AP CALCULUS

1001 TI-89 pt.2

III. ALGEBRA SYSTEM

Example 1:

2 4

2

x

x

Cool!This Thing does

Algebra!

III. ALGEBRA SYSTEM

Example 2: 2 2cos ( ) sin ( )

Super Cool!

This Thing does

Trig!

Fractions

2

2

5 14

4

x x

x

Reducing and Dividing:

Reduce:

Divide/ Decompose: #3 expand(#7 propFrac(

2

2

5 14

4

x x

x

Fractions

21

2 3

x x

x x

Adding and Subtracting: #6 comDenom(

[F2] - Algebra Menu

[F2] - Algebra Menu

#2:factor( ) over the Integers

#2:factor( , x ) over the Real #’s

over the Complex #’s

#A: Complex 2:cFactor( )

2 4x

2 5x

2 4x

Cool!

Edit to: 2 5x

1: solve( , variable)

8: nSolve( , variable)

A: Complex1:cSolve( , variable)

2C r Solve for r.

2 2 1 0x x

3 25 8 6 0x x x

2( 3) 5 15x x 2( 3) 5 15x x

3 4 12x y+ = Solve for y.

[F2] Algebra

#3: expand(

2 3x x

sin

4( )x y

COOl! WAY COOL!

#9: Trig 1:tExpand(

Trig. 1sin( )

2x

Careful…..remember multiple answers!

REM: Three answer forms:

(a) principal answer

(b) all answers in [0,2]

c) all answers << +2k>>

Trig. 1sin( )

2x

solve( ,x) returns a weird answer

52 @ 2 2 @ 2

6 6x n or n

@n# = k 2k n [1,255]

if only one let n=0

Careful…..remember multiple answers!

52 2

6 6x k or k

Trig.

2cos( ) 2sin( ) cos( ) 0x x x

(2 @ 1 1) @ 1

2 2

2 @ 2 2 @ 22 2

nx or n

x n or n

@n# = k if more than one let k1=1 & k2 =2

Careful…..remember multiple answers!

IV. Graphing• Preliminaries

– 1. Define a function• [<>] [F1] y =

– 2. Viewing Window• [<>] [F2] Window

– 3. Graph Menus• [<>] [F3] GRAPH

F2 Zoom F6 Style F4

– 4. Alternate Paths• [F4]• [APPS]

Four Requirements:

4 23 2y x x x= - +3 2.01 .3 .2 4y x x x= - + +

Graph using an appropriate window.

(End Behavior, Roots, Max/Min)

Evaluate.

Find roots ( zeros, x-intercepts)

Find intersections

2 2

2

81

81

x y

y x

+ =

=± -21 81

2 1( )

y x

y y x

= -

=-

Zeros

Graph

[F5] Math#2: Zero

31 3 1y x x

Graph

[F5] Math #5:Intersection

31

2

3 1

3

y x x

y x

Intersection

Draw Inverse:( )3 1( ) ( 2) 1If f x x graph f x-= - +

Graphing by finding the Inverse.

Draw Inverse Function: [<>][F3] [F6] #2: DrawInv

[F6] #1: ClrDraw

3 26 12 7x y y y= - + -

EXAMPLE:

Job A pays $40,000 and promises a 4% annual raise. Job B pays $30,000 and promises a 6% annual raise.

When will the two jobs pay the same? When will Job B pay more?

---------------------------------------------------------------40,000(1.04)nA

30,000(1.06)nB

EXAMPLE (cont):Graph

Find an appropriate Window.Find the Intersection.Answer.

40,000(1.04)

30,000(1.06)

n

n

A

B

TRY: nSolve(y1(x)=y2(x),x)

Graph

[MODE]

Split Screen Left-Right

Split 1 App Graph

Split 2 App Table

31

2

3 1

3

y x x

y x

Split Screen

Regression on the 89[APPS]

#6:Data/MatrixEditor 3: New

Variable : pressure <E> <E>

Enter the data into C1 and C2

[F2]:Plot Setup

[F1]

x c1

y c2 <E> <E>

[<>] [F2]

[F2]:zoom #9:ZoomData

Age Blood Pressure

35 128

24 108

48 140

50 135

34 119

55 146

Regression on the 89 cont.[APPS]

#6:Data/MatrixEditor 1: Current

[F5] : Calc

Type #5: LinReg <E>

x c1

y c2

Store to y1(x) <E>

[<>] [F1] Y =

[<>] [F3] GRAPH

Age Blood Pressure

35 128

24 108

48 140

50 135

34 119

55 146

Answer the following :

(a). Estimate the Blood Pressure of a person of age 40.

(b). Estimate the age of a person with Blood Pressure 143.

Last Update:

8/08/11