = 100 × C ⁄ Y × [e
– 1]
x
y
i
where:
=
=
P/Y ÷ C/Y
G = 1 + i × k
i
k
k
where:
= 0 for end-of-period payments
= 1 for beginning-of-period payments
PMT × G – FV × i
i
⎛
⎝
⎞
⎠
----------------------------------------------
ln
PMT × G + PV × i
i
N = ---------------------------------------------------------
ln(1 + i)
where: i ƒ 0
–
N = (PV + FV) ÷ PMT
Appendix B: Reference Information
636
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where: i = 0
–
i
PV + FV
× PV + ---------------------------
N
-----
PMT =
G
i
(1 + i) – 1
where: i ƒ 0
–
PMT = (PV + FV) ÷ N
where: i = 0
PMT × G
PMT × G
1
i
i
PV = ------------------------ – FV × ------------------ – ------------------------
N
i
i
(1 + i)
where: i ƒ 0
–
PV = (FV + PMT × N)
where: i = 0
PMT × G
PMT × G
N
i
i
⎠
⎛
⎞
FV = ------------------------ – (1 + i) × PV + ------------------------
⎝
i
i
where: i ƒ 0
–
FV = (PV + PMT × N)
where: i = 0
Appendix B: Reference Information
637
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Amortization
If computing bal(), pmt2 = npmt
Let bal(0) = RND(PV)
Iterate from m = 1 to pmt2
–
I
= RND[RND12( i × bal(m – 1))]
⎧
⎨
⎩
m
bal(m) = bal(m – 1) – I + RND(PMT)
m
then:
bal( ) = bal(pmt2)
ΣPrn( ) = bal(pmt2) – bal(pmt1)
ΣInt( ) = (pmt2 – pmt1 + 1) × RND(PMT) – ΣPrn( )
RND
where:
= round the display to the number of decimal
places selected
RND12
= round to 12 decimal places
Balance, principal, and interest are dependent on the values of PMT, PV, æ, and pmt1 and
pmt2.
Appendix B: Reference Information
638
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Cash Flow
-
nj
N
-
Sj – 1(1 – (1 + i)
)
----------------------------------
npv( ) = CF +
CF (1 + i)
0
j
∑
i
j = 1
⎧
⎪
⎪
⎨
⎪
⎪
⎩
j
n
j ≥ 1
i
∑
where: S =
j
i = 1
0
j = 0
Net present value is dependent on the values of the initial cash flow (CF ), subsequent
0
cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i).
irr() = 100 × i, where i satisfies npv() = 0
Internal rate of return is dependent on the values of the initial cash flow (CF ) and
0
subsequent cash flows (CFj).
i = I% ÷ 100
Interest Rate Conversions
4Eff
=
=
CP × ln(x + 1)
100 × (e
.01 × Nom ÷ CP
– 1)
x
where:
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4Nom =
1 ÷ CP × ln(x + 1)
100 × CP × [e
– 1]
x
where:
= .01 × Eff
Eff
CP
Nom
effective rate
=
=
=
compounding periods
nominal rate
Days between Dates
With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950,
through Dec. 31, 2049.
Actual/actual day-count method (assumes actual number of days per month and
actual number of days per year):
dbd( (days between dates) = Number of Days II - Number of Days I
Number of Days I = (Y1-YB) × 365
+ (number of days MB to M1)
DT1
+
+
(Y1 – YB)
------------------------
4
Number of Days II = (Y2-YB) × 365
Appendix B: Reference Information
640
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+ (number of days MB to M2)
+
+
DT2
(Y2 – YB)
------------------------
4
where: M1
= month of first date
DT1 = day of first date
Y1
= year of first date
M2
= month of second date
DT2 = day of second date
Y2
MB
DB
YB
= year of second date
= base month (January)
= base day (1)
= base year (first year after leap year)
Appendix B: Reference Information
641
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Important Things You Need to Know About Your
TI-84 Plus
TI-84 Plus Results
There may be a number of reasons that your TI-84 Plus is not displaying the expected
results; however, the most common solutions involve order of operations or mode
settings. Your calculator uses an Equation Operating System (EOS) which evaluates the
functions in an expression in the following order:
1. Functions that precede the argument, such as square root, sin(, or log(
2. Functions that are entered after the argument, such as exponents, factorial, r, ¡, and
conversions
3. Powers and roots, such as 2^5, or 5*square root(32)
4. Permutations (nPr) and combinations (nCr)
5. Multiplication, implied multiplication, and division
6. Addition and subtraction
7. Relational functions, such as > or <
8. Logic operator and
9. Logic operators or and xor
Remember that EOS evaluates from left to right and calculations within parentheses are
evaluated first. You should use parentheses where the rules of algebra may not be clear.
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If you are using trigonometric functions or performing polar and rectangular conversions,
the unexpected results may be caused by an angle mode setting. The Radian and
Degree angle mode settings control how the TI-84 Plus interprets angle values.
To change the angle mode settings, follow these steps:
1. Press z to display the Mode settings.
2. Select Degree or Radian.
3. Press Í to save the angle mode setting.
ERR:DIM MISMATCH Error
Your TI-84 Plus displays the ERR:DIM MISMATCH error if you are trying to perform an
operation that references one or more lists or matrices whose dimensions do not match.
For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an
ERR:DIM MISMATCH error because the number of elements in L1 and L2 do not match.
ERR:INVALID DIM Error
The ERR:INVALID DIM error message may occur if you are trying to graph a function that
does not involve the stat plot features. The error can be corrected by turning off the stat
plots. To turn the stat plots off, press y , and then select 4:PlotsOff.
Contrast Feature
If the contrast setting is too dark (set to 9) or too dim (set to 0) the unit may appear as if
it is malfunctioning or turned off. To adjust the contrast, press and release y, and then
press and hold } or †.
Appendix B: Reference Information
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TI-84 Plus Identification Code
Your graphing calculator has a unique identification (ID) code that you should record and
keep. You can use this 14 digit ID to register your calculator at education.ti.com or
identify your calculator in the event that it is lost or stolen. A valid ID includes numbers 0
through 9 and the letters A through F.
You can view the calculator’s Operating System, Product Number, ID, and Certificate
Revision Number from the About screen. To display the About screen, press y L
and then select 1:About.
Your unique product ID code: _____________________________
Backups
Your TI-84 Plus is similar to a computer, in that it stores files and Apps that are important
to you. It is always a good idea to back up your graphing calculator device files and Apps
using the TI Connect™ software and a USB computer cable. You can find the specific
procedures for backing up your calculator’s device files and Apps in the TI Connect™
Help file.
Appendix B: Reference Information
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Apps
TI-84 Plus Software Applications (Apps) is software that you can add to your calculator
in the same way you would add software to your computer. Apps let you customize your
calculator for peak performance in specific areas of study. You can find apps for the
TI-84 Plus at the TI Online Store at education.ti.com.
TI-Cares KnowledgeBase
The TI-Cares KnowledgeBase provides 24-hour access through the Web to find
answers to frequently asked questions. The TI-Cares KnowledgeBase searches its
repository of known solutions and presents you with the solutions that are most likely to
solve your problem. You can search the TI-Cares KnowledgeBase at
education.ti.com/support.
Appendix B: Reference Information
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Error Conditions
When the TI-84 Plus detects an error, it returns an error message as a menu title, such
as ERR:SYNTAX or ERR:DOMAIN. This table contains each error type, possible causes,
and suggestions for correction. The error types listed in this table are each preceded by
ERR: on your graphing calculator display. For example, you will see ERR:ARCHIVED as a
menu title when your graphing calculator detects an ARCHIVED error type.
Error Type
ARCHIVED
Possible Causes and Suggested Remedies
You have attempted to use, edit, or delete an archived
variable. For example, the expression dim(L1) produces
an error if L1 is archived.
You have attempted to archive a variable and there is
not enough space in archive to receive it.
ARCHIVE FULL
ARGUMENT
A function or instruction does not have the correct
number of arguments. See Appendix A for function and
instruction syntax.
Appendix A displays the arguments and punctuation
needed to execute the function or instruction. For
example, stdDev(list[,freqlist]) is a function of the TI-84
Plus. The arguments are shown in italics. The
arguments in brackets are optional and you need not
type them. You must also be sure to separate multiple
arguments with a comma (,). For example,
stdDev(list[,freqlist]) might be entered as stdDev(L1) or
stdDev(L1,L2) since the frequency list or freqlist is
optional.
BAD ADDRESS You have attempted to send or receive an application
and an error (e.g. electrical interference) has occurred
in the transmission.
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Error Type
Possible Causes and Suggested Remedies
BAD GUESS
•
•
•
In a CALC operation, you specified a Guess that is
not between Left Bound and Right Bound.
For the solve( function or the equation solver, you
specified a guess that is not between lower and upper.
Your guess and several points around it are
undefined.
Examine a graph of the function. If the equation has a
solution, change the bounds and/or the initial guess.
BOUND
•
In a CALC operation or with Select(, you defined
Left Bound > Right Bound.
•
In fMin(, fMax(, solve(, or the equation solver, you
entered lower ‚ upper.
BREAK
You pressed the É key to break execution of a
program, to halt a DRAW instruction, or to stop
evaluation of an expression.
DATA TYPE
You entered a value or variable that is the wrong
data type.
•
For a function (including implied multiplication) or an
instruction, you entered an argument that is an invalid
data type, such as a complex number where a real
number is required. See Appendix A and the
appropriate chapter.
•
•
In an editor, you entered a type that is not allowed,
such as a matrix entered as an element in the stat list
editor. See the appropriate chapter.
You attempted to store an incorrect data type, such as
a matrix, to a list.
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Error Type
Possible Causes and Suggested Remedies
DIM MISMATCH Your calculator displays the ERR:DIM MISMATCH error
if you are trying to perform an operation that references
one or more lists or matrices whose dimensions do not
match. For example, multiplying L1*L2, where
L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIM
MISMATCH error because the number of elements in
L1 and L2 do not match.
•
You attempted to divide by zero. This error is not
returned during graphing. The TI-84 Plus allows for
undefined values on a graph.
DIVIDE BY 0
DOMAIN
•
•
You attempted a linear regression with a vertical line.
You specified an argument to a function or instruction
outside the valid range. This error is not returned
during graphing. The TI-84 Plus allows for undefined
values on a graph. See Appendix A.
•
•
You attempted a logarithmic or power regression with
a LX or an exponential or power regression with a LY.
You attempted to compute GPrn( or GInt( with
pmt2 < pmt1.
DUPLICATE
You attempted to create a duplicate group name.
Duplicate Name A variable you attempted to transmit cannot be
transmitted because a variable with that name already
exists in the receiving unit.
EXPIRED
You have attempted to run an application with a limited
trial period which has expired.
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Error Type
Possible Causes and Suggested Remedies
•
The TI-84 Plus was unable to transmit an item. Check
to see that the cable is firmly connected to both units
and that the receiving unit is in receive mode.
Error in Xmit
•
•
You pressed É to break during transmission.
You attempted to perform a backup from a TI.82 to a
TI-84 Plus.
•
•
You attempted to transfer data (other than L1 through
L6) from a TI-84 Plus to a TI.82.
You attempted to transfer L1 through L6 from a TI-84
Plus to a TI.82 without using 5:Lists to TI82 on the
LINK SEND menu.
ID NOT FOUND
ILLEGAL NEST
INCREMENT
This error occurs when the SendID command is
executed but the proper graphing calculator ID cannot
be found.
•
You attempted to use an invalid function in an
argument to a function, such as seq( within expression
for seq(.
•
•
The increment in seq( is 0 or has the wrong sign. This
error is not returned during graphing. The TI-84 Plus
allows for undefined values on a graph.
The increment in a For( loop is 0.
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Error Type
INVALID
Possible Causes and Suggested Remedies
•
You attempted to reference a variable or use a
function where it is not valid. For example, Yn cannot
reference Y, Xmin, @X, or TblStart.
•
You attempted to reference a variable or function that
was transferred from the TI.82 and is not valid for the
TI-84 Plus For example, you may have transferred
UnN1 to the TI-84 Plus from the TI.82 and then tried
to reference it.
•
•
In Seq mode, you attempted to graph a phase plot
without defining both equations of the phase plot.
In Seq mode, you attempted to graph a recursive
sequence without having input the correct number of
initial conditions.
•
In Seq mode, you attempted to reference terms other
than (nN1) or (nN2).
•
•
You attempted to designate a graph style that is
invalid within the current graph mode.
You attempted to use Select( without having selected
(turned on) at least one xyLine or scatter plot.
INVALID DIM
•
The ERR:INVALID DIM error message may occur if
you are trying to graph a function that does not involve
the stat plot features. The error can be corrected by
turning off the stat plots. To turn the stat plots off,
press y , and then select 4:PlotsOff.
•
•
•
You specified a list dimension as something other
than an integer between 1 and 999.
You specified a matrix dimension as something other
than an integer between 1 and 99.
You attempted to invert a matrix that is not square.
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Error Type
Possible Causes and Suggested Remedies
ITERATIONS
•
The solve( function or the equation solver has
exceeded the maximum number of permitted
iterations. Examine a graph of the function. If the
equation has a solution, change the bounds, or the
initial guess, or both.
•
•
irr( has exceeded the maximum number of permitted
iterations.
When computing æ, the maximum number of
iterations was exceeded.
LABEL
The label in the Goto instruction is not defined with a
Lbl instruction in the program.
MEMORY
Memory is insufficient to perform the instruction or
function. You must delete items from memory before
executing the instruction or function.
Recursive problems return this error; for example,
graphing the equation Y1=Y1.
Branching out of an If/Then, For(, While, or Repeat
loop with a Goto also can return this error because the
End statement that terminates the loop is never
reached.
•
You are unable to transmit an item because the
receiving unit’s available memory is insufficient. You
may skip the item or exit receive mode.
MemoryFull
•
During a memory backup, the receiving unit’s
available memory is insufficient to receive all items in
the sending unit’s memory. A message indicates the
number of bytes the sending unit must delete to do the
memory backup. Delete items and try again.
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Error Type
MODE
Possible Causes and Suggested Remedies
You attempted to store to a window variable in another
graphing mode or to perform an instruction while in the
wrong mode; for example, DrawInv in a graphing mode
other than Func.
NO SIGN CHNG
•
The solve( function or the equation solver did not
detect a sign change.
•
You attempted to compute æ when FV, (Ú…PMT),
and PV are all ‚ 0, or when FV, (Ú…PMT), and PV are
all _ 0.
•
You attempted to compute irr( when neither CFList
nor CFO is > 0, or when neither CFList nor CFO is
< 0.
NONREAL ANS In Real mode, the result of a calculation yielded a
complex result. This error is not returned during
graphing. The TI-84 Plus allows for undefined values on
a graph.
OVERFLOW
You attempted to enter, or you have calculated, a
number that is beyond the range of the graphing
calculator. This error is not returned during graphing.
The TI-84 Plus allows for undefined values on a graph.
RESERVED
You attempted to use a system variable inappropriately.
See Appendix A.
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Error Type
Possible Causes and Suggested Remedies
•
A singular matrix (determinant = 0) is not valid as the
SINGULAR MAT
argument for L1.
•
The SinReg instruction or a polynomial regression
generated a singular matrix (determinant = 0)
because it could not find a solution, or a solution does
not exist.
This error is not returned during graphing. The TI-84
Plus allows for undefined values on a graph.
SINGULARITY
expression in the solve( function or the equation solver
contains a singularity (a point at which the function is
not defined). Examine a graph of the function. If the
equation has a solution, change the bounds or the initial
guess or both.
STAT
You attempted a stat calculation with lists that are not
appropriate.
•
•
•
Statistical analyses must have at least two data
points.
Med-Med must have at least three points in each
partition.
When you use a frequency list, its elements must be
‚ 0.
•
(Xmax N Xmin) à Xscl must be‚ 47 for a
histogram.
STAT PLOT
You attempted to display a graph when a stat plot that
uses an undefined list is turned on.
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Error Type
SYNTAX
Possible Causes and Suggested Remedies
The command contains a syntax error. Look for
misplaced functions, arguments, parentheses, or
commas. Appendix A displays the arguments and
punctuation needed to execute the function or
instruction.
For example, stdDev(list[,freqlist]) is a function of the
TI-84 Plus. The arguments are shown in italics. The
arguments in brackets are optional and you need not
type them. You must also be sure to separate multiple
arguments with a comma (,). For example
stdDev(list[,freqlist]) might be entered as stdDev(L1) or
stdDev(L1,L2) since the frequency list or freqlist is
optional.
TOL NOT MET
UNDEFINED
You requested a tolerance to which the algorithm
cannot return an accurate result.
You referenced a variable that is not currently defined.
For example, you referenced a stat variable when there
is no current calculation because a list has been edited,
or you referenced a variable when the variable is not
valid for the current calculation, such as a after
Med-Med.
VALIDATION
Electrical interference caused a link to fail or this
graphing calculator is not authorized to run the
application.
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Error Type
VARIABLE
Possible Causes and Suggested Remedies
You have tried to archive a variable that cannot be
archived or you have tried to unarchive an application
or group.
Examples of variables that cannot be archived include:
•
Real numbers LRESID, R, T, X, Y, Theta, Statistic
variables under Vars, STATISTICS menu, Yvars,
and the AppIdList.
VERSION
You have attempted to receive an incompatible variable
version from another graphing calculator.
WINDOW
RANGE
A problem exists with the window variables.
•
•
You defined Xmax Xmin or Ymax Ymin.
You defined qmax qmin and qstep > 0 (or vice
versa).
•
•
You attempted to define Tstep=0.
You defined Tmax Tmin and Tstep > 0 (or vice
versa).
•
Window variables are too small or too large to graph
correctly. You may have attempted to zoom in or zoom
out to a point that exceeds the TI-84 Plus’s numerical
range.
ZOOM
•
•
A point or a line, instead of a box, is defined in ZBox.
A ZOOM operation returned a math error.
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Accuracy Information
Computational Accuracy
To maximize accuracy, the TI-84 Plus carries more digits internally than it displays.
Values are stored in memory using up to 14 digits with a two-digit exponent.
•
•
•
You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl,
Tstep, and qstep).
Displayed values are rounded as specified by the mode setting with a maximum of
10 digits and a two-digit exponent.
RegEQ displays up to 14 digits in Float mode. Using a fixed-decimal setting other
than Float causes RegEQ results to be rounded and stored with the specified number
of decimal places.
Xmin is the center of the leftmost pixel, Xmax is the center of the next-to-the-rightmost
pixel. (The rightmost pixel is reserved for the busy indicator.) @X is the distance between
the centers of two adjacent pixels.
•
•
In Full screen mode, @X is calculated as (Xmax N Xmin) à 94. In G-T split-screen
mode, @X is calculated as (Xmax N Xmin) à 46.
If you enter a value for @X from the home screen or a program in Full screen mode,
Xmax is calculated as Xmin + @X É… 94. In G-T split-screen mode, Xmax is calculated
as Xmin + @X É… 46.
Ymin is the center of the next-to-the-bottom pixel; Ymax is the center of the top pixel. @Y
is the distance between the centers of two adjacent pixels.
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656
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•
•
In Full screen mode, @Y is calculated as (Ymax N Ymin) à 62. In Horiz split-screen
mode, @Y is calculated as (Ymax N Ymin) à 30. In G-T split-screen mode, @Y is
calculated as (Ymax N Ymin) à 50.
If you enter a value for @Y from the home screen or a program in Full screen mode,
Ymax is calculated as Ymin + @Y É… 62. In Horiz split-screen mode, Ymax is
calculated as Ymin + @Y … 30. In G-T split-screen mode, Ymax is calculated as
Ymin + @Y É … 50.
Cursor coordinates are displayed as eight-character numbers (which may include a
negative sign, decimal point, and exponent) when Float mode is selected. X and Y are
updated with a maximum accuracy of eight digits.
minimum and maximum on the CALCULATE menu are calculated with a tolerance of
1âL5; ‰f(x)dx is calculated at 1âL3. Therefore, the result displayed may not be accurate to
all eight displayed digits. For most functions, at least five accurate digits exist. For fMin(,
fMax(, and fnInt( on the MATH menu and solve( in the CATALOG, the tolerance can be
specified.
Function Limits
Function
Range of Input Values
12
sin x, cos x, tan x
0 |x| < 10 (radian or degree)
L1
L1
L1 x 1
sin x, cos
x
L
100
100
100
100
ln x, log x
ex
10
< x < 10
L10
< x 230.25850929940
10x
L10
< x< 100
Appendix B: Reference Information
657
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Function
sinh x, cosh x
tanh x
Range of Input Values
|x| 230.25850929940
100
|x| < 10
L1
99
sinh
x
|x| < 5 × 10
L1
99
cosh
x
1 x < 5 × 10
L1
L1 < x < 1
tanh
x
100
‡x (real mode)
‡x (complex mode)
x!
0 x < 10
100
|x| < 10
L.5 _x 69, where x is a multiple of .5
Function Results
Function
Range of Result
L1
L1
L90¡ to 90¡
or Lp à 2 to p à 2 (radians)
sin x, tan
x
L1
0¡ to 180¡
or 0 to p (radians)
cos
x
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Appendix C:
Service and Warranty Information
Texas Instruments Support and Service
For general information
Home Page:
e-mail inquiries:
Phone:
(800) TI-CARES / (800) 842-2737
For U.S., Canada, Mexico, Puerto Rico, and
Virgin Islands only
International
information:
For technical support
support by e-mail:
Phone
(972) 917-8324
(not toll-free):
For product (hardware) service
Appendix C: Service and Warranty Information
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Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact
Texas Instruments Customer Support before returning a product for service.
All other customers: Refer to the leaflet enclosed with this product (hardware) or contact
your local Texas Instruments retailer/distributor.
Appendix C: Service and Warranty Information
660
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Texas Instruments (TI) Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments ("TI") electronic product warranty extends only to the original purchaser and
user of the product.
Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of
one (1) year from the original purchase date.
Warranty Coverage. This TI electronic product is warranted against defective materials and con-
struction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR
UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT
OF DEFECTS IN MATERIALS OR CONSTRUCTION.
Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING BUT
NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PAR-
TICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS
INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCI-
DENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CON-
SUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential
damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights
that vary from state to state or province to province.
Warranty Performance. During the above one (1) year warranty period, your defective product will be
either repaired or replaced with a reconditioned model of an equivalent quality (at TI's option) when
the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the
repaired or replacement unit will continue for the warranty of the original unit or six (6) months,
whichever is longer. Other than the postage requirement, no charge will be made for such repair
and/or replacement. TI strongly recommends that you insure the product for value prior to mailing.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be
free from errors or meet your specific requirements. All software is provided "AS IS."
Copyright. The software and any documentation supplied with this product are protected by copy-
right.
Appendix C: Service and Warranty Information
661
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Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the original purchaser
and user of the product.
Warranty Duration. This Texas Instruments electronic product is warranted to the origi-
nal purchaser for a period of one (1) year from the original purchase date.
Warranty Coverage. This Texas Instruments electronic product is warranted against
defective materials and construction. This warranty is void if the product has been dam-
aged by accident or unreasonable use, neglect, improper service, or other causes not
arising out of defects in materials or construction.
Warranty Disclaimers. Any implied warranties arising out of this sale, including but
not limited to the implied warranties of merchantability and fitness for a particular
purpose, are limited in duration to the above one-year period. Texas Instruments
shall not be liable for loss of use of the product or other incidental or consequen-
tial costs, expenses, or damages incurred by the consumer or any other user.
Except as expressly provided in the One-Year Limited Warranty for this product,
Texas Instruments does not promise that facilities for the repair of this product or
parts for the repair of this product will be available.
Some jurisdictions do not allow the exclusion or limitation of implied warranties or conse-
quential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may also have
other rights that vary from jurisdiction to jurisdiction.
Warranty Performance. During the above one (1) year warranty period, your defective
product will be either repaired or replaced with a new or reconditioned model of an equiv-
alent quality (at TI's option) when the product is returned to the original point of purchase.
The repaired or replacement unit will continue for the warranty of the original unit or six
(6) months, whichever is longer. Other than your cost to return the product, no charge will
be made for such repair and/or replacement. TI strongly recommends that you insure the
product for value if you mail it.
Software. Software is licensed, not sold. TI and its licensors do not warrant that the soft-
ware will be free from errors or meet your specific requirements. All software is pro-
vided "AS IS."
Copyright. The software and any documentation supplied with this product are protected
by copyright.
Appendix C: Service and Warranty Information
662
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All Other Customers
For information about the length and terms of the warranty, refer to your package and/or to the war-
ranty statement enclosed with this product, or contact your local Texas Instruments retailer/distribu-
tor.
Appendix C: Service and Warranty Information
663
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Battery Information
When to Replace the Batteries
The TI-84 Plus uses five batteries: four AAA alkaline batteries and one SR44SW or 303
silver oxide backup battery. The silver oxide battery provides auxiliary power to retain
memory while you replace the AAA batteries.
When the battery voltage level drops below a usable level, the TI-84 Plus:
Displays this message when
you turn on the unit.
Displays this message when you attempt
to download an application.
Message A
Message B
After Message A is first displayed, you can expect the batteries to function for about one
or two weeks, depending on usage. (This one-week to two-week period is based on tests
with alkaline batteries; the performance of other types of batteries may vary.)
If Message B is displayed, you must replace the batteries immediately to successfully
download an application.
Replace the silver oxide battery every three or four years.
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Effects of Replacing the Batteries
Do not remove both types of batteries (AAA and silver oxide) at the same time. Do not
allow the batteries to lose power completely. If you follow these guidelines and the steps
for replacing batteries, you can replace either type of battery without losing any
information in memory.
Battery Precautions
Take these precautions when replacing batteries.
•
•
Do not leave batteries within reach of children
Do not mix new and used batteries. Do not mix brands (or types within brands) of
batteries.
•
•
•
•
Do not mix rechargeable and nonrechargeable batteries.
Install batteries according to polarity (+ and N) diagrams.
Do not place nonrechargeable batteries in a battery recharger.
Properly dispose of used batteries immediately. Do not leave them within the reach
of children.
•
Do not incinerate or dismantle batteries.
Replacing the Batteries
To replace the batteries, follow these steps.
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1. Turn off the graphing calculator. Replace the slide cover over the keyboard to avoid
inadvertently turning on the graphing calculator. Turn the back of the unit toward
you.
2. Hold the graphing calculator upright, push downward on the latch on the top of the
battery cover, and then pull the cover toward you.
Note: To avoid loss of information stored in memory, you must turn off the graphing
calculator. Do not remove the AAA batteries and the silver oxide battery
simultaneously.
3. Replace all four AAA alkaline batteries simultaneously. Or, replace the silver oxide
battery.
•
To replace the AAA alkaline batteries, remove all four discharged AAA batteries
and install new ones according to the polarity (+ and N) diagram in the battery
compartment.
•
To replace the silver oxide battery, remove the screw from the silver oxide
battery cover, and then remove the cover. Install the new battery, + side up.
Replace the cover and secure it with the screw. Use a SR44SW or 303 (or
equivalent) silver oxide battery.
4. Replace the battery compartment cover. Turn the graphing calculator on and adjust
the display contrast, if necessary, by pressing y } or †.
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In Case of Difficulty
Handling a Difficulty
To handle a difficulty, follow these steps.
1. If you cannot see anything on the screen, you may need to adjust the graphing
calculator contrast.
To darken the screen, press and release y, and then press and hold } until the
display is sufficiently dark.
To lighten the screen, press and release y, and then press and hold † until the
display is sufficiently light.
2. If an error menu is displayed, follow these steps:
•
•
Note the error type (ERR:error type).
Select 2:GOTO, if it is available. The previous screen is displayed with the cursor
at or near the error location.
•
•
Deteremine the error.
Correct the expression.
Refer to the Error Conditions table for details about specific errors, if necessary.
3. If the busy indicator (dotted line) is displayed, a graph or program has been paused;
the TI-84 Plus is waiting for input. Press Í to continue or press É to break.
4. If a checkerboard cursor ( # ) is displayed, then either you have entered the
maximum number of characters in a prompt, or memory is full. If memory is full:
•
Press y L 2 to display the MEMORY MANAGEMENT / DELETE menu.
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•
•
Select the type of data you want to delete, or select 1:All for a list of all variables
of all types. A screen is displayed listing each variable of the type you selected
and the number of bytes each variable is using.
Press } and † to move the selection cursor (4) next to the item you want to
delete, and then press {.
5. If the graphing calculator does not seem to work at all, be sure the alkaline batteries
are fresh and that they are installed properly.
6. If the TI-84 Plus does not function even though you are sure that the batteries are
fresh, you can try manually resetting it.
•
•
•
•
Remove all of the AAA batteries from the graphing calculator.
Press and hold the É key for ten seconds.
Replace the batteries.
Turn on the unit.
When you reset your graphing calculator, the contrast sometimes changes. If the
screen is faded or blank, adjust the contrast by pressing y and releasing } or †.
7. If the above solutions do not work you can reset all of the memory. The RAM, user
data archive memory, and system variables are restored to factory settings when
you reset all memory. All nonsystem variables, applications (Apps), and programs
are deleted.
•
•
•
•
•
Press y L to display the MEMORY menu.
Select 7:Reset to display the RAM ARCHIVE ALL menu.
Press ~ ~ to display the ALL menu.
Select 1:All Memory to display the RESET MEMORY menu.
To continue with the reset, select 2:Reset. The message Mem cleared is
displayed on the home screen.
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Index
Symbols
Index
670
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accuracy information
Numerics
alpha cursor . . . . . . . . . . . . . . . . . . . . . . 9
amortization
1-PropZInt (one-proportion z confidence
2-PropZInt (two-proportion z confidence
2-SampTInt (two-sample t confidence
2-SampZInt (two-sample z confidence
A
Index
671
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archived variables . . . . . . . . . . . . . . . 628
automatic residual list (RESID) . . . . . 302
C
C/Y (compounding-periods-per-year
cash flow
calculating . . . . . . . . . . . . . . . . . . 397
clearing
B
Index
672
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complex
compounding-periods-per-year variable
conversions
4DMS (to degrees/minutes/ seconds)
4Nom (to nominal interest rate
Equ4String( (equation-to-string
P4Rx(, P4Ry( (polar-to-rectangular
R4Pr(, R4Pq( (rectangular-to-polar
conversion) . . . . . . . . . . . . . . 603
R4Pr(, R4Pθ( (rectangular-to-polar
conversion) . . . . . . . . . . . . . . . 86
String4Equ( (string-to-equation
Index
673
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cumulative sum (cumSum( ) . . . . . . . 572
determinant (det( ) . . . . . . . . . . . . . . . 237
determinant (det( ) . . . . . . . . . . . . . . . 573
diagnostics display mode(r, r2, R2) . . 304
DISTR DRAW (distributions drawing
distribution functions
D
defragmenting . . . . . . . . . . . . . . . . . . 541
Index
674
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distribution shading instructions
DMS (degrees/minutes/seconds entry
drawing on a graph
E
Equ4String( (equation-to-string
errors
diagnosing and correcting . . . . . . . 49
examples—applications
functions and inverses (DrawF,
DrawInv) . . . . . . . . . . . . . . . 194
line segments (Line( ) . . . . . . . . . 189
points (Pt-Change, Pt-Off, Pt-On) 201
tangents (Tangent) . . . . . . . . . . . 192
area between curves . . . . . . . . . . 496
Index
675
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defining a 466
defining a table of values 467
setting the viewing window 470
tracing the graph 472
zooming in on the graph 474
zooming in on the table 468
cobweb attractors . . . . . . . . . . . . 489
unit circle . . . . . . . . . . . . . . . . . . . 211
examples—miscellaneous
calculating outstanding loan balances
convergence . . . . . . . . . . . . . . . . 167
examplesóGetting Started
expr( (string-to-expression conversion) . .
guess the coefficients . . . . . . . . . 491
inequalities . . . . . . . . . . . . . . . . . 483
parametric equations, ferris wheel
quadratic formula
converting to a fraction 461
displaying complex results 463
entering a calculation 460
Sierpinski triangle . . . . . . . . . . . . 487
solving a system of nonlinear
equations . . . . . . . . . . . . . . . 485
examples—Getting Started
converting from string (expr( ) . . . 419
converting from string (expr( ) . . . 576
generating a sequence . . . . . . . . 246
Index
676
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interest rate conversions . . . . . . . 639
two-sample t test . . . . . . . . . . . . . 633
function graphing
F
Faceplates . . . . . . . . . . . . . . . . . . . . . 10
factorial (!) . . . . . . . . . . . . . . . . . . . . . 620
family of curves . . . . . . . . . . . . . . . . . 112
financial functions
formulas
CALC (calculate menu) . . . . . . . . 126
defining on the home screen, in a
deselecting . . . . . . . . . . . . . . . . . . 99
evaluating . . . . . . . . . . . . . . . . . . . 98
family of curves . . . . . . . . . . . . . . 112
graph styles . . . . . . . . . . . . . . . . . 101
maximum of (fMax( ) . . . . . . . . . . . 59
maximum of (fMax( ) . . . . . . . . . . 578
minimum of (fMin( ) . . . . . . . . . . . 578
amortization . . . . . . . . . . . . . . . . 638
Index
677
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pausing or stopping a graph . . . . 111
Smart Graph . . . . . . . . . . . . . . . . 111
function, definition of . . . . . . . . . . . . . . 17
getDate, get current date . . . . . . . . . . 581
Getting Started See examples, Getting
graph style
graphing modes . . . . . . . . . . . . . . . . . . 23
G
Index
678
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inferential statistics
H
home screen . . . . . . . . . . . . . . . . . . . . . 7
data input or stats input . . . . . . . . 337
insert cursor . . . . . . . . . . . . . . . . . . . . . . 9
I
If instructions
Index
679
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interest rate conversions
L
4Eff( (compute effective interest rate)
4Nom( (compute nominal interest rate)
labels
calculating . . . . . . . . . . . . . . . . . 402
inverse cumulative normal distribution
inverse cumulative normal distribution
inverse trig functions . . . . . . . . . . . . . . 53
invNorm( (inverse cumulative normal
invT (inverse Student T distribution) . 375
linking
to a TI-84 Plus Silver Edition or TI-84
K
keyboard
Index
680
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LinReqTInt (confidence interval for slope)
LIST MATH menu . . . . . . . . . . . . . . . 269
lists
M
math operations . . . . . . . . . . . . . . . . . . 52
matrices
dimension . . . . . . . . . . . . . . . . . . 249
indicator ({ }) . . . . . . . . . . . . . . . . 249
using in expressions . . . . . . . . . . 256
editing matrix elements . . . . . . . . 226
math functions . . . . . . . . . . . . . . . 231
matrix math functions (det(, T, dim(,
Fill(, identity(, randM(, augment(,
Matr4list(, List4matr(, cumSum( )
row operations (ref(, rref(, rowSwap(,
Index
681
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memory
clearing all list elements from . . . 521
clearing entries from . . . . . . . . . . 521
deleting items from . . . . . . . . . . . 519
minimum of a function (fMin( ) . . . . . . . 59
minimum of a function (fMin( ) . . . . . . 578
Index
682
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one-sample t confidence interval
N
nonrecursive sequences . . . . . . . . . . 157
normal distribution probability
normalcdf( (normal distribution probability)
normalpdf( (probability density function) .
P
P/Y(number-of-payment-periods-per-year
P4Rx(, P4Ry( (polar-to-rectangular
parametric equations . . . . . . . . . . . . . 138
parametric graphing
CALC (calculate operations on a
defining and editing . . . . . . . . . . . 138
graph styles . . . . . . . . . . . . . . . . . 137
moving the cursor to a value . . . . 142
O
one-proportion z confidence interval
Index
683
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zoom operations . . . . . . . . . . . . . 143
parentheses . . . . . . . . . . . . . . . . . . . . 41
Pic (pictures) . . . . . . . . . . . . . . . . . . . 206
pictures (Pic) . . . . . . . . . . . . . . . . . . . 206
polar graphing
CALC (calculate operations on a
equations . . . . . . . . . . . . . . . . . . 147
graph styles . . . . . . . . . . . . . . . . . 146
moving the cursor to a value . . . . 151
window variables . . . . . . . . . . . . . 147
PolarGC (polar graphing coordinates) . . .
PRGM EXEC menu . . . . . . . . . . . . . . 434
probability . . . . . . . . . . . . . . . . . . . . . . 79
Index
684
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probability density function (normalpdf( )
probability density function (normalpdf( )
programming
Q
creating new . . . . . . . . . . . . . . . . 427
entering command lines . . . . . . . 430
executing . . . . . . . . . . . . . . . . . . 431
instructions . . . . . . . . . . . . . . . . . 435
running assembly language program
R
R4Pr(, R4Pq( (rectangular-to-polar
conversions) . . . . . . . . . . . . . . . . 603
R4Pr(, R4Pθ( (rectangular-to-polar
conversions) . . . . . . . . . . . . . . . . . 86
subroutines . . . . . . . . . . . . . . . . . 456
Index
685
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RectGC (rectangular graphing
recursive sequences . . . . . . . . . . . . . 158
regression model
automatic regression equation . . 303
diagnostics display mode . . . . . . 304
resetting
root of a function . . . . . . . . . . . . . . . . 127
S
scientific notation . . . . . . . . . . . . . . . . . 16
second key (2nd) . . . . . . . . . . . . . . . . . . 3
selecting
functions from the home screen or a
sequence graphing
CALC (calculate menu) . . . . . . . . 164
evaluating . . . . . . . . . . . . . . . . . . 165
Index
686
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selecting and deselecting . . . . . . 156
TI-84 Plus versus TI-82 table . . . 173
Simul (simultaneous graphing order
solving for variables in the equation solver
split-screen modes
setting
modes from a program . . . . . . . . . 21
split-screen modes . . . . . . . . . . . 213
Horiz (horizontal) mode . . . . . . . . 215
shade below graph style . . . . . . . . . . 101
Index
687
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stat list editor
2-SampTInt (two-sample t confidence
interval) . . . . . . . . . . . . . . . . . 355
2-SampZInt (two-sample z confidence
interval) . . . . . . . . . . . . . . . . . 354
ANOVA( (one-way analysis of
variance) . . . . . . . . . . . . . . . . 363
LinRegTTest (linear regression t test)
attaching formulas to list names . 289
displaying . . . . . . . . . . . . . . . . . . 283
edit-elements context . . . . . . . . . 296
editing elements of formula-generated
entering list names . . . . . . . . . . . 284
formula-generated list names . . . 291
restoring list names L1–L6 . . . . . 287
stat tests and confidence intervals
1-PropZInt (one-proportion z
TInterval (one-sample t confidence
interval) . . . . . . . . . . . . . . . . . 353
ZInterval (one-sample z confidence
interval) . . . . . . . . . . . . . . . . . 352
STAT TESTS menu . . . . . . . . . . . . . . 340
statistical distribution functions See
Histogram . . . . . . . . . . . . . . . . . . 320
NormProbPlot (normal probability
2-PropZInt (two-proportion z
Index
688
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statistical variables table . . . . . . . . . . 315
storing
student-t distribution
subroutines . . . . . . . . . . . . . . . . . . . . 445
String4Equ( (string-to-equation
strings
T
tables
description . . . . . . . . . . . . . . . . . . 180
converting . . . . . . . . . . . . . . . . . . 418
displaying contents . . . . . . . . . . . 416
functions in CATALOG . . . . . . . . 416
indicator (”) . . . . . . . . . . . . . . . . . 413
student-t distribution
Index
689
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Text(
TInterval (one-sample t confidence
TInterval (one-sample t confidence
tpdf( (student-t distribution probability
TRACE
TI-84 Plus
key code diagram . . . . . . . . . . . . 454
time value of money (TVM)
C/Y variable (number of compounding
calculating . . . . . . . . . . . . . . . . . 394
FV variable (future value) . . . . . . 406
N variable (number of payment
periods) . . . . . . . . . . . . . . . . 406
P/Y variable (number of payment
tvm_I% (interest rate) . . . . . . . . . 615
transmitting
from a TI-83 Plus Silver Edition or
from a TI-84 Plus Silver Edition or
to a TI-84 Plus Silver Edition or TI-84
turning on and off
Index
690
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calculator . . . . . . . . . . . . . . . . . . . . 4
coordinates . . . . . . . . . . . . . . . . . 109
expressions . . . . . . . . . . . . . . . . 110
two-proportion z confidence interval
V
variables
independent/dependent . . . . . . . 180
statistical . . . . . . . . . . . . . . . . . . . 315
VARS and Y-VARS menus . . . . . . 38
VARS menu
U
Statistics . . . . . . . . . . . . . . . . . . . . 38
ungrouping . . . . . . . . . . . . . . . . . . . . 535
Index
691
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viewing window . . . . . . . . . . . . . . . . . 105
Y-VARS menu
Parametric . . . . . . . . . . . . . . . . . . . 39
W
w sequence function . . . . . . . . . . . . . 154
window variables
Z
ZInterval (one-sample z confidence
X
polar graphing . . . . . . . . . . . . . . . 151
x-intercept of a root . . . . . . . . . . . . . . 127
Y
Y= editor
Index
692
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