Chapter 1: Operating the TI-84 Plus Silver Edition

Using the Color-Coded Keyboardp. 2

The keys are color-coded to help you find them quickly. The light-colored keys are the number keys. The keys down the right-hand side are the common math operations. The keys across the top set up and display graphs. The APPS key opens applications such as Inequality Graphing, Transformation Graphing, Conic Graphing, the Polynomial Root Finder and Simultaneous Equation Solver, and Catalog Help.

The main job of each key is printed on the key itself. For example, pressing MATH opens the MATH menu.

Using the 2nd and ALPHA Keysp. 2

Most keys have more than one job. The second function is printed above the key in the same color as the 2nd key. Press 2nd and the next key you press does its second function. For example, 2ndTEST opens the TEST menu.

The third function is printed above the key in the same color as the ALPHA key. These enter letters and a few special symbols, run SOLVE, and open the shortcut menus. For example, ALPHAA types the letter A. In this manual that is written ALPHAA.

Turning On the Graphing Calculatorp. 3

Press ON to switch the calculator on. After a RAM reset, or until you ask it not to, a start-up information screen reminds you that ALPHAF1 to ALPHAF5 open the shortcut menus. Press 1 to continue and never show it again, or 2 to continue and see it again next time.

• If you switched off with 2ndOFF, the home screen returns just as you left it, and any error is cleared. If the home screen looks blank, press ▲︎ to scroll back through the history of earlier calculations.
• If Automatic Power Down (APD) switched it off, everything returns exactly as it was, including the display, the cursor and any error.
• A switched-off calculator that is connected to another calculator or a computer will wake up when it receives data. This does not apply to the emulator.

Turning Off the Graphing Calculatorp. 4

Press 2ndOFF (OFF) to switch off manually. All settings and memory are kept (Constant Memory), and any error condition is cleared.

To save the batteries, Automatic Power Down (APD) switches the calculator off by itself after about five minutes without any key presses.

Batteriesp. 4

The TI-84 Plus uses four AAA alkaline batteries and one button-cell backup battery. The backup battery keeps memory alive while you change the AAAs.

Adjusting the Display Contrastp. 4

• 2nd▲︎ darkens the screen one level at a time.
• 2nd▼︎ lightens the screen one level at a time.

When to Replace Batteriesp. 4

A real TI-84 Plus shows a low-battery message when it is switched on once the batteries are running down. It usually keeps working for one or two weeks afterwards (longer if you use it rarely), then switches itself off until the batteries are replaced. Memory is kept. Always replace the batteries before installing a new operating system.

Types of Displaysp. 5

The calculator shows both text and graphs. Chapter 3 describes graphs. Chapter 9 describes the split-screen modes that show a graph and text together.

Home Screenp. 5

The home screen is the main screen. You type calculations and instructions here, and the answers appear on the same screen. Most of your work is kept in the history above the cursor. Use ▲︎ and ▼︎ to scroll through the history and paste an earlier entry or answer onto the current line.

Using Shortcut Menusp. 6

Shortcut menus give quick access to:

• templates for fractions and for selected functions from the MATH MATH and MATH NUM menus, drawn the way they appear in a textbook: absolute value, summation, numeric differentiation, numeric integration and log with any base;
• quick matrix entry;
• the names of the function variables from the VARS Y-VARS menu.

The menus are hidden until you ask for one. Press ALPHA plus the key that is the matching "F-key", then choose an item with its number, or move the cursor with ▲︎ and ▼︎ and press ENTER.

Every shortcut-menu item except the matrix templates can also be reached through the regular menus. For example, you can paste the summation template from the FUNC shortcut menu, from the MATH MATH menu (0:summation Σ(), or from the CATALOG.

Returning to the Home Screenp. 7

To return to the home screen from any other screen, press 2ndQUIT (QUIT).

Busy Indicatorp. 8

While the calculator is working or drawing a graph, a vertical moving line appears in the top-right corner. If you pause a graph or program, the line turns into a vertical moving dotted line.

Display Cursorsp. 8

The shape of the cursor tells you what the next key press will do.

If you press ALPHA while inserting, the cursor becomes an underlined A. If you press 2nd while inserting, it becomes an underlined arrow. When the highlighted character is very narrow, such as a colon or comma, the cursor does not change shape. Graphs and editors sometimes show extra cursors; they are described in the chapters that use them.

Interchangeable Faceplatesp. 8

The TI-84 Plus Silver Edition has snap-on faceplates that let you change its look. Extra ones are sold in the TI Online Store at education.ti.com.

Displaying the Clock Settingsp. 9

1. Press MODE.
2. Press ▼︎ to move the cursor to SET CLOCK (the last row).
3. Press ENTER.

Changing the Clock Settingsp. 10

On the clock screen, move between rows with ▼︎ and ▲︎. For the format choices, use ◀︎ or ▶︎ to pick one and press ENTER. For the numbers, press CLEAR and type the new value.

Clock Error Messagesp. 10

If you enter a day that does not exist for the month, for example June 31, you get an error message with two choices:

Turning the Clock Onp. 10

There are two ways to turn the clock on: through the MODE screen, or through the CATALOG.

From the MODE screen. If the clock is off, the bottom row of the MODE screen reads TURN CLOCK ON.

1. Press MODE and move down to TURN CLOCK ON.
2. Press ENTER twice.

From the CATALOG.

1. Press 2ndCATALOG to open the CATALOG.
2. Use ▼︎ or ▲︎ to scroll until the selection cursor is on ClockOn.
3. Press ENTER twice: once to paste the command, once to run it.

Turning the Clock Offp. 11

1. Press 2ndCATALOG to open the CATALOG.
2. Scroll with ▼︎ or ▲︎ until the selection cursor is on ClockOff.
3. Press ENTER twice.

What Is an Expression?p. 11

An expression is any combination of numbers, variables, functions (with their arguments) that works out to a single answer. You type an expression in the same order you would write it on paper. For example, πR² is an expression.

On the home screen, an expression gives you an answer. In most places where a number is needed, you can type an expression instead.

Entering an Expressionp. 12

Build an expression by typing numbers, variable names and functions from the keyboard and menus. The expression is complete when you press ENTER, wherever the cursor happens to be in the line. The whole thing is then evaluated using the Equation Operating System (EOS) rules, and the answer is shown in the format set by the Answers mode.

Most functions are single symbols that happen to look like several letters. Always press the key or choose the item from a menu; never spell a function out. To take the log of 45, press LOG 45. If you typed the letters L, O and G instead, the calculator would read them as the variables L, O and G multiplied together.

Multiple Entries on a Linep. 12

To put two or more expressions or instructions on one line, separate them with colons (ALPHA: types :). When you press ENTER they all run in order and all are saved together in ENTRY (the last entry).

Entering a Number in Scientific Notationp. 12

1. Type the part of the number before the exponent. It can be an expression.
2. Press 2ndEE (EE). A small ᴇ is pasted at the cursor.
3. Type the exponent, one or two digits. If it is negative, press (−) first and then type the exponent.

Functionsp. 12

A function takes a value and returns a value. In the example above, ÷, −, +, √ and log( are all functions. By convention, function names start with a lowercase letter on the TI-84 Plus. Most take at least one argument, which you can recognise by the opening parenthesis at the end of the name. For example, sin( needs one argument: sin(value).

Instructionsp. 13

An instruction starts an action. For example, ClrDraw clears everything drawn on a graph. Instructions cannot be used inside expressions. By convention, instruction names start with an uppercase letter. Some instructions take several arguments, again shown by an opening parenthesis at the end of the name. For example, Circle( needs three: Circle(X,Y,radius).

Interrupting a Calculationp. 13

To stop a calculation or graph that is in progress (the busy indicator is showing), press ON. When you interrupt a calculation, a menu appears:

When you interrupt a graph, a partial graph is left on the screen. To go back to the home screen, press CLEAR or any key that is not a graphing key. To start graphing again, press a graphing key or run a graphing instruction.

TI-84 Plus Edit Keysp. 13

Checking Mode Settingsp. 14

The mode settings control how the calculator interprets and displays numbers and graphs. They are kept when the calculator is switched off. Every number, including matrix and list elements, is displayed according to the current settings.

Press MODE to see them. The current settings are highlighted. Here is every row, with the default shown first:

Changing Mode Settingsp. 15

1. Press ▼︎ or ▲︎ to move the cursor to the row you want to change.
2. Press ▶︎ or ◀︎ to move to the setting you want.
3. Press ENTER to select it.

Setting a Mode from a Programp. 15

A program can change a mode by running the mode's name as an instruction, for example Func or Float. On a blank line in the program editor, press MODE, select the setting you want, and press ENTER: the instruction is pasted at the cursor.

Normal, Sci, Engp. 15

The notation modes only change how answers are displayed on the home screen. An answer can have up to 10 digits and a two-digit exponent, and can also be a fraction. You can always type numbers in any format.

• Normal is the everyday way to write numbers, with digits on both sides of the decimal point: 12345.67.
• Sci (scientific) has one digit before the decimal point and a power of 10 after the ᴇ: 1.234567ᴇ4.
• Eng (engineering) has one, two or three digits before the decimal point, and the power of 10 is always a multiple of three: 12.34567ᴇ3.

Float, 0123456789p. 16

Float (floating decimal) shows up to 10 digits plus the sign and decimal point. The digits 0 to 9 (fixed decimal) set the exact number of digits shown to the right of the decimal point for decimal answers. The decimal setting works with Normal, Sci and Eng.

The decimal setting applies to these numbers, in line with the Answers mode:

• an answer on the home screen;
• coordinates on a graph (Chapters 3, 4, 5 and 6);
• the equation of the line, x and dy/dx values from the Tangent( DRAW instruction (Chapter 8);
• the results of CALCULATE operations (Chapters 3, 4, 5 and 6);
• the regression equation stored after a regression model is run (Chapter 12).

Radian, Degreep. 16

Angle modes control how the calculator reads angles in trigonometric functions and in polar/rectangular conversions. In Radian mode angles are read, and answers shown, in radians. In Degree mode they are read, and shown, in degrees.

Func, Par, Pol, Seqp. 16

The graphing modes set which kind of equations the calculator graphs. Chapters 3, 4, 5 and 6 explain each in detail.

• Func (function) plots functions where Y is a function of X (Chapter 3).
• Par (parametric) plots relations where X and Y are both functions of T (Chapter 4).
• Pol (polar) plots functions where r is a function of θ (Chapter 5).
• Seq (sequence) plots sequences (Chapter 6).

Connected, Dotp. 17

Connected draws a line between each pair of calculated points of the selected functions. Dot plots only the calculated points themselves.

Sequential, Simulp. 17

Sequential evaluates and plots one function completely before starting the next. Simul (simultaneous) evaluates and plots every selected function for one value of X, then moves on to the next value of X.

Real, a+bi, re^θip. 17

Real mode gives no complex results unless you typed complex numbers into the calculation. The other two modes show complex results:

• a+bi (rectangular complex) shows complex numbers as a+bi.
• re^θi (polar complex) shows complex numbers as re^θi.

Full, Horiz, G-Tp. 17

Full uses the whole screen for a graph or an edit screen. The two split-screen modes show two screens at once:

• Horiz (horizontal) shows the current graph in the top half of the screen and the home screen or an editor in the bottom half (Chapter 9).
• G-T (graph-table) shows the current graph on the left half and the table on the right half (Chapter 9).

MathPrint, Classicp. 18

MathPrint shows most inputs and outputs the way a textbook would: stacked fractions, a true radical sign, and so on. Classic writes everything on a single line, such as 1/2+3/4.

n/d, Un/dp. 18

n/d shows results as a simple fraction. The numerator can have at most six digits, and the denominator can not be larger than 9999.

Un/d shows results as a mixed number when that is possible. U, n and d must all be integers. If U is not an integer, the result may be converted to the form U n/d. If n or d is not an integer, you get a syntax error. The whole number, numerator and denominator can each have at most three digits.

Answers: Auto, Dec, Fracp. 18

• Auto gives an answer in a form like the input: a fraction in the expression gives a fraction answer if possible, and a decimal in the expression gives a decimal answer.
• Dec shows answers as integers or decimal numbers.
• Frac shows answers as fractions whenever possible.

GoTo Format Graph: No, Yesp. 18

No keeps the Format Graph screen out of the way; you can still open it any time with 2ndFORMAT (FORMAT). Yes takes you to the Format Graph screen as soon as you press ENTER on the MODE screen, so you can change the graph format. Press MODE to go back to the MODE screen.

Stat Diagnostics: Off, Onp. 19

Off shows a regression result without the correlation coefficient (r) or the coefficient of determination (r²). On includes r and r², where they apply to the regression.

Stat Wizards: On, Offp. 19

On (the default): choosing a menu item in STAT CALC, DISTR DISTR, DISTR DRAW, or seq( in LIST OPS opens a wizard screen that helps you fill in the required and optional arguments. The command is then pasted, with those arguments, into the home-screen history or into most other places where input is allowed. Some calculations run straight from the wizard. Commands pasted from 2ndCATALOG (CATALOG) skip the wizard. The Catalog Help application (APPS) gives more syntax help.

Off: the command is pasted at the cursor with no wizard. The tutorial below shows both settings.

Speed: Fast, Realistic (emulator only)

This row is not on a real TI-84 Plus; it belongs to the emulator. FAST (the default) runs everything as quickly as your computer can, so graphs appear almost at once and programs finish instantly. REALISTIC paces the emulator like a real TI-84 Plus Silver Edition: graphs are drawn from left to right at about the speed of the calculator, long calculations such as fnInt(, solve( or a regression show the busy indicator for a moment, and programs run at TI-BASIC speed — useful for checking that a game or animation will feel right on a real calculator.

To change it, press MODE, press ▲︎ twice (the cursor wraps from the top row to the bottom), move to FAST or REALISTIC with ▶︎ or ◀︎, and press ENTER. While a graph is being drawn in REALISTIC, ENTER pauses and resumes the drawing, and TRACE or an arrow key waits until the graph is finished, as on the calculator. The setting is kept when you reset RAM or defaults.

Set Clockp. 19

Use this row to set the time and date and the clock display formats. See Using the Clock.

Variables and Defined Itemsp. 19

You can enter and use several kinds of data: real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures and strings. Each kind has its own set of names. For lists you can also make up your own names of up to five characters.

Notes about Variablesp. 20

• You can create as many list names as memory allows (Chapter 11).
• Programs have user-defined names and share memory with variables (Chapter 16).
• From the home screen or 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 every Y= function (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 one element of a matrix or list.
• The DRAW STO menu items store and recall graph databases and pictures (Chapter 8).
• Most variables can be archived, but system variables including r, T, X, Y and θ cannot (Chapter 18).
• Apps are independent applications stored in Flash ROM. AppVars is a holder for variables created by those applications. You can only edit or change variables in AppVars through the application that created them.

Storing Values in a Variablep. 20

You store values in variables, and later recall them, by name. Whenever an expression that contains a variable name is evaluated, the variable's value at that moment is used.

To store a value in a variable from the home screen or a program with STO►, start on a blank line:

1. Type the value to store. It can be an expression.
2. Press STO►. An arrow → is pasted at the cursor.
3. Press ALPHA and then the letter of the variable.
4. Press ENTER. If you typed an expression it is evaluated, and the result is stored in the variable.

Displaying a Variable Valuep. 21

To see the value of a variable, type its name on a blank line of the home screen and press ENTER.

Archiving Variables (Archive, Unarchive)p. 21

You can move data, programs and other variables into a protected area of memory called the user data archive, where they cannot be edited or deleted by accident. An archived variable has an asterisk to the left of its name in memory menus. Archived variables cannot be edited or run; you can only see them and unarchive them. For example, if you archive L₁, it still exists, but if you paste its name on the home screen you will not be able to see or change its contents until you unarchive it. Chapter 18 explains archiving in full.

Using Recall (RCL)p. 21

RCL copies the contents of a variable to the cursor. To leave RCL without pasting, press CLEAR.

1. Press 2ndRCL (RCL). Rcl and an edit cursor appear on the bottom line.
2. Enter the variable name in one of these ways: press ALPHA and the letter of the variable; press 2ndLIST and choose a list, or press 2ndL1 to 2ndL6 for L₁ to L₆; press 2ndMATRIX (MATRIX) and choose a matrix; press VARS (or VARS ▶︎ for Y-VARS) and choose the type and name of the variable or function; press ALPHAF4 for the YVAR shortcut menu and choose a function; or press PRGM ◀︎ and choose a program (in the program editor only). The name appears on the bottom line and the cursor disappears.
3. Press ENTER. The contents of the variable are inserted where the cursor was before you began.

Scrolling Through Previous Entries on the Home Screenp. 22

You can scroll back through earlier entries and answers on the home screen, even after the screen has been cleared. When you find one you want, you can paste it on the current entry line.

• Press ▲︎ or ▼︎ to move to the entry or answer you want to copy, then press ENTER. It is pasted on the input line at the cursor.
• If the cursor is inside a MathPrint expression, press 2nd▲︎ first to move it out of the expression, then move to the entry or answer.
• Press DEL to delete an entry and answer pair. After you delete it, it cannot be shown or recalled again.

There are worked examples in Displaying Entries and Answers.

Using ENTRY (Last Entry)p. 22

Each time you press ENTER on the home screen to evaluate an expression or run an instruction, it is copied into a storage area called ENTRY (last entry). ENTRY is kept when you switch the calculator off.

To recall it, press 2ndENTRY (ENTRY). The last entry is pasted at the cursor, where you can edit and run it. On the home screen or in an editor, the current line is cleared first and the last entry is pasted in its place.

ENTRY is only updated when you press ENTER, so you can recall the previous entry even after you have started typing the next expression.

Accessing a Previous Entryp. 23

The calculator keeps as many earlier entries in ENTRY as fit, up to 128 bytes in all. Press 2ndENTRY repeatedly to step back through them. After the oldest stored entry is shown, one more press brings back the newest, then the next-newest, and so on. A single entry of more than 128 bytes can be run, but is not saved in ENTRY.

Executing the Previous Entry Againp. 23

Once the last entry is pasted (and edited, if you want), press ENTER to run it. Press ENTER again to run the displayed entry once more. Each repetition shows the entry and its new answer.

Multiple Entry Values on a Linep. 23

To store two or more expressions or instructions in ENTRY at once, separate them with colons and press ENTER. When you press 2ndENTRY, the whole colon-separated line is pasted at the cursor. You can edit any part of it, and everything runs again when you press ENTER.

Clearing ENTRYp. 24

The Clear Entries command (Chapter 18) empties everything held in the ENTRY storage area.

Continuing an Expressionp. 25

You can use Ans as the first thing in the next expression without typing the value again or pressing 2ndANS. On a blank line, type an operation such as × or +; the calculator pastes Ans at the start for you, followed by the operation.

Storing Answersp. 25

To keep an answer, store Ans in a variable before you evaluate anything else.

Using a TI-84 Plus Menup. 25

Most operations are reached through menus. When you press a key that opens a menu, one or more menu names appear along the top line of the screen.

• The menu name at the left of the top line is highlighted. Up to seven of its items are listed below it, starting with item 1, which is highlighted too.
• Each item is numbered or lettered: 1 to 9, then 0, then A, B, C and so on. The LIST NAMES, PRGM EXEC and PRGM EDIT menus label only items 1 to 9 and 0.
• If the menu continues beyond what is shown, a down arrow replaces the colon next to the last item.
• An item that ends with an ellipsis (...) opens a second menu or an editor when you select it.
• An asterisk to the left of an item shows that the item is stored in the user data archive (Chapter 18).

Displaying a Menup. 26

While you work, you will often need an item from a menu. When you press a key that opens a menu, the menu temporarily replaces the screen you were working on. For example, MATH shows the MATH menu full-screen. After you pick an item, you normally return to the screen you were working on.

Selecting an Item from a Menup. 27

There are two ways to choose an item from a menu:

• Press the number or letter next to the item. The cursor can be anywhere in the menu, and the item does not need to be on screen.
• Press ▼︎ or ▲︎ to move the cursor to the item, then press ENTER.

After you pick an item, the calculator usually returns to the previous screen.

Leaving a Menu without Making a Selectionp. 27

There are four ways to leave a menu without choosing anything:

• Press 2ndQUIT to go to the home screen.
• Press CLEAR to go back to the previous screen.
• Press the key combination for a different menu, such as MATH or 2ndLIST.
• Press the key combination for a different screen, such as Y= or 2ndTABLE.

VARS Menup. 27

The VARS and VARS Y-VARS menus let you paste the names of functions and system variables into an expression, or store directly to them. Press VARS to open the VARS menu. Every item opens a secondary menu of system variable names. 1:Window, 2:Zoom and 5:Statistics each have more than one secondary menu.

VARS Y-VARS Menup. 28

Press VARS ▶︎ to display the VARS Y-VARS menu. 1:Function, 2:Parametric and 3:Polar open secondary menus of the Y= function variables.

Selecting a Variable from the VARS Menu or VARS Y-VARS Menup. 28

1. Display the menu: press VARS for the VARS menu or VARS ▶︎ for the VARS Y-VARS menu.
2. Select the type of variable, such as 2:Zoom from VARS or 3:Polar from Y-VARS. A secondary menu opens.
3. If you chose 1:Window, 2:Zoom or 5:Statistics, press ▶︎ or ◀︎ to see the other secondary menus.
4. Select the name of the variable. It is pasted at the cursor.

Order of Evaluationp. 29

The Equation Operating System (EOS) decides the order in which the parts of an expression are worked out. Thanks to EOS you can type numbers and functions in a simple left-to-right sequence. Within one priority level, EOS works from left to right, and anything in parentheses is calculated first.

Implied Multiplicationp. 29

The calculator understands implied multiplication, so you do not always need to press ×. It treats 2π, 4sin(46), 5(1+2) and (2×5)7 as products.

Parenthesesp. 29

Everything inside a pair of parentheses is calculated first. In 4(1+2), EOS first works out 1+2, then multiplies the result, 3, by 4.

Negationp. 30

To type a negative number, press (−) and then the number. On the TI-84 Plus, negation is on the third level of the EOS ranking, so functions on the first level, like squaring, are worked out before the negation. This means −X² is a negative number (or 0). To square a negative number, use parentheses.

Flash – Electronic Upgradabilityp. 30

Flash technology lets a real TI-84 Plus be upgraded to new software versions over the Internet, without buying a new calculator. Maintenance upgrades are free, while new applications and major software upgrades are sold on education.ti.com. Chapter 19 has the details.

1.5 Megabytes of Available Memoryp. 30

The TI-84 Plus Silver Edition has 1.5 MB of memory (0.5 MB on the TI-84 Plus). About 24 KB of RAM is available for calculations and for storing functions, programs and data. About 1.5 MB of user data archive gives a safe place to store data, programs, applications or other variables where they cannot be edited or deleted by accident. You can also free up RAM by archiving variables. See Chapter 18.

Applicationsp. 30

Many applications come preloaded, and others can be installed to suit your needs. The 1.5 MB archive can hold up to 94 applications at one time on the Silver Edition (the TI-84 Plus has 30 App slots). Applications can also be kept on a computer or sent from one calculator to another. See Chapter 18.

Archivingp. 31

The user data archive is a protected part of memory, separate from RAM. It lets you keep data, programs, applications and other variables in a safe place, and it frees RAM for things that need more room. Archive anything that you do not need to edit often. See Chapter 18.

Other TI-84 Plus Featuresp. 31

The calculator's own guidebook introduced the basic operations. The rest of this manual covers the other features in greater detail. Here is a map of what is where.

Communication Linkp. 33

A real TI-84 Plus has a USB port and a unit-to-unit cable for connecting to another TI-84 Plus or Silver Edition. It also has an I/O port for talking to older calculators, CBL 2 and CBR systems. With TI Connect software and a USB computer cable, it can connect to a personal computer, and receive software upgrades from the TI website. See Chapter 19.

Diagnosing an Errorp. 33

The calculator can detect an error while it is evaluating an expression, running an instruction, plotting a graph, or storing a value. When it does, it shows a menu whose title is the error message, such as ERR:SYNTAX or ERR:DOMAIN. Appendix B describes every error and its likely causes.

Correcting an Errorp. 34

1. Note the error type (ERR: followed by the name).
2. Choose 2:Goto if it is offered. The previous screen returns with the cursor at or near the mistake.
3. Work out what is wrong. If you do not recognize the error, look it up in Appendix B.
4. Correct the expression.