ACP Algebra II Final Exam Review Packet Name

ACP Algebra II Final Exam Review Packet Name ______________________________

Section 4-1 Operations with Polynomials

If you want additional practice go to pages 233-234 odd answers are in the back of the textbook.

1. Simplify, assume no variable equals zero.

a. 3

5 46g h b.

37 2

6

5a b

ab

2. Simplify

a. 2 2( )( 2 )x y x xy y b. 2 34( 5 6) 3(2 4 5)x x x x

c. ( )( )(2 )x y x y x y d. (3 4 ) (6 6 )x y x y

e. 2 2 2 33 (2 3 4 )x xy xy x y

3. Connor has hired two painters to paint his house. The first painter charges $12 per hour and the second

painter charges $11 per hour. It will take 15 hours of labor to paint the house.

a. Write a polynomial to represent the total cost of the job if the first painter does x hours of the

labor.

b. Write a polynomial to represent the total cost of the job if the second painter does y hours of the

labor.

4. Find the perimeter of the figure.

4-3 Dividing Polynomials

If you want additional practice go to pages 247 odd answers are in the back of the textbook.

5. Simplify

a. 2 2 1(3 6 5 )( )a b ab ab ab b.

2(2 4 8) (5 5)x x x

c. 3 2 2 324 16

8

x y x y

xy

d.

3( 8 26) ( 2)x x x

e. 3 211 10 6

2

y y y

y

f.

3 2

2

2 3 1

2

x x x

x x

4-4 Graphing Polynomial Functions

If you want additional practice go to pages 257 - 259 odd answers are in the back of the textbook.

6. State the degree and leading coefficient of the polynomial. Determine the end behavior.

a. 7 310 5 4 22x x x b.

5 24 5 8 3xy x x

7. Simplify - If 3 2( ) 4 5 2c x x x and

2( ) 3 6 10d x x x , find each value.

a. 4 (3 )d z b. 3 (2 ) 6 (4 3)c b d b

8. For each graph:

Describe the end behavior

Determine whether it represents an odd-degree or an even-degree function

State the number of real zeros

a. b.

9. Describe the end behavior of the following equations.

a. 5 4( ) 2 6g x x x b.

2( ) 6 7f x x x c. 6 7 29 5 3x x x

4-5 Analyzing Graphs of Polynomial Functions


10. Graph each polynomial function. Estimate the x-coordinate at which the relative maxima and relative

minima occur. State the domain and range for each function.

3 23 6 2 2x x x

11. For each function:

Factor if necessary

Find the zeros and their multiplicity

Find the degree and state the end behavior

graph the polynomial

a. 3 23x x b. ( 1)( 5)y x x x

c. 3 22 12 8x x x d.

3 2( 1) ( 2)y x x

5-1 Operations with Functions


12. Use the functions2( ) 5f x x and ( ) 8g x x to find each. Indicate any restrictions in the

domain.

a. ( )f g x b. ( )f g x c. ( )f

xg

13. Use the functions ( ) 1f x x , ( ) 4 2g x x , and 2( ) 6 8h x x x to find each value.

a. 3 2 (0)f h b. 3

(2)f

g

c. 2 (3)f g

5-2 Composition of Functions


14. Use the functions ( ) 5f x x , ( ) 2 1g x x and 2( ) 2 1h x x x to find each function composition or

value.

a. ( )( )f g x b. ( )( )h g x

c. ( )( 2)g h d. ( )(4)g g

5-3 Inverse Functions

If you want additional practice go to pages 333 odd answers are in the back of the textbook.

15. Find the inverse of each function.

a. (4,3),( 4, 4),(3, 5),( 5,2) b. 5

( ) 83

f x x

c. ( ) 8 9f x x d. 2 4

( )3

xf x

16. Determine if each pair are inverses using composition of functions. Show your work and state yes or no.

a. ( ) 2 3

( ) 2 3

f x x

g x x

b.

1( ) ( 9)

3

( ) 3 9

f x x

g x x

5-5 Graphing Square Root and Cube Root Functions


17. Graph each. State the domain and range.

a. ( ) 6 8f x x b. ( ) 2 7 4f x x

c. 3( ) 3 5f x x d. 3( ) 2 4f x x

5-6 Solving Radical Equations


18. Solve each equation. Check for extraneous solutions.

a. 3 4 5 4x b. 36 2 1 3x

c. 2 5 9 0x x d. 3 4x x

e. 34 9 8x

7-1 Multiplying and Dividing Rational Expressions


19. Simplify each expression. Under what conditions is the expression undefined (find the restrictions)?

a. 2

2

5 24

64

x x

x

b.

2 2ax b x

by ay

c. 27 8

16 9

x z

y x d.

2 2 3

4 2

15 6

21 14

x y xy

xz x z

e. 2 2

2

9 20 25

8 16 4 16 16

x x x

x x x

f.

2 2

3

2

2

x y

y

y xy

x

g.

2

2

2

2

2 7 30

6 13 5

4 12 72

3 11 4

x x

x x

x x

x x

7-2 Adding and Subtracting Rational Expressions


20. Simplify each expression.

a. 4 4 3

5

24 36

a a

cf bc f b.

2

8 2 3

3 9 10y y

c. 2 2

2 3

4 9 2 2 8 24

x

x x x x

d.

2

2 3

1 46

5 4

x x

x x

7-6 Solving Rational Equations


21. Solve each equation. Check your solution.

a. 7 3 19

3 5 12x

b.

14 1015

3 2x x

c. 2

3 21

2 2 4 2 7 4

x

x x x x

d.

2

2 3 2 2

3 4 12

x

x x x x

e. 2

2 4 8

3 3 9x x x

9-1 Trigonometric Functions in Right Triangles


22. Use the properties of special right triangles to find the exact value of each missing side.

a. b.

12

23. Find the exact value of the trig function indicated.

a. sin b. sec

24. Solve each word problem.

a. Brian is flying his kite above a field at the end of 65 feet of string. If the angle of elevation to the

kite measures 70, how high is the kite above Brian’s head if Brian is 6 feet tall?

b. From an airplane at an altitude of 1200 m, the angle of depression to a rock on the ground

measures 28. Find the air distance from the plane to the rock.

c. From a point on the ground 12 ft from the base of a flagpole, the angle of elevation of the top of

the pole measures 53. How tall is the flagpole?

9-2/9-3 Angles and Angle Measure

If you want additional practice go to pages 607-609, 615-617 odd answers are in the back of the textbook.

25. Draw an angle with the given measure in standard position. Then find the reference angle.

a. 590° b. -175°

c. 7

3

d.

11

6

26. Find the reference angle.

a. 700° b. -95°

c. 7

4

d.

19

6

27. Find a positive and a negative coterminal angle for each given angle.

a. -540° b. 285°

c. 13

12

d.

6

28. Convert each degree measure into radians and each radian measure into degrees.

a. 280° b. 35

18

c. -110° d. 11

6

9-3 Trigonometric Functions of General Angles


29. Find the exact value of the given trigonometric function.

a. cos300 b. sec240 c. tan 210 d. sin315

e. csc150 f. tan 630 g. tan 150 h. cot 585

i. 9

cos2

j. cot

3

k.

21csc

4

l. sin1020

m. csc 5 n. 17

cot6

o. sec

3

p. cot 900

q. cos 2 r. tan 540 s. csc360

30. Find the exact value of the remaining five trigonometric functions of .

a. Suppose is an angle in standard position whose terminal side is in Quadrant IV and cot 2 .

b. Suppose is an angle in standard position whose terminal side is in Quadrant III and 10

csc3

.

31. Find the exact values of the six trigonometric functions of if the terminal side of in standard

position contains each given point.

a. 4, 3 b. 5, 10

6-1 Graphing Exponential Functions


32. Determine whether the function is exponential growth or decay.

a. 8xf x b. 2

53

x

f x

33. Sketch the graph of the given function. Then, state the function’s domain and range.

23 3xf x

34. Sketch the graph of the given function. Then, state the function’s domain and range.

1

4 22

x

f x

6-2 Solving Exponential Equations


35. Solve

a. 4181

9

n

n

b.

5 66 1, 296n c. 364 16r

d.

3 11 1

216 6

x

e. 3 1

464

x f. 3 2216 36m m

6-4 Logarithms and Logarithmic Functions


36. Rewrite each equation in exponential form.

a. 3log 243 5 b. 6

1log 2

36

37. Rewrite each equation in logarithmic form.

a. 2 1

13169

b. 27 49

38. Evaluate the logarithmic expression.

a. 12log 144 b. 2

1log

8

c. 8log 32768 d. 7

5log 5

39. Solve each equation.

a. 3log 6x b. 2

10log 1 1x

c. 2 2log 4 10 log 1y y d. log 121 2b

e. log 3 2 log 3 2r r f. log3 log 5 8n

6-7 Common Logarithms


40. Use a calculator to approximate each to the nearest thousandth.

a. 5log 55 b. log53

c. 6log 2.1 d. log 4

6-6 Properties of Logarithms


41. Solve and check each equation.

a. 3 3 32log log 4 log 25x b. 2 2log log 2 3x x

c. 3 3 3log 3 log 4 1 log 5x x d. 5 5log 3 log 2 1 2x x

e. 4 42log 1 log 11x x f. 6 6log 2 5 1 log 7 10x x

g. 2 2 24log log 5 log 405x h. 2 23log 2log 5 2x x

i. log5 log5 log30x j. 2log 4 log 6 1x

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ACP Algebra II Final Exam Review Packet Name