Texas Instruments TI-84 User Manual

Getting to Know Your TI-84 Plus Silver Edition

Turning Your TI-84 Plus Silver Edition On and Off

To turn on your TI-84 Plus Silver Edition, press ….

■

If you had previously turned off your TI-84 Plus Silver Edition by pressing
y M, it will display the home screen as it was when you last used it.

To turn off your TI-84 Plus Silver Edition manually, press yM.

■

All settings and memory contents are retained by Constant Memory

To prolong the life of the batteries, Automatic Power Down™(APD™) turns

off your TI-84 Plus Silver Edition automatically after about five minutes

without any activity.

Using the y and É Keys

The secondary function of each key is printed in blue above the key.
When you press the blue y key, the character, abbreviation, or word

printed in blue above the other keys becomes active for the next
keystroke. For example, when you press y and then ç, the TEST

menu is displayed.

The alpha function of each key is printed in green above the key. When
you press the green É key, the alpha character printed in green

above the other keys becomes active for the next keystroke. For
example, when you press É and then ç, the letter A is entered.

TI-84 Plus Silver Edition Keyboard

å key accesses the Handheld
Software Applications (Apps) loaded
on your TI-84 Plus Silver Edition

É accesses the alpha function

™.

printed in green above each key

y accesses the second function
printed in blue above each key

Operations keys

}~ Ü| keys let you move
the cursor in four directions

ë erases (clears) the entry line
or deletes an entry and answer on
the home screen

Õ evaluates an expression,

executes an instruction, or selects

a menu item

Adjusting the Display Contrast

To adjust the contrast, follow these steps:

1 Press and release the y key.
2 Press and hold } or Ü (which are above

and below the contrast symbol).

} Darkens the screen
Ü Lightens the screen

Home Screen

The home screen is the primary screen of the

TI-84 Plus Silver Edition. On this screen, you can enter

instructions to execute and expressions to evaluate.

The answers are displayed on the same screen.

To return to the Home Screen from any other screen,
press y5.

Darker

Lighter

Special Features of the TI-84 Plus Silver Edition,
TI-84 Plus, and TI-83 Plus

Flash™— Electronic Upgradability

The TI-84 Plus Silver Edition, TI-84 Plus, and TI-83 Plus use Flash

technology, which lets you update your operating system and

add Handheld Software Apps, such as Topics in Algebra 1, Inequality

Graphing, NoteFolio™, TImeSpan™, CellSheet™, and many more!

Comparing the TI-84 Plus Silver Edition and the TI-83 Plus

TI-84 Plus Silver Edition TI-83 Plus

Flash ROM 1.54 Mb 160 Kb

Holds up to 94 Apps 10 Apps

Preloaded Apps 18 4

Connectivity USB cable included TI Connectivity USB

cable sold separately

Case Color SILVER & Customizable Classic dark gray

Z80 Processor Speed 15 MHz 6 MHz

RAM 24 Kb 24 Kb

TI Connectivity Kit

With the TI Connect™software and TI Connectivity USB cable, you

can link your TI-84 Plus to a personal computer. As future software

updates become available on the TI website, you can download

the software to your computer and use the TI Connect software

and TI Connectivity USB cable to update your TI-84 Plus.

© Texas Instruments, 2007

education.ti.com

Getting Started Using Your TI-84 Plus Silver Edition

TI-84 Plus Silver Edition Edit Keys

Keystroke Result

~ or | Moves the cursor within an expression.
} or Ü Moves the cursor from line to line within an expression that

occupies more than one line. On the top line of an expression
on the home screen, } moves the cursor to the beginning of
the expression. On the bottom line, Ü moves the cursor to
the end of the expression.

y| Moves the cursor to the beginning of an expression.
y~ Moves the cursor to the end of an expression.
Õ Executes an instruction and/or an expression.
ë On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everything on the
home screen. In an editor, clears the expression or value
where the cursor is located.

{ Deletes a character at the cursor.
y 6 Changes the cursor to an underline (__) and inserts characters

in front of the underline cursor; to end insertion, pressy6,
or press |}~or Ü.

y Changes the cursor to ; the next keystroke performs a

2nd operation (in blue above a key); to cancel 2nd,
press y again.

É Changes the cursor to ÿ; the next keystroke pastes an alpha

character (in green above a key); to cancel É press

É again, or press |}~or Ü.

y7 Changes the cursor to ÿ; sets alpha-lock; subsequent

keystrokes paste alpha characters; to cancel alpha-lock, press
É. If you are prompted to enter a name for a group or a
program, alpha-lock is set automatically.

Ñ Pastes an X in Func mode, a T in Par mode, a␪␪in Pol mode,

or an n in Seq mode with one keystroke.

Display Cursors

In most cases, the appearance of the cursor indicates what will happen
when you press the next key.

Cursor Appearance Effect of next keystroke

Entry Solid rectangle A character is entered at the cursor;

$ any existing character is overwritten.

Insert Underline A character is inserted in front of the

__ cursor location.

Second Up arrow A 2nd character (blue on the keyboard)

} is entered or a 2nd operation is executed.

Alpha Reverse A An alpha character (green on the keyboard)

ÿ is entered or SOLVE is executed.

Full Checkerboard No entry; the maximum number of

rectangle # characters has been entered at a prompt

or memory is full.

Using a TI-84 Plus Silver Edition Menu

You can access most TI-84 Plus Silver Edition operations using menus.

When you press a key or key combination to display a menu, one or

more menu names appear on the top line of the screen.

■

The menu name on the left side of the top line is highlighted.
Up to seven items in that menu are displayed, beginning with item 1,
which is also highlighted.

■

A number or letter identifies each menu item’s place in the menu.
The order is 1 through 9, then 0, then A, B, C, and so on.

■

When the menu continues beyond the displayed items, a down arrow
( ) replaces the colon next to the last displayed item.

■

When a menu item ends in an ellipsis (...), selecting the item will
display a secondary menu or editor.

Displaying a Menu

While using your TI-84 Plus Silver Edition, you will often

need to access items from its menus. When you press

a key that displays a menu, that menu temporarily

replaces the screen where you are working.

Example: Calculate 5 + 9

1. 5 + 9 Enter the expression in the home screen

2. Press ç

3. Press 3 to choose the correct item from the menu

4. Press Õ to calculate

Keystrokes: 2T6 ç 0 Õ 734

3

Moving Between Menus

Some of the keys on your TI-84 Plus Silver Edition

access more than one menu. When you press such

a key, the names of all accessible menus are

displayed on the top line. When you highlight a

menu name, the items in that menu are displayed.
Press ~ and |to highlight each menu name.

Setting Modes

Mode settings control how your TI-84 Plus Silver Edition displays and

interprets numbers and graphs. Mode settings are retained by the

Constant Memory™feature when you turn off your TI-84 Plus Silver Edition.

All numbers, including elements of matrices and lists, are displayed

according to the current mode settings.

To display the mode settings on your TI-84 Plus Silver Edition, press
z . The current settings will be highlighted. Default settings are

highlighted below.

Normal Sci Eng Numeric notation
Float 0123456789 Number of decimal places
Radian Degree Unit of angle measure
Func Par Pol Seq Type of graphing
Connected Dot Whether to connect graph points
Sequential Simul Whether to plot simultaneously
Real a+bi re ␪i Real, rectangular complex, or polar complex
Full Horiz G-T Full screen, two split-screen modes

© Texas Instruments, 2007

Changing Mode Settings

To change mode settings:

1 Press Ü or } to move the cursor to the line of the setting you want.
2 Press ~ or | to move the cursor to the setting you want.
3 Press Õ.

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TI-84 Plus Silver Edition Expressions, Menus, and Graphing

efining or Editing a Function for Graphing

Entering Expressions and Instructions

What is an Expression?

An expression is a group of numbers, variables, or functions and

their arguments, or a combination of these elements. An expression
evaluates to a single answer. For example, ()2is an expression. On the

TI-84 Plus Silver Edition, you enter an expression in the same order as

you would write it on paper. You can enter an

expression on the home screen to calculate

an answer.

Entering an Expression

To create an expression, you enter numbers, variables, and functions

from the keyboard and menus on your TI-84 Plus Silver Edition. An
expression is completed when you press Õ, regardless of the

cursor location. The entire expression is evaluated according to

™

Equation Operating System (EOS

and the answer is displayed. When an entry is

executed on the home screen, the answer is

displayed on the right side of the next line.

The mode settings control the way the TI-84 Plus Silver Edition interprets

expressions and displays answers. If an answer, such as a list or matrix,

is too long to display entirely on one line, an

ellipsis (...) is displayed to the right or left.
Press ~ or | to display the rest of the answer.

To display the MATH menu, press

MATH NUM CPX PRB
1: Frac Displays answer as a fraction
2: Dec Displays answer as a decimal

3

3:

(

4: 3√
5: x√ Calculates xth root
6: fMin( Finds minimum of a function
7: fMax( Finds maximum of a function
8: nDeriv( Computes numeric derivative
9: fnInt( Computes integral of a function
0: Solver... Displays equation solver

To display the MATH NUM menu, press

MATH NUM CPX PRB
1: abs( Computes absolute value
2: round( Rounds value to specified decimal place
3: iPart( Calculates integer part
4: fPart( Calculates fractional part
5: int( Finds greatest integer less than or equal to number
6: min( Finds minimum value
7: max( Finds maximum value
8: lcm( Calculates least common multiple
9: gcd( Calculates greatest common divisor

To display the MATH PRB menu, press

MATH NUM CPX PRB
1: rand Generates random number between 0 and 1
2: nPr Computes number of permutations
3: nCr Computes number of combinations
4: ! Calculates factorial
5: randInt( Generates random integer in specified range
6: randNorm( Generates random # from Normal distribution
7: randBin( Generates random # from Binomial distribution

Calculates cube
Calculates cube root

) rules (see General Math page),

çç

1
3

çç ~~

çç ||

D

To Define or Edit a Function

1 Press o to display the Y= editor.

2 Press Ü to move the cursor to the

function you want to define or edit.
To erase a function, press ë.

3 Enter or edit an expression to define

the function.

Displaying a New Graph

To display a graph of the selected function,
press s. TRACE, ZOOM, and CALC

operations display the graph automatically.

As the graph is plotted, the busy indicator is

on, and the X and Y values are updated.

Free-Moving Cursor

When you first display the graph, no cursor is visible. You must press
|~}or Ü for the cursor to move from the center of the viewing
window. Continue pressing |~}or Ü to move the cursor around.

Tracing a Function

Use the TRACE operation to move the cursor from one plotted point
to the next along a function. To begin, press r. The TRACE cursor

is on the first selected function in the Y= editor, centered horizontally

on the screen. The cursor coordinates are displayed at the bottom of
the screen if CoordOn format is selected. The Y= expression is displayed
in the top left corner of the screen if ExprOn format is selected.

Moving the TRACE Cursor

To move the TRACE cursor Do this:

To the previous or next plotted point Press | or ~
Five plotted points on a function Press y | or y ~

(Xres affects this)
To any valid X value on a function Enter a value & press Õ
From one function to another Press } or Ü

To alter the viewing area of the graph, press

ZOOM MEMORY
1: ZBox Draws a box to define the viewing window
2: Zoom In Magnifies the graph around the cursor
3: Zoom Out Views more of a graph around the cursor
4: ZDecimal Sets ⌬X and ⌬Y to 0.1
5: ZSquare Sets equal-size pixels on the X and Y axes
6: ZStandard Sets the standard window variables
7: ZTrig Sets the built-in trig window variables
8: ZInteger Sets integer values on the X and Y axes
9: ZoomStat Sets the values for current stat plots
0: ZoomFit Fits Ymin and Ymax between Xmin and Xmax

To display the CALCULATE menu, press

CALCULATE
1: value Calculates a function Y value for a given X
2: zero Finds a zero (x-intercept) of a function
3: minimum Finds a minimum of a function
4: maximum Finds a maximum of a function
5: intersect Finds an intersection of two functions
6: dy/dx Finds a numeric derivative of a function
7: ∫f(x)dx Finds a numeric integral of a function

To return to the Home Screen from any other screen, press

qq

yy //

yy 55

.

© Texas Instruments, 2007

education.ti.com

All About Apps for the TI-84 Plus Silver Edition

If you’ve ever wondered...

So what is that little å key on your TI-84 Plus Silver Edition

for, anyway?

Handheld Software Applications, or Apps, are pieces of software you

can add on to your TI-84 Plus Silver Edition or TI-84 Plus, in the same

way you would add software to your computer. This allows you to

customize your TI handheld to meet your class needs and update it

from one year to the next. Pretty cool, huh?

The TI-84 Plus Silver Edition comes preloaded with lots of Apps ––

StudyCards™, Probability Simulation, CBL™/CBR™, Conic Graphing,

™

Cabri

Jr., Organizer, CellSheet™, Puzzle Pack, Science Tools, Catalog

Help, Vernier EasyData™, to name a few! The TI-84 Plus comes

preloaded with StudyCards, Probability Simulation, CBL/CBR, Catalog

Help, and other Apps. Some of the coolest Apps for the TI-84 Plus Silver

Edition and TI-84 Plus are:

Cabri™Jr.

Add a new dimension to your learning experience

with Cabri Jr., our interactive Geometry App.

Construct, analyze and transform mathematical

models and geometric diagrams. Then alter

geometric objects on the fly to see patterns, make

conjectures and draw conclusions.

To access the Apps on your

I-84 Plus Silver Edition

T

All you have to do is press the å key, scroll down the list to the App
you‘d like to explore, and press Õ. If you get stuck using an App,

visit education.ti.com/guides to download the FREE instruction guide.

But that’s not all…

We also have dozens of other Apps you can download, and all of

them are FREE! Visit the TI website at education.ti.com/apps to find

out more information on all of the Apps you can download.

So how do you get these free Apps?

First, you’ll need a TI Connectivity USB cable – one is included with

the TI-84 Plus Silver Edition and is available as an accessory with the

TI-83 Plus model. You can purchase a TI Connectivity USB cable at a

retail store or the TI Online Store. USB and serial cables are available

for both Windows®PCs and Macintosh®computers.

Inside the TI Connectivity kit (and TI-84 Plus Silver Edition) package,

you will find a CD with TI Connect™ link software, which allows

your computer to communicate with your TI-84 Plus Silver Edition

handheld. Follow the directions to install the software from the CD

into your computer.

© Texas Instruments, 2007

Organizer

Keep track of where you’re going and where

you’ve been. Put your future and your friends at

your fingertips when you input contacts and tasks.

CellSheet

™

You have a spreadsheet to your TI-84 Plus Silver

Edition! Create graphs, including pie charts, and

fill a range of cells with formulas. You can even

import and export files to and from Excel®.

StudyCards

™

Create electronic flash cards to use as a study tool for

quiz or test review. Download ready made StudyCard

stacks for the SAT*and ACT from our collection

at education.ti.com/studycards. Create and share

stacks with other students from all over the

world.

NoteFolio

™

Easily type notes for all your classes with the

TI Keyboard. Select, cut, copy, paste, delete

and insert text in your notes. Best of all, use

the NoteFolio Creator PC utility to transfer

notes to and from Word®files.

Topics in Algebra 1

Walk, run or ride a bicycle through basic concepts

in algebra. You can be the envy of all your friends

by grasping this mystical subject with this fun and

easy tutorial.

Next, visit education.ti.com/apps to browse through the FREE Apps

that are available for the TI-84 Plus and TI-83 Plus families of graphing

calculators. All Apps are FREE to download – simply follow the steps

online. Just be sure to save the file in a location you’ll remember.

Now it’s time to transfer the App from your computer to your

TI-84 Plus Silver Edition. This is the easy part! Just plug your USB

cable into your computer and your TI-84 Plus Silver Edition,

launch the TI Connect software, and click on Device Explorer.

TI Connect will automatically detect your device. All you have to do

is find the App file you saved, drag it to the Device Explorer window,
drop it, and wait for it to transfer. Voilà! Press the å key to see your

newly transferred App! Good luck and happy downloading!

We know you’ll have an Appsolute blast!

® Excel, Word, Windows, and Macintosh are registered trademarks of their respective owners.

* SAT & AP are registered trademarks of the College Entrance Examination Board.

PSAT/NMSQT is a registered trademark of the College Entrance Examination Board and
National Merit Scholarship Corporation. ACT is a registered trademark of ACT, Inc. None of
these were involved in the production of nor do they endorse this product.Policies subject
to change. Visit www.collegeboard.com

and www.act.org.

education.ti.com

General Math with the TI-84 Plus Silver Edition

Arithmetic Operations and Properties

Arithmetic Operations with the TI-84 Plus Silver Edition

Addition: valueA + valueB Returns valueA plus valueB √
Subtraction: valueA - valueB Subtracts valueB from valueA π

Multiplication: valueA x valueB Returns valueA times valueB Ø
Division: valueA ÷ valueB Returns valueA divided by valueB •

Properties of Addition & Multiplication

Commutative property of addition a+b = b+a

Commutative property of multiplication ab = ba

Associative property of addition a+(b+c) = (a+b)+c

Associative property of multiplication a(bc) = (ab)c

Distributive property of multiplication over addition a(b+c) = ab+ac

Distributive property of multiplication over subtraction a(b–c) = ab–ac

Numbers

Prime Numbers

A whole number with only two factors: itself and 1

EXAMPLES: 2, 3, 5, 7, 11, 13, 17

Common Factors

A number that divides exactly into two or more given numbers

EXAMPLES: 1, 2, 3, 4, 6, and 12 are factors of 12

Greatest Common Factor

The greatest number that is a factor of two or more numbers

EXAMPLE: 4 is the greatest common factor of 12 and 16.

To calculate the greatest common factor on your TI-84 Plus Silver Edition,
press ç ~ 9:gcd(. This will compute the greatest common factor of
valueA and valueB, which can be real numbers or lists.

Least Common Multiple

The smallest number that is a multiple of two or more numbers

EXAMPLE: 12 is the least common multiple of 2, 3, 4 and 6.

To calculate the least common multiple on your TI-84 Plus Silver Edition,
press ç ~ 8:lcm(. This will compute the least common multiple of
valueA and valueB, which can be real numbers or lists.

Math Symbols

To access many math symbols,

go to the TEST Menu on your

TI-84 Plus Silver Edition, by pressing
y : .

Powers and Roots

Square: value

Square root: √(value) y C returns the square root of a real

Common Squares and Roots

n n

111.0

241.414

391.732

4 16 2.0

5 25 2.236

6 36 2.449

7 49 2.646

8 64 2.828

Cube: value

Cube root:

th

x

root:

Power: value^power The õ key returns a value raised to a power. Value

Power of 10: 10^(value) Press y G. Returns 10 raised to the value power.

2

The ° key returns a value multiplied by itself.
The value can be a real or complex number,
expression, or list.

or complex number, expression, or list.

2

√n

n n

2

9 81 3.0

10 100 3.162

15 225 3.873

20 400 4.472

25 625 5.0

100 10,000 10.0

1

/

2

1

/

4

3

Press ç. 3:3Returns the cube of a real or

1

/

4

1

/

6

1

complex number, expression, list, or square matrix.

3

√

(value) Press ç. 4:3√ ( Returns the cube root of a

real or complex number, expression, or list.

x

√

value Press ç. 5:x√ ( Returns xth root of a value.

can be a real or complex number or expression.

Value can be a real or complex number or expression.

√n

0.707

1

/

2

Order of Operations

General Rules

1 Do all operations within parentheses

2 Do all powers and roots

3 Do multiplication and division in order from left to right

4 Do addition and subtraction in order from left to right

Equation Operating System (EOS™) for the TI-84 Plus Silver Edition

EOS defines the order in which functions and expressions are entered and

evaluated. EOS evaluates the functions in an expression in this order:

1 Functions that precede the argument, such as √ (, sin(, or log(

2 Functions that are entered after the argument, such as 2, -1, !, °, or r,

and conversions

3 Powers and roots, such as 25or

4 Permutations (nPr) and combinations (nCr)

5 Multiplication, implied multiplication, and division

6 Addition and subtraction
7 Relational functions, such as > or ≤

8 Logic operator and

9 Logic operators or and xor

Within a priority level, EOS evaluates functions from left to right.

Calculations within parentheses are evaluated first.

5

√

32

Fractions, Decimals and Percents

1=1.0 = 100%

1

/

2

1

/

3

1

/

4

1

/

5

1

/

6

1

/

8

1

/

9

1

/

10

1

/

12

2

/

3

3

/

4

value ➧Dec Press ç. 2: ➧Dec Displays a real or complex

value ➧Frac Press ç. 1: ➧Frac Displays a real or complex

= 0.5 = 50%

= 0.333 = 33.3%

= 0.25 = 25%

= 0.2 = 20%

= 0.166 = 16.7%

= 0.125 = 12.5%

= 0.1 1 1 = 11.1%

= 0.1 = 10%

= 0.083 = 8.3%

= 0.666 = 66.7%

= 0.75 = 75%

number, expression, list or matrix in decimal format.

number, expression, list or matrix as a fraction
simplified to its simplest terms.

© Texas Instruments, 2007

education.ti.com

Algebra with the TI-84 Plus Silver Edition

Law of Exponents & Radicals

Formulas Examples Keystrokes

arx as= a

r

a

= a

s

a

ap a

r

a

(ab)r= arb

a

(

b

r

s

a = √a

r + s

r – s

q

p + q – r

= a

r

r

r

a

)

r

= (b ≠ 0) = 0 G 1 W / G 1 Õ 5.0625

b

s

r

a0= 1 (a ≠ 0) 30= 1 0 G 7 Õ 1

1

a–r= (a ≠ 0) 3-4= . W 0 G 1 Õ .0123

r

a

(where a=3, b=2, P=5,

=6, r=4, s=2)

Q

= 3

6

= 3

4 – 2

5 + 6 – 4

4 + 2

0 G D 1 T / E Õ 729

0 G D 1 U / E Õ 9

0GD2T3U1EÕ 2187

34x 32= 3

4

3

2

3

5

3

x 3

4

3

(3 x 2)4= 34 x 240 G 1 V / G 1 Õ1296

4

3

(

2

9=√9

4

3

)

4

2

2

4

2

4

1 ç 2 D 6 G / E Õ3

1

4

3

Binomial Expansion

a (b + c) = ab + ac

(a + b) (c + d) = a c + a d + bc + bd

(a + b)2= a2+ 2ab + b

(a – b)2= a2– 2ab + b

(a + b)3= a3+ 3a2b + 3ab2+ b

(a – b)3= a3– 3a2b + 3ab2– b

(a + b)4= a4+ 4a3b + 6a2b2+ 4ab3+ b

(a + b)5= a5+ 5a4b + 10a3b2+ 10a2b3+ 5ab4+ b

2

2

3

3

4

5

Factoring

a2– b2= (a + b) (a – b)

a2+ 2ab + b2= (a + b)

a2– 2ab + b2= (a – b)

a3+ b3= (a + b) (a2– ab + b2)

a3b – ab = ab (a + 1) (a – 1)

a3– b3= (a – b) (a2 + ab + b2)

2

2

Graphing Inequalities

≤

The Inequality Graphing App for

the TI-84 Plus Silver Edition is

The intersection of y

and y > .5x2-7 is shaded.

2x-3

used here to enter the equations

y ≤ 2x-3 and y > .5x2-7.

Solving Linear Systems by Graphing

The intersection of two functions is the solution to the system.

Graphing provides a quick and powerful way to solve linear systems.

1 Enter equations in the o editor.
2 Press s to graph both equations.

(You may need to adjust the viewing window.)

3 Press y / 5: intersect to find the point of intersection.
4 Press Õ to select the 1st curve and again to select the 2nd curve.

5 Enter your best guess and press Õ.

Quadratic Formula

2

–b ±

√b

If a ≠ 0, the roots of ax2+ bx + c = 0 are

x =

Example: 3x2+ 2x - 4 (where a=3, b=2, c=-4)

2

√2

x =

-2 ±

- 4(3)(-4)

2(3)

Keystrokes

Step 1 22- 4(3)(-4) / F U 1 V 0 V M 1 Õ 52

Step 2 -2 + √52 M / T % b 2 / E Õ 5.211

-2 - √52 M / U % b 2 / E Õ -9.211

Step 3 5.211 28/..WD/V0EÕ 0.869

2(3)

-9.211 M68/..WD/V0EÕ -1.535

2(3)

- 4ac

2a

Factorial

n! = n (n-1) (n-2) ... (2) (1)

Example: 5! = 5 (4) (3) (2) (1)

Keystrokes: 5! =  ç | 4 Õ 120

Logarithms

y = logax means ay= x loga xr= r logax log x = log

logaxy = logax + logay loga1 = 0

x

loga= logax – logay logaa = 1 logax =

y

In x = logex ln e = 1

© Texas Instruments, 2007

´´ µµ JJ

10

log10x

log

10

Using the Equation Solver

Use the Equation Solver on your TI-84 Plus Silver Edition to solve for any

variable in an equation. In this example, the Solver is being used to find

one of the roots of the polynomial x2- 5x + 6.

x

a

1 Press ç 0: Solver…

2 Enter equation (must be in form where equation is set equal to 0)

and press Õ.

3 Place cursor next to variable for which you would like to solve.

4 Enter a guess for the value.
5 Press É \ to see a solution.

education.ti.com

More Algebra with the TI-84 Plus Silver Edition

Definition of Slope

This section uses the Topics in Algebra 1 App for the TI-84 Plus Silver Edition

to help define slope.

vertical change

m =

horizontal change run x2– x

rise =y2– y

=

1

1

Equations of Lines

This section features the Topics in Algebra 1 App for the TI-84 Plus Silver Edition.

The Distance Formula

The Distance Formula is used to calculate the distance between two points.

d(P1, P2) = √(x2– x1)2+ (y2– y1)

Example: Find the distances between the points P1(2, 5) and P2(-3, 1).

d(P1, P2) = √(-3 – 2)2+ (1 – 5)2= √(-5)2+ (-4)

= √25 + 16 = √41 ≈ 6.403

Keystrokes

- z £ M [ T Z E 6 \ D Y T R E 6 E b ≈ 6.403

To draw the line segment between (-3, 1) and (2, 5) on your

TI-84 Plus Silver Edition:

y< 2:Line M ¬ ¢ ¿ ¢ ¡ ¢  § Õ

2

2

Quadratic Functions

This section features the Conic Graphing App for the TI-84 Plus Silver Edition.

Ax + By = C Standard form — graph using intercepts

y = mx + b Slope-intercept form — graph using m and (0,b)

y – y1= m(x – x1) Point-slope form — graph using m and (x1, y1)

Standard form example

Given 3x + 2y = 6, find intercepts:

3(0) + 2y = 6 3x + 2(0) = 6 xy

2y = 6 3x = 6 03

y = 3 x = 2 20

Point-slope form example

Given m=3 and (2,-3)

Equation y – (-3) = 3(x-2)

y + 3 = 3x – 6

y = 3x – 9

Equation of a circle: (x – H)2+ (y – k)2= R

Values are entered for the center and the radius. The Conic Graphing App

produces a circle you can now trace.

Equation of a parabola: (x – H)2= 4P(y – k)

Values are entered for the vertex (H, K) and the distance (P) between

the directrix and the vertex. The Conic Graphing App produces a

parabola you can now trace.

The Transformation Graphing App allows you to see what happens to a

graph as you change its coefficient(s).

2

Keystrokes o ë ¬ Ñ π Æ q _

© Texas Instruments, 2007

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Geometry with the TI-84 Plus Silver Edition

Lines

Creation of primitive geometric objects

as Points, Lines, Line Segments and many

others is fun and easy using the Cabri Jr.

App for the TI-84 Plus Silver Edition.

™

Triangles

This section features the Cabri Jr. App for the TI-84 Plus Silver Edition.

Equilateral: all sides and angles equal

Isosceles: two sides and angles equal

Right: one 90 degree angle

Example: Draw an Isosceles Triangle

1 2

3 4

Pythagorean Theorem

1. Create a segment

2. Find the middle of
the segment

3. Trace a
perpendicular
line crossing the
middle point

4. Trace a triangle
using the two
existing points of
the segment and
a point on the
perpendicular line

Angles

Polygons

The information in this section is presented using screen shots from the

StudyCards™and Cabri Jr. Apps for the TI-84 Plus Silver Edition.

Circles

This section features the Cabri Jr. App for the TI-84 Plus Silver Edition.

Diameter = 2*(radius)
Circumference = π*(diameter)

Circle Area = π*(radius)

2

Geometric Formulas

All Perimeters

P = a+b+c+ ...

Square

Perimeter P = 4s
Area A = s

Rectangle

Perimeter P = 2l+2w
Area A = lw

Circle

Circumference C = 2πr
Area A = πr

© Texas Instruments, 2007

2

2

Triangle

Perimeter P = a+b+c
Area A = bh

Parallelogram

Perimeter P = a+b+c+d
Area A = bh

Trapezoid

Perimeter P = a+b+c+d
Area A = (a+b)h

Diameter Chord

Area

Circle’s

Equation

Rectangular Prism

1
2

2

Surface S = 2(hl+lw+hw)
Volume V = lwh

Sphere

Surface S = 4πr
Volume V = 4πr

Right Circular Cylinder

Lateral
Surface S = 2πrh

Total
Surface S = 2πrh + 2πr

Volume V = πr2h

2

3

3

2

Right Circular Cone

Lateral
Surface S = πr √r2+h

Total
Surface S = πr √r2+h2+πr

Volume V = πr2 h

Frustum of a Cone

Volume V = πh(r2+rR+R2)

Circular Sector

Area A = r2 ␪

Circular Ring

Area A = π(R2–r2)

2

1
3

1
3

1
2

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2

Trigonometry with the TI-84 Plus Silver Edition

opp

adj

u

hyp

opp

y

r

(a,b)

x

adj

u

u

hyp

opp

y

r

(a,b)

x

adj

u

u

hyp

y

t

(1,0)

t radians

(x,y)

x

opp

y

r

(a,b)

x

adj

u

u

hyp

1

1

π

4

y

t

(1,0)

t radians

(x,y)

x

=45°

1

√3

π

6

2

40°

60°

60°

4

2

c

3

b

=30°

π

3

=60°

√2

opp

y

r

(a,b)

x

adj

u

u

hyp

1

1

π

4

y

t

(1,0)

t radians

(x,y)

x

=45°

1

√3

π

6

2

40°

60°

60°

4

2

c

3

b

=30°

π

3

=60°

√2

90°

270°

300°240°

315°

225°

330° 210°

0°180°

30°150°

45°135°

60°

120°

(0,1)

(1,0)

(0,-1)

(-1,0)

(,)

1 √3
2

2

(

,

)

1 √3
2

2

(

, -

)

1 √3
2

2

(

, -

)

1 √3

2

2

(

,

)

√2 √2

2

2

(

,

-

-

)

√2 √2

2

2

(

, -

)

√2 √2

2

2

(

, -

)

√2 √2

2

2

(,)

√31

2

2

(

,-

)

√31

2

2

(

, -

)

√31

2

2

(

, -

-

-

-

)

√31

2

2

Trigonometric Functions

Acute Angles

ò sin ␪=

ô cos ␪=

ö tan ␪=

Arbitrary Angles

sin ␪= b/

cos ␪= a/

tan ␪= b/

Real Numbers

sin t = y csc t = 1/

cos t = x sec t = 1/

tan t = y/

Special Triangles

Trigonometric Identities

csc t = 1/sin t tan t = sin t/cos t

sec t = 1/cos t cot t = cos t/sin t

cot t = 1/tan t

sin2t + cos2t = 1 sin (–t) = –sin t

1 + tan2t = sec2t cos (–t) = cos t

1 + cot2t = csc2t tan (–t) = –tan t

sin (u + v) = sin u cos v + cos u sin v

cos (u + v) = cos u cos v – sin u sin v

tan (u + v) =

sin (u – v) = sin u cos v – cos u sin v

cos (u – v) = cos u cos v + sin u sin v

tan (u – v) =

sin 2u =2 sin u cos u

cos 2u = cos2u – sin2u = 1 – 2 sin2u = 2 cos2u – 1

tan 2u =

sin = cos =

tan = = tan2u =

sin2u = cos2u =

sin u cos v =

cos u sin v =

cos u cos v =

sin u sin v =

© Texas Instruments, 2007

u
2

u
2

r

x

opp

/

hyp

adj

/

hyp

opp

/

adj

r

a

tan u + tan v

1 – tan u tan v

tan u – tan v

1 + tan u tan v

2 tan u

2

1 – tan

1 – cos u

1 – cos 2u

u

1 – cos u

√

2

sin u

2

1

/

[sin (u + v) + sin (u – v)]

2

1

/

[sin (u + v) – sin (u – v)]

2

1

/

[cos (u + v) + cos (u – v)]

2

1

/

[cos (u – v) – cos (u + v)]

2

1 + cos u

csc ␪=

sec ␪=

cot ␪=

csc ␪= r/

sec ␪= r/

cot ␪= a/

cot t = x/

sin u

hyp

hyp

adj

b

a

b

y

x

y

/

/

/

opp

u
2

opp

adj

1 + cos u

√

2

1 - cos 2u

1 + cos 2u

1 + cos 2u

2

Special Values of Trigonometric Functions

␪␪ ␪␪

degrees) (radians)

(

° 0010–1 –

0

30° 2

5° 11

4

0° 2

6

90° 10–0– 1

sin ␪␪cos ␪␪tan ␪␪cot ␪␪sec

3

π

6

π

4

π

3

π

2

1
2

√

2

√

2

√3

2

2

√

2

3

1
2

√

3

2

3

√

√3

√3

3

␪␪

2√3

3

2 √2

√

csc

2√3

␪␪

3

Inverse Trigonometric Functions

Function Domain Range

π

1

? y = sin

y

y @ y = cos-1x –1 ≤ x ≤ 1 0 ≤ y

y A y = tan-1x All real numbers – < y <

y = cot-1x All real numbers 0 < y <

y = sec-1x x ≥ 1 0, ∪

-1

y = csc

-

x

x x ≥ 1 – , 0 ∪ 0,

–1

x

1 –

≤

≤

π

2

π

y

≤

≤

2

2

≤π

π

π

2

2

π

π

π

,

2

π

2

π

2

Laws of Sines and Cosines

Sine Cosine

sin A = sin B = sin C a2= b2+ c2– 2bc cos A

a b c

Unit Circle

c2= a2+ b2– 2ab cos C

b2= c2+ a2– 2ac cos B

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Math References

Metric Prefixes

Prefix Symbol Magnitude

Exa- E 10

Peta- P 10

Tera- T 10

Giga- G 10

Mega- M 10

kilo- k 10

hecto- h 10

deka- da 10

18

15

12

9

6

3

2

1

Weights and Measures

Annular and Circular Measure

60 seconds = 1 minute

90 minutes = 1 degree

90 degrees = 1 right angle

180 degrees = 1 straight angle

360 degrees = complete angle

Apothecaries’ Fluid Measure

60 minims = 1 fluid dram

8 fluid drams = 1 fluid ounce

16 fluid ounces = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

Apothecaries’ Weight

20 grains = 1 scruple

3 scruples = 1 dram

8 drams = 1 ounce

12 ounces = 1 pound

Avoirdupois Weight

11

27

/

grains = 1 dram

32

16 drams = 1 ounce

16 ounces = 1 pound

100 pounds = 1 short cwt.

1 short ton = 2,000 pounds

Prefix Symbol Magnitude

deci- d 10

centi- c 10

milli- m 10
micro- ∝ 10

nano- n 10

pico- p 10

femto- f 10

atto- a 10

-1

-2

-3

-6

-9

-12

-15

-18

Cubic Measure

1728 cubic inches = 1 cubic foot

27 cubic feet = 1 cubic yard

1000 cu. millimeters = 1 cu. cm.

1000 cu. centimeters = 1 cu. dcm.

1000 cu. decimeters = 1 cu. meter

Linear Measure

12 inches = 1 foot

3 feet = 1 yard

1

5

/

yards = 1 rod

2

40 rods = 1 furlong

5,280 feet = 1 mile

10 millimeters = 1 centimeter

10 centimeters = 1 decimeter

10 decimeters = 1 meter

10 meters = 1 dekameter

10 dekameters = 1 hectometer

10 hectometers = 1 kilometer

Greek Alphabet

Upper Lower Name Upper Lower Name Upper Lower Name

Αα
Ββ
Γγ
∅δ
Εε
Ζζ
Ηη
Θθ

alpha

beta

gamma

delta

epsilon

zeta

eta

theta

Liquid Measure

4 gills = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

1

31

/

gallons = 1 barrel

2

2 barrels = 1 hogshead

10 milliliters = 1 centiliter

10 centiliters = 1 deciliter

10 deciliters = 1 liter

10 liters = 1 dekaliter

10 dekaliters = 1 hectoliter

10 hectoliters = 1 kiloliter

Mass Measure

10 milligrams = 1 centigram

10 centigrams = 1 decigram

10 decigrams = 1 gram

10 grams = 1 dekagrams

10 dekagrams = 1 hectogram

10 hectograms = 1 kilogram

100 kilograms = 1 quintal

10 quintals = 1 ton

Ιι
Κκ
Λλ
Μ∝
Νν
Ξξ
Οο
Ππ

Square Measure

Troy Weight

iota

kappa

lambda

mu

nu

xi

omicron

pi

Ρρ
Σσ
Ττ
Υυ
Φφ
Χχ
Ψψ
Ωω

144 square inches = 1 square foot

9 square feet = 1 square yard

1

30

/

square yards = 1 sq. rod

4

160 square rods = 1 acre

640 acres = 1 square mile

100 sq. millimeters = 1 sq. cm.

100 sq. centimeters = 1 sq. dcm.

100 sq. decimeters = 1 sq. meter

100 sq. meters = 1 sq. dekameter

100 sq. dekameters = 1 sq. hm.

100 sq. hectometers = 1 sq. km.

24 grains = 1 pennyweight

20 pennyweights = 1 ounce

12 ounces = 1 pound

rho

sigma

tau

upsilon

phi

chi

psi

omega

Liquid or Volume Measures (approximate)

1

/

teaspoon = 0.042 fluid ounce

4

1

/

teaspoon = 0.083 fluid ounce

2

1 teaspoon = 0.167 fluid ounce

1 tablespoon = 0.5 fluid ounce

2 tablespoons = 1 fluid ounce

1

/

cup = 2 fluid ounces

4

1

/

cup = 2.67 fluid ounces

3

1

/

cup = 4 fluid ounces

2

2

/

cup = 5.33 fluid ounces

3

3

/

cup = 6 fluid ounces

4

7

/

cup = 7 fluid ounces

8

1 cup = 8 fluid ounces

1 pint = 16 fluid ounces

1 quart = 32 fluid ounces

1 gallon = 128 fluid ounces

1 liter = 33.82 fluid ounces

© Texas Instruments, 2007

This section uses the Science Tools App for the TI-84 Plus Silver Edition

to help convert any unit.

Example: Convert 250km to fathoms

1. Select LENGTH from the unit converter Menu.

2. Enter 250, the numerical value to convert.

3. Use the arrow keys to select km, the conversion unit to convert

from, and then press Õ.

4. Use the arrow key to select fath, the conversion unit to convert to,

and then press Õ.

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