Semester 2 Final Exam Review Packet Name Chapter 8: Exponents and Exponential Functions In #1-4 simplify the expression. Write your answer using exponents.

1) 52 )2)(2()2( 2) 53 )6(

3) 7

11

4

4 4)

8

127

6

66

In #5-7 simplify the expression

5) 85

1

6) 22 )4( nm 7)

33

r

In #8-11, Simplify the expression. Write your answer using only positive exponents.

8)

2

3

22

yz

x 9)

2

23

2

1

c

ab

a

10) 432 )2()6( mm 11) 4

32 )2(

4

)3(

n

m

m

mn

12) In the following, use the function y = 3x

a) Complete the table for the function b) Graph the function c) Identify the domain and range. Domain: Range:

13) Write 0.00384 in scientific notation 14) Write 1,308,000 in scientific notation 15) A company is offering its employees a retirement benefit of $24,000 per year and guarantees an annual cost of living increase of 2% of the benefit.

a) Write a function that models the retirement benefit over time. Assume that the retirement benefit only increases by the cost of living increase.

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b) Use the function to find the amount of the retirement benefit after 6 years. 16) You buy a new car for $32,000. It depreciates at the rate of 12% per year.

a) Write a function that models the value of your car over time.

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b) Use the function to find the amount the car is wroth after 5 years. In 17 and 18, Tell whether the graph represents exponential growth or exponential decay. Then write a rule for the function. 17) 18)

In 19 and 20, simplify the expression.

19) 22 2x when x = 5 20) 32 12 x when x = 3

Chapter 9: Polynomials and Factoring In 21 and 22, find the sum of the polynomials.

21) )3()3573( 323 xxxxx 22) )119()1437( 22 aaaa

In 23 and 24, find the difference of the polynomials.

23) )8211()5617( 22 yyyy 24) )113()162( 323 bbbbb

In #25-28, find the product of the polynomials. (double-distribute/FOIL)

25) )12)(39( rr 26) )35)(27( 22 ttt

27) 2)53( ba 28) )29)(29( zz

In #29- 34, factor the polynomial.

29) 21102 xx 30) 6234 2 yy

31) 20205 2 xx 32) 1212 x

33) 3072 2 xx 34) 121669 2 yy

In #35-36, what are the x-intercepts? (Also called Zeros/Roots/Solutions) 35) ( 7)( 3)x x y 36) (5 2)( 11)x x y

In #37-42, solve the equation.

37) 0562 xx 38) zz 261692

39) 01512 2 x 40) 453114 2 xxx

41) 5523 xxx 42) 1226 23 mmm

x

y

43) A rectangle has the length of (3x+2) inches, a width of (x+4) inches, and an area of 153 square inches. Find the value of x. (hint: draw a picture!) Chapter 10: Quadratic Equations and Functions Find the vertex of the following quadratics:

44) 2 4 1x x 45) 22 8 5x x 46) Given the following information about the parabola, answer the questions.

382 2 xxy

a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex) e) Find a plot the vertex. Find more points on the graph and graph the parabola Vertex

x

y

47) Given the following information about the parabola, answer the questions.

342 xxy

a) a = b = c = b) Does the parabola open up or down? c) Does the parabola have a maximum or minimum? d) Find and draw the axis of symmetry ( Also known as the x coordinate of the vertex) e) Find a plot the vertex. Find more points on the graph and graph the parabola Vertex

In 48-49 solve the equation. Round to the nearest hundredth, if necessary

48) 02252 x 49) 71881 2 x

50) Use the Quadratic Formula to solve. 527 2 xx

Use the discriminant to tell whether the equation has two, one, or zero solutions.

51) 09124 2 xx 52) 4292 2 www

53) The discriminant of 2 5x x c is -7. What is the value of c?

Chapter 11: Radicals and Geometry Connections In # 54-61, simplify the expression

54) 24

108

x 55) 3218 xx 56) 5232

57) 4275 npm 58) 5

108 59)

6

5

49

81

d

k

60) 2723515 61) 500253

x

y

Und.

In #62-64, solve for x.

62) 2463 x 63) 124 xx 64) 034 xx

Chapter 12: Rational Equations and Functions 65) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 6.

x = 4, y = 3 66) Given that y varies inversely with x, use the specified values to write an inverse variation equation that relates x and y. Then find y when x = 18.

x = 6, y = 9 Graph the function.

67) x

y2

Simplify the expressions.

68) 152

5

42

1032

2

xx

x

x

xx 69)

62

672

2

1232

22

xx

xx

x

x

70)

2 12 35

7

x x

x

71)

3

2(2 )

5 14

xx

x x

72)

8

5 5

6 8

2 14

x x

x x 73)

2

2

3 3 2

2 3 1

n n

n n

Name: ____________________________ Date: _____________ Hour:___________

Algebra Practice Exam – Chapters 8-13 – Multiple Choice

Please select the choice that best answers the question and mark your answer on the provided Scantron

sheet.

_____ 74. What is the equation of the graph?

a.) y = 2x

b.) y = 3x

c.)

y 1

3

x

d.)

y 1

2

x

_____ 75. Simplify

5a5b2

3a3b

6a2b5

15a5b2.

a.)

2a5b4

3

b.)

15a5

6b2

c.)

2a5

3b2

d.)

15a5b4

6

_____ 76. Rewrite 6.5 x 106 in standard form.

a.) 0.0000065

b.) 0.00000065

c.) 65,000,000

d.) 6,500,000

_____ 77. Which of the models below are exponential decay models?

I. y = 1.19x II. y = 0.12x

III.

y 5

3

x

IV.

y 2

3

x

a.) I and II

b.) II and III

c.) I and III

d.) II and IV

_____ 78. You buy a used tractor for $55,120. It depreciates at the rate of 8.8% per year.

What is the value of the tractor after 6 years?

tr-1y a

a.) $16,458.74

b.) $91,428.71

c.) $31,715.99

d.) $2,433,639.82

_____ 79. You deposit $2700 in an account that pays 8% interest compounded yearly. How

much money is in the account after 10 years?

tr1y a

a.) $13,000

b.) $5829.10

c.) $1172.84

d.) $964,026.15

_____ 80. Simplify 242 44 ?

a.) 4

8

b.) 416

c.) 410

d.) 412

_____ 81. Which number represents 65,006,000 in scientific notation?

a.) 6.5006 x 10

-7

b.) 6.5006 x 107

c.) 65.006 x 10-6

d.) 65.006 x 106

_____ 82. Which of the following is equal to

8x3 12x2 25x 13 4x2 14x 40 ?

a.)

7x3 2x2 3x 8

b.)

8x3 16x2 11x 53

c.)

8x3 16x2 39x 27

d.)

12x3 2x2 3x 8

_____ 83. Which of the following is equal to (6a – 4b)2 ?

a.)

36a2 48ab16b2

b.)

36b2 48ab16a2

c.)

36a2 16b2

d.)

16b2 49a 36

_____ 84. Which of the following is equal to the expression 25x4 + 30x3 – 35x – 42 ?

a.) (3x – 7)(6x + 5)

b.) (5x3 + 6)(x

2 – 7)

c.) (6x2 + 7)(x + 5)

d.) (5x3 – 7)(5x + 6)

_____ 85. Which of the following is a solution of the equation 7x2 –11 = 4x2 +97 ?

a.) 0

b.) -5

c.) -6

d.) -3

_____ 86. What is the x-coordinate of the vertex of the graph of the equation

y = -2x2 + 12x – 7 ?

a.) 2

b.) -2

c.) 3

d.) 12

_____ 87. What are the zeros of the function

y 3x2 24x 36 ?

a.) -2 and 3

b.)

3 and2

3

c.) -2 and 6

d.) 6 and 2

_____ 88. What is the discriminanat of the equation y = 2x2 – x – 1 ?

a.) 0

b.) 9

c.) -7

d.) -8

_____ 89. Name the type of model that the graph suggests.

a.) Quadratic

b.) Exponential Decay

c.) Exponential Growth

d.) Linear

_____ 90. What is the correct factorization of -3x2 +16x + 35 ? (Factor the expression)

a.) (3x + 5)(x – 7)

b.) -(3x + 5)(x – 7)

c.) -(3x – 5)(x + 7)

d.) (3x – 5)(x – 7)

_____ 91. What is the simplest form of (5x + 2)(5x – 2)?

a.) 25x

2 -4

b.) 10x2

c.) 25x2 + 10x - 4

d.) 25x2 + 20x – 4

_____ 92. What are the x-intercepts for the graph of y = (x – 3)(x + 2)

a.) 2 and 3

b.) -2 and 3

c.) -3 and 2

d.) -3 and -2

_____ 93. Which of the following is

7 6 2 12 24 , in simplified form?

a.) 95

b.) 3469

c.) 186

d.) 6233

_____ 94. Solve

8 x - 5 34= 58.

a.) 710x

b.) 4x

c.) 14x

d.)

x 77

_____ 95. Which function is graphed?

a.) 2xy = 0

b.) 2

xy

c.) 22

1

xx

d.) xy = 2

_____ 96. Which expression is equivalent to 72 ?

a.) 270

b.) 36

c.) 26

d.)

3 2

_____ 97. Find the area of the rectangle. (A = l * w)

a.) 34

b.) 316

c.) 122

d.) 212

_____ 98. Which of the following equations models inverse variation??

a.) y = 3x

b.) y = 3

x

c.) y = x + 3

d.) xy = 3

34

2 34

24