Texas Instruments TI-84+SE, TI-84 Plus User Manual

TI-84 Plus

TI-84 Plus Silver Edition

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iii

About the TI-84 Plus and TI-84 Plus Silver Edition

The TI-84 Plus Silver Edition is the same as the TI-84 Plus except:

• it has more memory, and thus more spaces for graphing handheld software applications (Apps).

• it has interchangeable faceplates that let you customize the appearance of your TI-84 Plus Silver Edition.

Since all the functions of the TI-84 Plus Silver Edition and the TI-84 Plus are the same, this guidebook can be used for either the TI-84 Plus or the TI-84 Plus Silver Edition.

The CD included with your TI-84 Plus / TI-84 Plus Silver Edition package also includes an electronic guidebook, which is a complete reference manual for the TI-84 Plus / TI-84 Plus Silver Edition. If the CD is not available, you can download a copy of the electronic guidebook from the Texas Instruments web page at:

education.ti.com/guides

The TI-84 Plus / TI-84 Plus Silver Edition has some graphing handheld software applications (Apps) preinstalled. For information about these Apps, see the electronic documentation files on the Texas Instrument web page at:

education.ti.com/guides

About this book

This guidebook gives a quick overview of each topic, along with keystroke instructions for easy examples. All examples assume that the TI-84 Plus is using default settings. For complete information on any topic, see the electronic guidebook on the CD that came with your graphing handheld.

1 Getting Started..................................................................1

TI-84 Plus keys................................................................................. 1

Turning the TI-84 Plus on and off.................................................. 2

Home screen ................................................................................... 2

y and ƒ keys ........................................................................ 3

‘ and y 5 ....................................................................... 4

Entering an expression................................................................... 4

Interchangeable Faceplates........................................................... 5

Using the Clock............................................................................... 6

TI-84 Plus menus ............................................................................. 8

Editing and deleting .................................................................... 11

Using ¹ and Ì............................................................................. 13

Using parentheses ........................................................................ 14

Storing a value.............................................................................. 15

Graphing a function..................................................................... 17

Changing mode settings.............................................................. 18

Setting the graphing window ..................................................... 21

Using q ................................................................................... 23

Building a table ............................................................................ 23

Using the CATALOG...................................................................... 25

Performing simple calculations ................................................... 26

Using the equation solver............................................................ 28

Entering data into lists................................................................. 30

Plotting data................................................................................. 32

Calculating a linear regression .................................................... 35

Calculating statistical variables.................................................... 36

Using the MATRIX Editor ............................................................. 37

Grouping....................................................................................... 39

Ungrouping .................................................................................. 41

Error messages.............................................................................. 42

Resetting defaults ........................................................................ 43

Installing applications .................................................................. 44

Running applications ................................................................... 45

Quick reference ........................................................................... 46

Battery precautions ...................................................................... 46

2 Activities ..........................................................................47

The Quadratic Formula ................................................................ 47

Box with Lid .................................................................................. 50

Comparing Test Results Using Box Plots...................................... 57

Graphing Piecewise Functions..................................................... 59

Graphing Inequalities................................................................... 60

Solving a System of Nonlinear Equations....................................62

Using a Program to Create the Sierpinski Triangle.....................63

Graphing Cobweb Attractors.......................................................64

Using a Program to Guess the Coefficients.................................65

Graphing the Unit Circle and Trigonometric Curves ..................66

Finding the Area between Curves ...............................................67

Using Parametric Equations: Ferris Wheel Problem ...................68

Demonstrating the Fundamental Theorem of Calculus .............71

Computing Areas of Regular N-Sided Polygons .........................73

Computing and Graphing Mortgage Payments .........................75

3 Memory and Variable Management .............................. 79

Checking Available Memory ........................................................79

Deleting Items from Memory.......................................................81

Clearing Entries and List Elements...............................................82

Archiving and UnArchiving Variables..........................................83

Resetting the TI-84 Plus................................................................87

Grouping and Ungrouping Variables ..........................................90

Garbage Collection.......................................................................93

ERR:ARCHIVE FULL Message ........................................................97

4 Communication Link....................................................... 99

Getting Started: Sending Variables .............................................99

TI-84 Plus LINK.............................................................................100

Selecting Items to Send ..............................................................102

Receiving Items ...........................................................................106

Backing Up RAM Memory..........................................................107

Error Conditions..........................................................................108

A Appendix A: Tables and Reference Information......... 111

Table of Functions and Instructions...........................................111

Variables......................................................................................154

Statistics Formulas.......................................................................155

Financial Formulas ......................................................................159

B Appendix B: General Information................................ 163

Battery Information....................................................................163

Important Things You Need to Know About Your TI-84 Plus .. 165

In Case of Difficulty ....................................................................167

Error Conditions..........................................................................169

Accuracy Information .................................................................176

Texas Instruments (TI) Support and Service............................... 179

Texas Instruments (TI) Warranty Information ...........................180

Getting Started

TI-84 Plus keys

y Provides access to the function or character shown above each key.

ƒ Provides access to the characters shown above each key.

Œ Displays a menu that lists Applications installed on the TI-84 Plus.

É Turns on the TI-84 Plus.

} ~ † | Let you move the cursor in four directions.

‘ Clears (erases) the entry line or deletes an entry and answer on the home screen.

Í Evaluates an expression, executes an instruction, or selects a menu item.

Getting Started 1

Turning the TI-84 Plus on and off

To turn on the TI-84 Plus, press É. The É key is located at the lower left corner of the TI-84 Plus.

To turn off the TI-84 Plus, press the y key followed by the É key. OFF

second function of É.

is the

When you turn off the TI-84 Plus, all settings and memory contents are retained. The next time you turn on the TI-84 Plus, the home screen displays as it was when you last used it.

Automatic Power Down™

To prolong the life of the batteries, Automatic Power Down™ (APD™) turns off the TI-84 Plus automatically after about five minutes without any activity. The next time you turn o?n the TI-84 Plus, it is exactly as you left it.

Home screen

When you turn on your TI-84 Plus the first time, you should see this screen:

To clear this text from your screen, press ‘ twice. You should now see the home screen, a blank screen with a flashing cursor. The home screen is where you enter problems and see results.

If you pressed ‘ above and you still do not see a blank home screen, press the y key followed by the z key (to select QUIT).

2 Getting Started

Example: Add 2 + 3 on the home screen.

Press Result

2 Ã 3

Entry line

Answer line

Note: Results are displayed on the next line (the answer line), not on the

entry line.

Example: Multiply 5 x 4.

Press Result

5 ¯ 4

and

Most keys on the TI-84 Plus can perform two or more functions. To use a function printed on a key, press the key. To use a function printed above a key, you must first press the y key or the ƒ key.

keys

y key

Second functions are printed above the keys (the same color as the y key). Some secondary functions enter a function or a symbol on the home screen (sinL1 or ‡, for example). Others display menus or editors.

To view the ANGLE menu, for example, look for ANGLE above the Œ key near the top of the TI-84 Plus keyboard. Press the y key (and then release it) and then press Œ. In this guidebook the key combination is indicated by y;, not yŒ.

Getting Started 3

Note: The flashing cursor changes to Þ when you press the y key.

ƒ key

The ƒ key lets you enter the alphabetic characters and some special symbols. To enter T, for example, press ƒ (and then release it) and then press ¶. In the guidebook this key combination is indicated by ƒ [T].

If you have several alphabetic characters to enter, press y7 to avoid having to press the ƒ key multiple times. This locks the alpha key in the On position until you press ƒ a second time to unlock it.

Note: The flashing cursor changes to Ø when you press the ƒ key.

‘

and y

‘ key

The ‘ key erases the home screen. This key is located just below the four arrow keys at the upper right corner of the TI-84 Plus keyboard. If you press ‘ during an entry, it clears the entry line. If you press ‘ when the cursor is on a blank line, it clears everything on the home screen.

Although it does not affect the calculation, it is frequently helpful to clear the previous work from the home screen before you begin a new problem. As you work through this guide, we recommend that you press ‘ each time you begin a new Example. This removes the previous example from the home screen and ensures that the screen you see matches the one shown in the example.

y 5

If you accidentally press a menu key, pressing ‘ will usually return you to the home screen, but in most cases pressing y5 to leave the menu and return to the home screen.

Entering an expression

An expression consists of numbers, variables, operators, functions, and their arguments that evaluate to a single answer. 2X + 2 is an expression.

Type the expression, and then press Í to evaluate it. To enter a function or instruction on the entry line, you can:

• Press its key, if available. For example, press «.

— or —

4 Getting Started

• Select it from the CATALOG, if the function appears on the

CATALOG. For example, press y N, press † to move down to

log(, and press Í to select log(.

— or —

• Select it from a menu, if available. For example, to find the

function, press , press ~ to select NUM, then select 2:round(.

Example: Enter and evaluate the expression p Q 2.

Press Result

y B ¯

Interchangeable Faceplates

round

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 at education.ti.com.

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 keypad.

Getting Started 5

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.

Displaying the Clock Settings

1. Press z

2. Press the † to move the cursor to

SET CLOCK.

3. Press Í.

6 Getting Started

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.

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 Press Í.

SAVE.

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.

Getting Started 7

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.

Using the Mode Screen to turn the clock on

1. If the Clock is turned off, Press † to

highlight

2. Press Í.

TURN CLOCK ON.

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

3. Press Í.

ClockOn.

Turning the Clock Off

1. Press y N.

2. Press † or } to scroll the CATALOG until

the selection cursor points to

3. Press Í.

ClockOff will turn off the Clock display.

ClockOff.

TI-84 Plus menus

Many functions and instructions are entered on the home screen by selecting from a menu.

To select an item from the displayed menu:

• Press the number or letter shown at the left of that item.

— or —

• Use the cursor arrow keys, † or }, to highlight the item, and then press Í.

8 Getting Started

Some menus close automatically when you make a selection, but if the menu remains open, press y5 to exit. Do not press ‘ to exit, since this will sometimes delete your selection.

Example: Enter on the home screen entry line.

Press Result



Menus containing an arrow next to the final item continue on a second page.

— or —

††† Í

2 7 ¤

Example: Change the FORMAT menu setting to display grid points on the graph.

Press Result

y .

Getting Started 9

Press Result

† † ~ Í

Example: Turn off the display of grid points.

Press Result

y . † † Í

Note: Press y5 or ‘ to close the FORMAT menu and return to

the home screen.

Summary of menus on the TI-84 Plus

Press To display

y 8

y L





y ,

10 Getting Started

APPLICATIONS menu — to see a list of TI-84 Plus

graphing handheld software applications (APPS).

LINK menu — to communicate with another graphing

handheld.

MEMORY menu — to check available memory and

manage existing memory.

MATH menu — to select a math operation.

VARS menu — to select variable names to paste to the

home screen.

STAT PLOTS menu — to define statistical plots.

Press To display

y N

CATALOG menu — to select from a complete,

alphabetic list of all TI-84 Plus built-in functions and instructions.

y .

y >

FORMAT menu — to define a graph’s appearance.

MATRIX menu — to define, view, and edit matrices.

y <

y =

DRAW menu — to select tools for drawing on graphs.

DISTRIBUTIONS menu — to select distribution

functions to paste to the home screen or editor screens.

y :

TEST menu — to select relational operators (=, ƒ, {, |,

etc.) and Boolean operators (and, or, xor, not) to paste to the home screen.

Editing and deleting

You can change any expression or entry using the backspace | key, the delete { key, or the insert y6 key. You can make a change before or after you press Í.

Example: Enter the expression 5

+ 5.

Press Result

5 ¡ Ã 1

| 5

+ 1, and then change the expression to

Getting Started 11

Example: Enter the expression 52 + 1, and then change the expression to

52 N 5.

Press Result

5 ¡ Ã 1

| | { {

Example: Change the example above to 5

+2N 5 using y[ to

recall the expression and y6 to insert + 2 into the expression.

Press Result

y [

| | y 6 Ã

12 Getting Started

Using ¹ and

Many graphing handhelds (including the TI-84 Plus) make a distinction between the symbols for subtraction and negation.

Use ¹ to enter subtraction operations. Use Ì to enter a negative number in an operation, in an expression, or on a setup screen.

Example: Subtract 10 from 25.

Press Result

2 5 ¹ 1 0

Example: Add 10 to L25.

Press Result

2 5 Ã 1 0

Ì Í

Example: Subtract L10 from 25.

Press Result

2 5 ¹ Ì 1 0

Note: Notice that the TI-84 Plus displays a slightly different symbol for

negation and subtraction to make it easier for you to distinguish between the two. The negative symbol is raised and slightly shorter.

Getting Started 13

Using parentheses

Since all calculations inside parentheses are completed first, it is sometimes important to place a portion of an expression inside parentheses.

Example: Multiply 4…1+2; then multiply 4…(1+2).

Press Result

4 ¯ 1 Ã 2

4 ¯ £ 1 Ã 2 ¤

Note: The closing parenthesis ¤ is optional. The operation will be

completed if you omit it. The exception to this rule occurs when there is another operation following the parenthetical operation. In this case, you must include the closing parenthesis.

Example: Divide 1/2 by 2/3.

Press Result

1 ¥ 2 ¤ ¥

2 ¥ 3 ¤

14 Getting Started

Example: Calculate 16 ^ .

Press Result

1 6 › £ 1 ¥ 2 ¤

Example: Calculate (L3)

Press Result

3 ¤ ¡

£ Ì Í

--2

Note: Try each of these examples without the parentheses and see what

happens!

Storing a value

Values are stored to and recalled from memory using variable names.

Example: Store 25 to variable A and multiply A by 2.

Press Result

2 5 ¿ ƒ [A]

Getting Started 15

Press Result

2 ¯ ƒ [A]

— or —

ƒ [A] ¯ 2 Í

Example: Find the value of 2X3 N 5X2 N 7X + 10 when X = L0.5.

Press Result

5 ¿ „

Ì Ë Í

L.5 to X)

(stores

2 „ › 3

¹ 5 „ ¡ ¹

7 „ Ã 1 0

You can remove a value stored to a variable using the DELVAR function or by storing 0 to the variable.

16 Getting Started

Example: Delete the value (L.5) stored to X above by storing 0.

Press Result

0 ¿„

„ Í

Graphing a function

o Displays the Y= Editor, where you can enter one or more functions or expressions to graph.

p Lets you set the viewing window to produce the best display of your graph.

„ Lets you enter one of four symbols: X (if you are in Function mode), T (in Parametric mode), q (in Polar mode), or n (in Sequence mode).

q Lets you quickly adjust the window to a predefined setting.

s Displays the graph you have defined.

r Lets you move the cursor along the graphed function using | and ~.

Getting Started 17

To graph a function, you must:

1. Display the Y= Editor.

2. Enter the function.

3. Display the graph.

Note: If you previously changed graph type in the mode settings, you

must change the type back to Func (the default setting) before you graph.

Example: Graph the function Y = X

Press Result

+ 1.

„ ¡ Ã

Note: If Y1 is not empty, press ‘. If there are additional entries in

the Y= Editor, press †‘ until all are clear.

Changing mode settings

The mode settings determine how entries are interpreted and how answers are displayed on the TI-84 Plus.

18 Getting Started

Example: Change the mode setting for decimals from Float to 3 decimal

places.

Press Result

† ~ ~ ~ ~ Í

y 5

1 Ë 2 3 4 5 6

Note: You must press Í to change a mode setting. If you highlight

the setting and then exit the mode menu without pressing Í, the setting will not be changed.

The mode menu includes the following settings:

Setting Choices

Numeric notation

Decimal

Angle measure

Getting Started 19

Normal: for example, 12345.67

•

Sci (scientific): for example, 1.234567â4

•

Eng (engineering): for example, 12.34567â3

Float

•

lets the number of decimal places change

based on the result (up to 10 digits)

0–9: sets the number of decimal places to a value

–9) that you specify

Radian: interprets angle values as radians

Degree: interprets angle values as degrees

Setting Choices

Type of graph

•

Func (functional): plots functions, where Y is a

function of X

•

Par (parametric): plots relations, where X and Y

are functions of T

•

Pol (polar): plots functions, where r is a function

of ô

Seq (sequence): plots sequences

•

Plot type

Sequential or simultaneous graphing

Real or complex mode

Screen display

•

Connected: draws a line connecting each point

calculated for the selected functions

•

Dot: plots only the calculated points of the

selected functions

•

Sequential: draws graphs one at a time

•

Simul (simultaneous): draws several graphs at the

same time

Real:

•

displays real numbers, such as 1, 1/2, ‡3

a+b× (rectangular complex): displays as 3+2× re^q× (polar complex): displays as re^q×

Full: displays full screen

Horiz: displays a horizontal split screen

G-T: displays a vertical split screen (graph &

table)

The importance of mode settings

Example: Multiply 2/3 Q 2.

Press Result

z † ~ Í

20 Getting Started

Press Result

2 ¥ 3 ¯ 2 Í

Your first reaction to this example is that the graphing handheld has produced a wrong answer. But you have set it to round to 0 decimal places (the nearest whole number), so for this setting the answer is correct. If you set rounding (decimals displayed) to 0 and then forget to reset it for later calculations, you may be surprised by some of your answers! With mode set to the default setting of Float, the result will be:

Press Result

2 ¥ 3 ¯ 2

Setting the graphing window

To obtain the best view of the graph, you may need to change the boundaries of the window.

To display the WINDOW Editor, press p.

Ymax

Xscl

Xmax

Yscl

Window variables (shown in

WINDOW Editor)

Xmin

Ymin

Corresponding viewing

window (shown on Graph

window)

Xmin, Xmax, Ymin, and Ymax variables represent the boundaries of

The the viewing window.

Getting Started 21

Xmin: the minimum value of X to be displayed. Xmax: the maximum value of X to be displayed. Ymin: the minimum value of Y to be displayed. Ymax: the maximum value of Y to be displayed. Xcsl (X scale): the distance between the tick marks on the X axis. Yscl (Y scale): the distance between the tick marks on the Y axis. Xres: pixel resolution—not usually changed except by advanced users.

To change the values:

1. Move the cursor to highlight the value you want to change.

2. Do one of the following:

• Type a value or an expression. The old value is erased when you

begin typing.

— or —

• Press ‘ to clear the old value; then type the new one.

3. Press Í, †, or }.

Note: Values are stored as you type them; you do not need to press

Í. Pressing Í simply moves the cursor to the next window variable.

4. After you have made all changes, press y5 to close the WINDOW Editor (or s to display the graph).

Example: Change the window settings to display a maximum X value of 25, a minimum X value of L25, a maximum Y value of 50, and a minimum Yvalue of L50.

Press Result

2 5 † 2 5 † †

Ì 5 0 † 5 0

22 Getting Started

Press Result

y 5

Using

The TI-84 Plus has ten predefined window settings that let you quickly adjust the graph window to a predetermined level of magnification. To display this menu, press q.

Selection Result

1: ZBox Lets you draw a box (using the cursor pad) to

2: Zoom In After you position the cursor and press Í,

3: Zoom Out After you position the cursor and press Í,

4: ZDecimal Sets the change in X and Y to increments of .1

5: ZSquare Adjusts the viewing window so that X and Y

6: ZStandard Sets the standard (default) window variables.

7: ZTrig Sets the built-in trigonometry window variables.

8: ZInteger After you position the cursor and press Í, sets

9: ZoomStat Sets the values for currently defined statistical lists.

define the viewing window.

magnifies the graph around the cursor.

displays more of the graph.

when you use r.

dimensions are equal.

the change in X and Y to whole number increments.

0: ZoomFit Fits

Ymin and Ymax between Xmin and Xmax.

Building a table

Tables are useful tools for comparing values for a function at multiple points.

Getting Started 23

Example: Build a table to evaluate the function Y = X3 N 2X at each

integer between L10 and 10.

Press Result

z † † † Í

(sets function graphing mode)

„ 

¹ 2 „

y -

1 0 Í

(sets TblStart; default settings shown for the other fields are appropriate)

y 0

24 Getting Started

Note: Press † repeatedly to see the changes in X and Y.

Clearing the Y= Editor

Before proceeding with the remaining examples in this guidebook, clear the Y= Editor.

Press Result

‘

Using the CATALOG

The CATALOG is an alphabetic list of all functions and instructions on the TI-84 Plus. Some of these items are also available on keys and menus.

To select from the CATALOG:

1. Position the cursor where you want to insert the item.

2. Press y N.

3. Press † or } to move the 4 indicator to the function or instruction.

(You can move quickly down the list by typing the first letter of the item you need.)

4. Press Í. Your selection is pasted on the home screen.

Notes:

• Items are listed in alphabetical order. Those that do not start with a

letter (+, ‚, ‡, p, and so on) are at the end of the list.

• You can also paste from the CATALOG to an editor, such as the Y= Editor.

Getting Started 25

Example: Enter the rand function on the home screen.

Press Result

y N [R] †

The Ø indicates that Alpha-lock is on.

Performing simple calculations

Changing a decimal to a fraction

Example: Add 1/2 + 1/4 and change your answer to a fraction.

Press Result

1 ¥ 2 Ã 1 ¥ 4

 1 Í

26 Getting Started

Finding the least common multiple

Example: Find the least common multiple of 15 and 24.

Press Result

 ~ } } Í

1 5 ¢ 2 4 ¤

Finding the square root

Example: Find the square root of 256.

Press Result

y C 2 5 6 ¤ Í

Finding the factorial of numbers

Example: Compute the factorial of 5 and 30.

Press Result

5  ~ ~ ~ 4

3 0  ~ ~ ~ 4

Scientific notation

Getting Started 27

Solving trigonometric functions

Example: Find the sine of an angle of 72¡.

Press Result

7 2

˜ y ; Í ¤ Í

If you are solving multiple problems using angles, be sure that mode is set to Degree. If you are in Radian mode and do not wish to change the mode, you can use y;Í (as you did in this example) to add the degree symbol to the calculation and override the Radian mode setting.

Adding Complex Numbers

Example: Add (3+5×) + (2-3×).

Press Result

3 Ã 5 y V ¤

Ã £ 2 ¹ 3 y V ¤ Í

Note: The × character is the second function of Ë (the decimal key).

Using the equation solver

You can use the TI-84 Plus equation solver to solve for a variable in an equation.

28 Getting Started

Example: Find the roots for the equation X2 N 13X N 48 = 0.

Press Result

 }

If you do not see

eqn:0= as shown above, press } (the up arrow), and

then press ‘ to erase the existing equation.

Press Result

„ ¡ ¹

1 3 „ ¹ 4 8

ƒ \

Getting Started 29

Press Result

1 0 0

ƒ \

The two roots are M3 and 16. Since you did not enter a guess, the TI-84 Plus used 0 (the default guess) and first returned the answer nearest 0. To find other roots, you must enter another guess. In this example, you entered 100.

Entering data into lists

You can enter data into lists using either of two methods:

• Using braces and ¿ on the home screen

— or —

• Using the statistical list editor.

Using ¿

Example: Store 1, 2, 3, and 4 to list 1 (L1).

Press Result

y E

1 ¢ 2 ¢

3 ¢ 4 y F

30 Getting Started

Press Result

y d Í

Using the statistical list editor

Example: Store 5, 6, 7, and 8 to list 2 (L2).

Press Result

… Í

~ } ‘ Í

(if L2 already contains data)

5 Í 6 Í 7 Í 8 Í

Getting Started 31

Press Result

y 5 y e Í

(displays the contents of the list on the home screen)

Plotting data

When you have statistical data stored in lists, you can display the data you have collected in a scatter plot, xyLine, histogram, box plot, or normal probability plot.

You will need to:

1. Determine which lists contain your data.

2. Tell the TI-84 Plus which lists of data you want to plot and define the plot.

3. Display the plot.

Determine which lists contain your data

Press Result

…

Note: In some cases, you may have several lists stored and you may have

to press ~ several times to find the correct lists.

32 Getting Started

Tell the TI-84 Plus which lists you want to plot

Press Result

y ,

4 Í

(turns plots off if any plots are on)

y ,

(turns Plot1 on)

† † y 9 Í

(enters L1 as the Xlist)

Getting Started 33

Press Result

† y 9 † Í

(enters L2 as the Ylist)

† ~ Í

(selects + as the plotting mark)

o ‘

Note: This step is optional and is not necessary unless there is a previous

entry in the Y= Editor. If there are additional entries in the Y= Editor, press † ‘ until all are clear.

Display the plot

Press Result

q } } Í

(selects ZoomStat)

34 Getting Started

Note: If you would like to add the regression line to a scatter plot,

adding Y1 to the end of the instruction: LinReg(ax+b) L1, L2, Y1. (Press  ~ Í Í to add Y1.) Press s to see the regression line.

Calculating a linear regression

If you wish to calculate the linear regression for data, you can do so using

LinReg instruction from the … CALC menu.

the

Example: Calculate the linear regression for the data entered in L1 and L2.

Press Result

… ~ † † †

y d ¢ y e

Note: The information on the last screen means that the points in L1 and

L2 [(1,5) (2,6) (3,7) (4,8)] all lie on the line Y = X + 4.

Getting Started 35

Calculating statistical variables

The TI-84 Plus lets you easily calculate one-variable or two-variable statistics for data that you have entered into lists.

Example: Using the data that you entered into L1 from the previous section “Using ¿“, calculate one-variable statistics.

Press Result

… ~

y d

36 Getting Started

Using the MATRIX Editor

Creating a new matrix

Press Result

y > |

2 Í 2 Í

1 Í 5 Í 2 Í 8 Í

Note: When you press Í, the cursor automatically highlights the

next cell so that you can continue entering or editing values. To enter a new value, you can start typing without pressing Í, but you must press Í to edit an existing value.

Using matrices to solve systems of equations

You can solve several equations simultaneously by entering their coefficients into a matrix and then using the form) function. For example, in the equations below, enter 3, 3, and 24 (for 3X, 3Y, and 24) in the first row, and 2, 1, 13 (for 2X, 1Y, and 13) in the second row.

Getting Started 37

rref (reduced row-echelon

Example: Solve 3X + 3Y = 24 and 2X + Y = 13

Press Result

y > ~ ~ †

2 Í 3 Í

3 Í 3 Í 2 4 Í 2 Í 1 Í 1 3 Í

y 5

y > ~

38 Getting Started

Press Result

}}}}}

y > † Í

You can interpret the resulting matrix as:

[1 0 5] represents 1X + 0Y = 5 or X = 5

[0 1 3] represents 0X + 1Y = 3 or Y = 3

The solution to this system of equations is X = 5, Y = 3.

Grouping

Grouping lets you make a copy of two or more variables and store them in the Flash memory of the TI-84 Plus. This function is similar to “zipping” a computer file and storing it. For example, suppose that you want to save data you collected for time, temperature, humidity, and barometric pressure because you may need to use the data for another assignment.

Getting Started 39

Grouping lets you keep these lists together for future use. Instead of trying to locate the correct lists and remember which ones were collected together, you can simply recall the group. Grouping also saves space on your graphing handheld by copying variables from RAM to Flash memory.

Example: Group lists L1, L2, and L3 and name them GROUPA.

Press Result

y L

Caution: You are in alpha mode.

[G] [R] [O] [U] [P] [A]

40 Getting Started

Press Result

Í † Í † Í

Ungrouping

To use variables that have been grouped, you must ungroup.

Example: Ungroup GROUPA.

Press Result

y L

Getting Started 41

Press Result

(to overwrite all three lists)

Error messages

Occasionally, when you enter a function or instruction or attempt to display a graph, the TI-84 Plus will return an error message.

For more details, see Appendix B

42 Getting Started

Example: Enter the least common multiple function lcm( followed by

only one number.

Press Result

 ~ } } Í

2 7 ¢

If you select new entry line. If you select the cursor is flashing at the location of the error. You can now correct the error and continue.

You can find a complete list of error conditions with explanations in Appendix B: General Information.

1:Quit, you return to the home screen with the cursor on a

2:Goto, you return to the original entry line;

Resetting defaults

If you are getting unexpected results, or if another person has used your TI-84 Plus and may have changed the settings, you should consider resetting defaults on the TI-84 Plus.

Press Result

y L

Getting Started 43

Press Result

WARNING: If you reset All RAM in step 3 above, you will delete stored

variables, lists, applications, and programs. Be sure you have backed up any essential data before you select this option.

Installing applications

Graphing handheld software applications (Apps) let you update the functionality of your TI-84 Plus by installing Apps. This is similar to the way that you add new features to your computer by installing new software applications.

You can find applications for the TI-84 Plus at the TI Online Store at

education.ti.com. Once you have downloaded an application to your

computer, you must use TI Connect™ or TI-GRAPH LINK™ software and the USB computer cable or TI Connectivity Cable USB to install the application on your TI-84 Plus.

Instructions for Windows®

1. Connect the USB computer cable between your computer and TI-84 Plus. Make sure the TI-84 Plus is on the home screen.

2. Using Windows (or NT) Explorer, locate the application file you want to transfer to the connected device.

44 Getting Started

3. Reduce the size of the Explorer window so you can see the TI Connect desktop icon.

4. Click the application file you want to transfer.

5. Drag the application file out of Explorer and drop it on the TI Connect desktop icon.

Instructions for Macintosh®

1. Connect the TI Connectivity Cable USB for Macintosh/Windows between your computer and TI-84 Plus, and make sure the TI-84 Plus is on the home screen.

2. Launch the TI-GRAPH LINK 2 software and establish a connection to your TI-84 Plus.

3. Drag the application to the TI-84 Plus window in TI-GRAPH LINK. Follow any on-screen instructions that are given.

Running applications

Once you have installed an application on your TI-84 Plus, you must start the application to use its features.

Example: Start the Catalog Help (CtlgHelp) app on the TI-84 Plus.

Press Result

† † Í

Getting Started 45

Quick reference

Press To

y } Darken the screen

y † Lighten the screen

y ~ Move the cursor to the end of an expression

y | Move the cursor to the beginning of an

expression

ƒ † Page down to the next screen (on menus)

ƒ } Page up to the next screen (on menus)

y [ Place your last entry on the current entry line on

the home screen

y Z Place Ans (a reference to your last answer) on the

current entry line on the home screen, allowing you to use the answer in the next calculation

{ Delete the character under the cursor

y 6 Insert additional characters at the cursor

† } Move the cursor from line to line

~ | Move the cursor from character to character

within a line

‘ Clear the current line. (If the cursor is on a blank

line, clears everything on the home screen.)

Battery precautions

Take these precautions when replacing batteries.

• Do not leave batteries within the 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 non-rechargeable batteries.

• Install batteries according to polarity (+ and N ) diagrams.

• Do not place non-rechargeable batteries in a battery recharger.

• Properly dispose of used batteries immediately.

• Do not incinerate or dismantle batteries.

46 Getting Started

Activities

The Quadratic Formula

Entering a Calculation

Use the quadratic formula to solve the quadratic equations

+5x+2=0 and 2x2N x + 3 = 0. Begin with the equation

3x 3x2+5x+2=0.

1. Press

2. Press ƒ [:] (above Ë). The colon allows

3. Press 5 ¿ ƒ [B] (above Œ) to

4. Press Í to store the values to the

5. Press £ Ì ƒ [B] Ã y C ƒ [B] ¡

3 ¿ ƒ [A] (above ) to

store the coefficient of the x

you to enter more than one instruction on a line.

store the coefficient of the X term. Press ƒ [:] to enter a new instruction on the same line. Press ) to store the constant.

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.

4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2 ƒ

[A] ¤ to enter the expression for one of the solutions for the quadratic formula,

b– b24ac–±

-------------------------------------2a

2 ¿ ƒ [C] (above

term.

Activities 47

6. Press Í to find one solution for the

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.

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 quadraticformula expression,

b– b24ac–+

--------------------------------------2a

48 Activities

5. Press } to move the cursor onto the in the formula. Press ¹ to edit the quadratic-formula expression to become:

b– b24ac––

-------------------------------------2a

+ sign

6. Press Í to find the other solution for

the quadratic equation 3x

+5x+2=0.

Displaying Complex Results

Now solve the equation 2x2N 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.

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.

The coefficient of the x2 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– b24ac––

-------------------------------------2a

5. Press Í to find one solution for the

equation 2x

Activities 49

N x+3=0.

6. Press y [ repeatedly until this

quadratic-formula expression is displayed:

b– b

---------------------------------------

4ac–+

7. Press Í to find the other solution for

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.

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 × 12.5 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.

From the diagram: 2X + A = 20 2X + 2B = 25 V = A…B…X

Substituting: V = (20 N 2X) (25à2 N X) X

1. Press o to display the

Y= editor, which is

where you define functions for tables and graphing.

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

50 Activities

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

TABLE SETUP menu.

the

2. Press Í to accept

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 (box’s volume) occurs when between 3 and 5.

5. Press and hold † to scroll the table until a

negative result for

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

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 displayed in the table is 6.)

TblStart=0.

X is about 4,

Y1 is displayed.

10 and 11.

Activities 51

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.

2. Press y 0.

3. Press † and } to scroll the table.

Notice that the maximum value for

410.26, which occurs at X=3.7. Therefore,

Y1 is

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.

52 Activities

7. Press † to display the other maximum.

The value of Y1 at X=3.68 in full precision

410.264064, at X=3.69 is 410.262318 and

is 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.

The standard window variables define the viewing window as shown.

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.

Xmin, Xmax,

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

Xscl as 1.

5. Press

0 Í 500 Í 100 Í 1 Í

to define the remaining window variables.

Activities 53

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

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.

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

at a time, evaluating

You also can enter your estimate for the maximum value of

6. Press 3 Ë 8. When you press a number key

while in TRACE, the X= prompt is displayed in the bottom-left corner.

TRACE feature.

Y1, one X dot

Y1 at each X.

54 Activities

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.

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

1. Press q to display the ZOOM menu.

2. Press

ZOOM instructions.

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 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.

Activities 55

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.

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.

Guess? prompt is displayed.

4. Press | to trace to a point near the maximum, and then press Í.

56 Activities

Or, press enter a guess for the maximum.

When you press a number key in TRACE, the X= prompt is displayed in the bottomleft 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.

3 Ë 8, and then press Í to

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.

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.

Correct Guesses

Women

Left

84712

9186

12 8 7 12

11 12 5 12

10 11 7 7

811811

12 13 11 12

Activities 57

Women

Right

Men

Left

Men

Right

Correct Guesses

Women

Left

Women

Right

Men Left

Men

Right

7124 8

9 111012

11 12 14 11

13 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 (

4. Likewise, enter each man’s correct guesses in

MRGHT (Men Right).

5. Press y ,. Select modified box plot Õ that uses and select Plot2. Turn on plot 2; define it as a modified box plot that uses WRGHT.

6. Press o. Turn off all functions.

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 Right).

MLEFT (Men Left) and

1:Plot1. Turn on plot 1; define it as a

WLEFT. Move the cursor to the top line

Women’s left-hand data

Women’s right-hand data

58 Activities

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

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?

11. Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use

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?

MRGHT, and then press r to examine minX, Q1,

MLEFT, redefine

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 Y = 50 + 5 Y = 50 + 5

Activities 59

N 45) … 10 + 10 (X N 55) … 10 + 10 … 10 + 20 (X N 65)

0 < X 45 < X 55 < X 65 < X

 45

 55  65

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).

3. Press p and set

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. @ 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?

X and @Y specify the horizontal and vertical distance

Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10.

Graphing Inequalities

Problem

Graph the inequality 0.4x 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.

N 3x + 5 < 0.2x + 4. Use the TEST menu

60 Activities

3. Enter the statement of the inequality as Y6. This function evaluates to 1 if true or 0 if false.

4. Press q

5. Press r † † to move to inequality, observing the value of

6 to graph the inequality in the standard window.

Y6. Then press | and ~ to trace the

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.

Activities 61

Solving a System of Nonlinear Equations

Problem

Using a graph, solve the equation x3N2x=2cos(x). Stated another way, solve the system of two equations and two unknowns: y = x 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.

N2x and y =

2. Press q

solutions may exist (points where the two functions appear to intersect).

3. Press q ~

menu. Set XFact=10 and YFact=10.

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

X and Y values have one decimal place.

the

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. The display shows that two

4 to select 4:SetFactors from the ZOOM MEMORY

4 to select 4:ZDecimal to redisplay the original graph.

62 Activities

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.

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

:0!Xmin:1!Xmax :0!Ymin:1!Ymax

:rand!X:rand!Y

:For(K,1,3000) :rand!N

:If N1 à3 :Then :.5X!X :.5Y!Y :End

:If 1 à3 <N and N2à3 :Then :.5(.5+X)!X :.5(1+Y)!Y :End

:If 2 à3<N :Then :.5(1+X)!X :.5Y!Y :End

Set viewing window.

Beginning of For group.

If/Then group

If/Then group.

Activities 63

: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.

Draw point. End of For group. Store picture.

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))

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 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.

64 Activities

Xmin=0 Xmax=1 Xscl=1

Ymin=

M.26

Ymax=1.1 Yscl=1

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.

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

:"Asin(BX)"!Y1

Define equations.

:"Csin(DX)"!Y2

:GraphStyle(1,1)

Set line and path graph styles.

:GraphStyle(2,5)

:FnOff 2

:randInt(1,10)!A :randInt(1,10)!B

Initialize coefficients.

:0!C:0!D

Activities 65

:L2p!Xmin :2p!Xmax :pà2!Xscl :L10!Ymin :10!Ymax :1!Yscl

:DispGraph :Pause

:FnOn 2 :Lbl Z

Set viewing window.

Display graph.

:Prompt C,D

Prompt for guess.

:DispGraph :Pause

Display graph.

:If C=A :Text(1,1,"C IS OK") :If CƒA :Text(1,1,"C IS

Display results.

WRONG") :If D=B :Text(1,50,"D IS OK") :If DƒB :Text(1,50,"D IS WRONG")

:DispGraph :Pause

Display graph.

:If C=A and D=B :Stop

Quit if guesses are correct.

:Goto Z

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 mode by defining the X component as T and the Y component as F(T).

66 Activities

Func mode can be plotted in Par

Procedure

1. Press z. Select Par, Simul, and the default settings.

2. Press p. Set the viewing window.

Tmin=0 Tmax=2 Tste p=. 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.

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.

Xmin= Xmax=7.4

pà2

Xscl=

Ymin= Ymax=3 Yscl=1

Note: You can generalize the unwrapping. Replace sin(T) in Y2T with

any other trig function to unwrap that function.

Finding the Area between Curves

Problem

Find the area of the region bounded by:

f(x) g(x) x

Activities 67

300x / (x2 + 625)

3cos(.1x)

Procedure

1. Press z. Select the default mode settings.

2. Press p. Set the viewing window.

Xmin=0 Xmax=100 Xscl=10

Ymin=

Ymax=10 Yscl=1

Xres=1

3. Press o. Turn off all functions and stat plots. Enter the upper and

lower functions.

Y1=300Xà(X2+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

at the intersection, which is the lower limit of the integral, is stored in Ans and X.

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.

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.

68 Activities

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 equations below describe the location of the ball at time T.

X(T) = b N Tv0 cosq Y(T) = Tv0 sinq N (gà2) T2where g = 9.8 m / sec

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 Tste p=. 1

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).

Ymin=0 Ymax=31 Yscl=10

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.

Activities 69

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.

5. Press p. Change the viewing window to concentrate on this

portion of the graph.

Tmin=1 Tmax=3 Tste p=. 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?

You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.

70 Activities

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:

Fx() td

∫

---

∫

x() x 0>,ln==

---=

Procedure 1

1. Press z. Select the default settings.

2. Press p. Set the viewing window.

and that

Xmin=.01 Xmax=10 Xscl=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).

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).

Ymin=

L1.5

Ymax=2.5 Yscl=1

Xres=3

Activities 71

6. Press r. Again, use the cursor keys to compare the values of the

two graphed functions, Y3 and Y4.

Problem 2

Explore the functions defined by

yt2td

= t2td

∫

,,and

∫

t2td

∫

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

2. Press q

3. Press r. Notice that the functions appear identical, only shifted

vertically by a constant.

4. Press o. Enter the numerical derivative of

6 to select 6:ZStandard.

Y5 in Y6.

Y5.

5. Press r. Notice that although the three graphs defined by

different, they share the same derivative.

72 Activities

Y5 are

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 case is the area of a circle, pr

Consider the formula A = NB polygon with N sides of equal length and B distance from the center to a vertex.

sin(pàN) cos(pàN) for the area of a regular

N = 4 sides

N = 8 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. Enter the formula as 0=ANNB Í. The interactive solver editor is displayed.

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.

Activities 73

sin(p / N)cos(p / N), and then press

4. Press } } to move the cursor onto A, and then press Äƒ \.

The solution for A is displayed on the interactive solver editor.

5. Now solve for

A=200 and N=6. To find the distance B, move the cursor onto B, and

B for a given area with various number of sides. Enter

then press ƒ \.

6. Enter N=8. To find the distance B, move the cursor onto B, and then

press ƒ \. Find

Find the area given your results with p6

B=6, and N=10, 100, 150, 1000, and 10000. Compare

(the area of a circle with radius 6), which is

B for N=9, and then for N=10.

approximately 113.097.

7. Enter

B=6. To find the area A, move the cursor onto A, and then

press ƒ \. Find

N=1000, and finally N=10000. Notice that as N gets large, the area A

approaches p

A for N=10, then N=100, then N=150, then

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 Xmax=200 Xscl=10

Ymin=0 Ymax=150 Yscl=10

Xres=1

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

X=100. Press 150 Í. Press 188 Í. Notice that as X increases,

the value of

74 Activities

Y converges to p6

, which is approximately 113.097.

100 Í to trace to

Y2=pB

area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr as N gets large.

(the area of the circle) is a horizontal asymptote to Y1. The

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.

0 for FV, since the future value of a loan is 0 once it is paid in

Enter 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.

Activities 75

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 Tmax=360 Tste p=1 2

Xmin=0 Xmax=360 Xscl=10

Ymin=0 Ymax=1000 Yscl=100

Note: To increase the graph speed, change Tst ep to 24.

7. Press r. After the graph is drawn, press

trace cursor to

T=240, which is equivalent to 20 years of payments.

240 Í to move the

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.

76 Activities

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.

At which monthly payment will the principal allocation surpass the interest allocation?

Activities 77

78 Activities

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 y L.

MEMORY 1: About...

2: Mem Mgmt/Del...

3: Clear Entries

4: ClrAllLists 5: Archive... 6: UnArchive... 7: Reset... 8: Group...

To check memory usage, first press y L and then select

2:Mem Mgmt/Del.

MEMORY menu. To access this menu, press

Displays information about the graphing handheld.

Reports memory availability and variable usage.

Clears ENTRY (last-entry storage).

Clears all lists in memory.

Archives a selected variable.

UnArchives a selected variable.

Displays the RAM, ARCHIVE, and ALL menus

Displays GROUP and UNGROUP menus.

RAM FREE displays the amount of available RAM.

ARC FREE displays the amount of available Archive.

Memory and Variable Management 79

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, and groups. The App slots are actually individual sectors of Flash ROM where Apps are stored.

Graphing Handheld

Available RAM Available

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

Displays the type of graphing handheld.

Displays the OS version. As new software upgrades become available, you can electronically upgrade your unit.

1:About.

Displays the Product ID. Each Flash-based graphing handheld 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 handheld at education.ti.com, or identify your handheld in the event that it is lost or stolen.

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

) and Archive (ARC FREE) memory. By selecting menu items on this

FREE

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 applications.

To check memory usage, follow these steps.

80 Memory and Variable Management

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

3. Select variable types from the list to display memory usage.

menu. The TI-84 Plus expresses memory quantities in bytes.

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

independent applications. You cannot edit or change variables in

AppVars unless you do so through the application which created

them.

To leave the MEMORY MANAGEMENT/DELETE menu, press either y5 or ‘. Both options display the home screen.

Deleting Items from Memory

Deleting an Item

To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, AppVars, picture, graph database, or string), follow these steps.

1. Press y L to display the

Memory and Variable Management 81

Y= variable, program, Apps,

MEMORY menu.

2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/

DELETE

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.

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.

menu.

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 y5, which displays the home screen.

You cannot delete some system variables, such as the last-answer variable

Ans and the statistical variable RegEQ.

Clearing Entries and List Elements

Clear Entries

Clear Entries clears the contents of the ENTRY (last entry) storage area.

To clear the

1. Press y L to display the

2. Select 3:Clear Entries to paste the instruction to the home screen.

3. Press Í to clear the

To c ancel

ENTRY storage area, follow these steps.

MEMORY menu.

ENTRY storage area.

Clear Entries, press ‘.

Note: If you select 3:Clear Entries from within a program, the Clear

Entries

entry) is cleared when the program is executed.

82 Memory and Variable Management

instruction is pasted to the program editor, and the Entry (last

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

3. Press Í to set the dimension of each list in memory to 0.

4:ClrAllLists to paste the instruction to the home screen.

To cancel

ClrAllLists does not delete list names from memory, from the LIST NAMES

ClrAllLists, press ‘.

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.

Archiving and UnArchiving Variables

Archiving lets you store data, programs, or other variables to the 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 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?

Variab le Type Names

Real numbers

Complex numbers

Matrices

Memory and Variable Management 83

A, B, ... , Z yes yes

[A], [B], [C], ... , [J]

(yes/no)

yes yes

UnArchive? (yes/no)

Variab le Type Names

Lists L1, L2, L3, L4, L5, L6,

Archive? (yes/no)

yes yes

UnArchive? (yes/no)

and user-defined names

Programs yes yes

Functions

Y1, Y2, . . . , Y9, Y0 no not

applicable

Parametric equations

Polar functions

X1T and Y1T, ... , X6T

Y6T

and

r1, r2, r3, r4, r5, r6 no not

no not

applicable

Sequence functions

Stat plots

u, v, w no not

applicable

Plot1, Plot2, Plot3

no not

applicable

Graph

GDB1, GDB2,...

yes yes

databases

Graph pictures

Strings

Tab l es

Pic1, Pic2, ... , Pic9, Pic0

Str1, Str2, . . . Str9, Str0

TblStart, Tb1, TblInput no not

yes yes

applicable

Apps Applications see Note

above

AppVars Application variables yes yes

Groups see Note

above

Variables with reserved names

System variables

minX, maxX, RegEQ,

and others

Xmin, Xmax, and

others

84 Memory and Variable Management

no not

applicable

no not

applicable

Archiving and unarchiving can be done in two ways:

• Use the menu or

5:Archive or 6:UnArchive commands from the MEMORY

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

UnArchive RAM free size > variable size

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.

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 edit screen.

3. Press y d to place the L1 variable in the edit screen.

4. Press Í to complete the archive process.

Memory and Variable Management 85

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.

2. Select

3. Select

2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/

DELETE

menu.

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.

86 Memory and Variable Management

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.

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 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.

Y= functions. For instance, you can

• Mode settings such as (numbers); and Full (screen)

• Y= functions off

• Window variable values such as

Xres=1

and

• Stat plots off

• Format settings such as CoordOn (graphing coordinates on);

AxesOn; and ExprOn (expression on)

• rand seed value to 0

Normal (notation); Func (graphing); Real

Xmin=L10, Xmax=10, Xscl=1, Yscl=1,

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

2. Select 7:Reset to display the RAM ARCHIVE ALL menu.

Memory and Variable Management 87

MEMORY 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.

1. From 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.

RAM ARCHIVE ALL menu, select 1:All RAM to display the

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.

88 Memory and Variable Management

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.

• 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.

Memory and Variable Management 89

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

3. Read the message below the

1:All Memory to display the RESET MEMORY menu.

RESET MEMORY menu.

• To cancel the reset and return to the home screen, press Í.

• To continue with the reset, select

MEM cleared is displayed on the home screen.

2:Reset. The message

When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or †.

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.

To create a group of variables:

1. Press y L to display the

MEMORY menu.

2. Select

90 Memory and Variable Management

8:Group to display GROUP UNGROUP menu.

3. Press Í to display the GROUP menu.

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

1: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

1:All- displays the following screen.

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.

Memory and Variable Management 91

Repeat the selection process until all variables for the new group are selected and then press ~ to display the

7. Press Í to complete the grouping process.

DONE menu.

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

1: Rename

2: Overwrite

3: Overwrite All

4: Omit

5: Quit

Prompts to rename receiving variable.

Overwrites data in receiving duplicate variable.

Overwrites data in all receiving duplicate variables.

Skips transmission of sending variable.

Stops transmission at duplicate variable.

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.

92 Memory and Variable Management

• 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

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

4:Omit, the unit does not ungroup the variable in

MEMORY menu.

2. Select

3. Press ~ to display the UNGROUP menu.

4. Press } and † to move the selection cursor (4) next to the group

8:Group to display the GROUP UNGROUP menu.

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.

Garbage Collection

Garbage Collection Message

If you use the user data archive extensively, you may see a Garbage

Collect?

is not enough free contiguous archive memory.

message. This occurs if you try to archive a variable when there

Memory and Variable Management 93

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.

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 choose 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.

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.

94 Memory and Variable Management

Texas Instruments TI-84+SE, TI-84 Plus User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Important Information

USA FCC Information Concerning Radio Frequency Interference

About the TI-84 Plus and TI-84 Plus Silver Edition

About this book

Table of Contents

Getting Started

TI-84 Plus keys

Turning the TI-84 Plus on and off

Automatic Power Down™

Home screen

Entering an expression

Interchangeable Faceplates

Removing a Faceplate

Installing New Faceplates

Using the Clock

Displaying the Clock Settings

Changing the Clock settings

Error Messages

Turning the Clock On

Turning the Clock Off

TI-84 Plus menus

Summary of menus on the TI-84 Plus

Editing and deleting

Using parentheses

Storing a value

Graphing a function

Changing mode settings

The importance of mode settings

Setting the graphing window

Building a table

Clearing the Y= Editor

Using the CATALOG

Performing simple calculations

Changing a decimal to a fraction

Finding the least common multiple

Finding the square root

Finding the factorial of numbers

Solving trigonometric functions

Adding Complex Numbers

Using the equation solver

Entering data into lists

Using the statistical list editor

Plotting data

Determine which lists contain your data

Tell the TI-84 Plus which lists you want to plot

Display the plot

Calculating a linear regression

Calculating statistical variables

Using the MATRIX Editor

Creating a new matrix

Using matrices to solve systems of equations

Grouping

Ungrouping

Error messages

Resetting defaults

Installing applications

Instructions for Windows®

Instructions for Macintosh®

Running applications

Quick reference

Battery precautions

Activities

The Quadratic Formula

Entering a Calculation

Converting to a Fraction

Displaying Complex Results

Box with Lid

Defining a Function

Defining a Table of Values

Zooming In on the Table

Setting the Viewing Window

Displaying and Tracing the Graph

Zooming In on the Graph

Finding the Calculated Maximum

Comparing Test Results Using Box Plots

Problem