algebra 2 - semester review packet no answers

7/28/2019 Algebra 2 - Semester Review Packet No Answers

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Algebra 2ID: 1

Name___________________________________

Period____Date________________Semester Review Packet

Find the value that completes the square and then rewrite as a perfect square.

1) x2 40x + __

A) 81; (x 9)2

B) 144; (x 12)2

C) 400; (x 20)2

D) 100; (x 10)2

2) y2 + 24y + __

A) 4; (y + 2)2

B) 144; (y + 12)2

C) 576; (y + 12)2

D) 144; (y + 12)2

3) m2 2m + __

A) 1; (m 1)2

B) 169; (m + 13)2

C) 4; (m 1)2

D) 1; (m 1)2

4) x2 + 10x + __

A) 36; (x + 6)2

B) 1; (x + 1)2

C) 256; (x + 16)2

D) 25; (x + 5)2

Find the discriminant of each quadratic equation then state the number and type of solutions.

5) x2 6x + 9 = 0

A) 0; one real solution

B) 72; two real solutions

C) 0; two real solutions

D) 0; two imaginary solutions

6) 4p2 8p + 4 = 0

A) 0; two real solutions

B) 0; one real solution

C) 144; two real solutions

D) 128; two real solutions

7) 3n2 + 6n 3 = 0

A) 72; two real solutions

B) 0; one real solution

C)81

; two real solutionsD) 0; two real solutions

8) 6m2 + 3m + 3 = 0

A) 63; one real solution

B) 63; two real solutions

C)63

; two imaginary solutionsD) 260; two imaginary solutions

Solve each equation.

9) 42 = 7(1 + p)

A) {5}

B) {11}C) { All real numbers. }

D) {16}

10) 3(4 + 3x) = 21

A) {2} B) {1}

C) {3} D) {6}

11) 55 = 5(7 + 4n)

A) {9} B) No solution.C) {1} D) {11}

12) 6(b + 7) = 24

A) {3}B) {3}C) { All real numbers. }

D) No solution.

Solve each equation by factoring.

13) x2 + 16 = 10x

A) {3, 8} B) {2, 8}

C) {6, 8} D) {2, 8}

14) r2 = 12r 35

A) {5, 4} B) {5, 6}

C) {5, 7} D) {5, 7}

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15) n2 13n = 40

A) {8, 8} B) {5, 8}

C) {3, 4} D) {5, 8}

16) a2 8 = 7a

A) {1, 6} B) {7, 0}

C) {1, 8} D) {8, 2}

Solve each equation with the quadratic formula.

17) x2 4 = 0

A) {5, 2} B) {2, 2}

C) {2, 5} D) {1, 1}

18) v2 + 12v 28 = 0

A) {14, 2}

B) {2, 14}

C) {11, 6}D) {6 + 43 , 6 43}

19) 4x2 64 = 0

A) {4, 4}

B) {8, 8}

C) {3 + 114, 3 114}D) {5, 7}

20) n2 5n 6 = 0

A) {3, 2}

B) {1, 6}

C) {5 + 312

,5 31

2}

D) {6, 1}

21) 4k2 + 6k 3 = 0

A) {2 77

, 2 7

7}

B) {3 + 214

,3 21

4}

C) { 305

, 30

5}

D) {2, 2}

22) 5p2 + 2p 13 = 0

A) {1 + 665

,1 66

5}

B) {7 + 372

,7 37

2}

C) {1 + 14, 1 14}

D) {7 + 612

,7 61

2}

23) 5n2 + 5n 9 = 0

A) {5 + 612 ,5 61

2 }B) {5 + 205

10,

5 205

10}

C) {5 + 7010

,5 70

10}

D) {5 + 612

,5 61

2}

24) 2x2 + 4x 11 = 0

A) {1 + 54 ,1 5

4 }B) {3 + 141

6,

3 141

6}

C) {1 + 54

,1 5

4}

D) {2 + 262

,2 26

2}

25) 2r2 + 2 = 0

A) {2 + i 62 ,2 i 6

2 }B) {i 22 ,

i 2

2 }C) { 2

2,

2

2}

D) {i, i}

26) 8m2 = 6

A) {2 + 22

,2 2

2}

B) {i 32 , i 3

2 }C) {1 + i, 1 i}

D) {4 + 2 2, 4 2 2}

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27) 6x2 = 2x 8

A) {2 + i 65 ,2 i 6

5 }B) {1, 43}C) {5 + i 1510 ,

5 i 15

10 }D) {1 + i 476 , 1 i 476 }

28) 2n2 = 2n 4

A) {2i 33 , 2i 3

3 }B) {1 + i 72 ,

1 i 7

2 }C) {2 + 2i 67 ,

2 2i 6

7 }D) {1 + i 72 , 1 i 72 }

Simplify. Your answer should contain only positive exponents.

29) 3nm3

4n2

A) 12n3m3 B) 12m4n

C) m2n2 D) 9n4

30) 3x4y

2 x

2y

2

A) 6yx B) 9x7y8

C)3

x2D) 8x5y4

31) 4x3y

3 4y

2

A) 6x2y8 B)4x5

y

C) 16x3y5 D)1

x6y4

32) m 4nm4

A)3n6

mB) 4m6n3

C) 8m5n3 D) 4m5n

33) (y1)3

A) 27y6 B)64y3

x6

C)1

y

3D) 27x6y6

34) (2vu4)4

A)256u8

v12B) 16v4u16

C)1

v

9D)

u3v3

8

35)4vu

2

4u3

A)3v4

4B)

v

u5

C)u4

3v6D)

v3u2

4

36)4xy

3

4yx4

A)y5x3

4B)

3

2

C)3y3

xD)

y2

x3

37)ba

4

a

A)4

a5B)

b

a5

C)b6

2D) 2a2b4

38)3x

xy4

A)4y4

3x2B)

3

4

C) 3y4 D)4y6

x

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Factor each completely.

39) v3 8v2 20v

A) v(v + 2)(v 10)B) (v + 4)(v 5)C) v(v + 2)(v + 10)D) v(v + 10)(v 2)

40) 2a2 + 8a 10

A) Not factorable

B) 3(a 10)(a 8)C) 2(a + 5)(a + 1)D) 2(a + 5)(a 1)

41) 2r2 + 8r 90

A) 2(r 9)(r 5)B) 2(r+ 9)(r+ 5)C) 2(r+ 9)(r 5)D) 2(r+ 15)(r 3)

42) x2 17x + 72

A) (x 9)(x + 8)B) (x 9)(x 8)C) (x + 4)(x + 18)D) (x + 9)(x + 8)

43) 27m3 + 125

A) (3m + 5)(9m2 15m + 25)B) (3m + 5)(9m2 + 15m + 25)C) (3m 5)(9m2 + 15m + 25)

D) (3m + 5)3

44) 125x3 8

A) (5x 2)3

B) (5x 2)(25x2 + 10x + 4)C) (5x 2)(5x + 2)D) (5x + 2)(25x2 10x + 4)

45) 125m3 + 27

A) (5m + 3)(25m2 15m + 9)B) (5m + 3)(25m2 + 15m + 9)

C) (5m + 3)3

D) (5m 3)(25m2 + 15m + 9)

46) 3x3 81

A) 3(x 3)3

B) 3(x 3)(x + 3)C) 3(x + 3)(x2 3x + 9)D) 3(x 3)(x2 + 3x + 9)

Evaluate each function.

47) h(a) = a2 + a; Find h(4)

A) 56 B) 72

C) 42 D) 20

48) h(t) = t+ 1; Find h(10)

A) 10 B) 2

C) 9 D) 449) h(x) = 3x + 1; Find h(6)

A) 25 B) 17

C) 7 D) 22

50) f(n) = n2 + 2n; Find f(8)

A) 15 B) 35

C) 48 D) 1

Find the inverse of each function.

51) f(x) =5 3x

5

A) f1(x) = x + 2

B) f1(x) = x + 26

C) f1(x) =

5x + 5

3

D) f1(x) = 3x 4

52) f(n) =2 5n

2

A) f1(n) =

4n

3

B) f1(n) =

4

3n +

4

3

C) f1(n) = 2n + 8

D) f1(n) =

2n + 2

5

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5/17

53) g(x) = 3x 5

A) g1(x) =

3

2x

B) g1(x) = 2

3

5x

C) g1(x) = 1

2

3x

D) g1(x) =1

3x +

5

3

54) g(x) =8 + x

2

A) g1(x) =

3x 15

7

B) g1(x) = 5 +

4

5x

C) g1(x) = 2x 8

D) g1(x) = x + 154

Sketch the graph of each line.

55) 5x 2y = 2

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

56) 5x + 4y = 12

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

-5-


6/17

57) y = 1

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

58) y = 2

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

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7/17

Sketch the graph of each linear inequality.

59) x > 1

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

60) y > x 5

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

-7-


8/17

61) y < 2x 1

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

62) y 1

5x 4

A)

6 4 2 0 2 4 6

6

4

2

2

4

6

B)

6 4 2 0 2 4 6

6

4

2

2

4

6

C)

6 4 2 0 2 4 6

6

4

2

2

4

6

D)

6 4 2 0 2 4 6

6

4

2

2

4

6

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9/17

Identify the vertex and axis of symmetry of each. Then sketch the graph.

63) y = x2 + 8x + 12

A)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6

8 Vertex: (4, 4)Axis of Sym.: x = 4

B)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


C)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


D)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


64) y = 2x2 + 16x 34

A)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


B)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


C)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


D)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


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10/17

65) y = (x + 2)2 6

A)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


B)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


C)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


D)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


66) y = 2(x + 4)2 4

A)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


B)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


C)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


D)

x

y

8 6 4 2 2 4 6 8

8

6

4

2

2

4

6


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11/17

Sketch the graph of each function.

67) y > 2x2 4x 5

A)

8 6 4 2 0 2

12

10

8

6

4

2

B)

8 6 4 2 0 2 4

14

12

10

8

6

4

2

C)

0 2 4 6 8 10

12

10

8

6

4

2

D)

7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

68) y > 2x2 + 12x 17

A)

0 1 2 3 4 5 6 7 8 9 10

10

8

6

4

2

B)

10 0 10 20 30

50

40

30

20

10

C)

6 5 4 3 2 1 0 1

6

5

4

3

2

1

1

D)

4 2 0 2 4

8

6

4

2

2

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12/17

69) y 2x2 8x 6

A)

6 4 2 0 2 4 6 8

2

4

6

8

10

12

14

B)

1 0 1 2 3 4 5

3

2

1

1

2

3

C)

0 1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

D)

6 4 2 0 2

6

4

2

2

70) y < x2 6x 13

A)

7 6 5 4 3 2 1 0 1

8

6

4

2

B)

2 0 2 4 6

2

4

6

8

10

C)

6 4 2 0 2 4

2

4

6

8

10

12

D)

6 5 4 3 2 1 0

1

2

3

4

5

6

7

Solve each system by graphing.

71) y = 2

3x + 4

y =4

3x 2

A) (1, 2) B) (3, 2)C) (2, 3) D) (3, 2)

72) y =7

4x + 3

y =1

4x 3

A) (4, 4) B) (5, 2)C) (5, 4) D) (5, 5)

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13/17

73) y = x 3

y = 2x + 3

A) (1, 2) B) (2, 1)C) (1, 4) D) (2, 1)

74) y =1

2x + 1

y =5

2x 3

A) (2, 2) B) (2, 2)C) (4, 4) D) (2, 2)

75) x + 4y = 8

5x + 4y = 8

A) (4, 3)B) Infinite number of solutions

C) No solution

D) (4, 3)

76) x y = 4

y = 2

A) (2, 2) B) (2, 4)C) (2, 4) D) (2, 2)

77) 2x + y = 3

x + 3y = 6

A) (3, 3) B) No solutionC) (3, 3) D) (3, 3)

78) x y = 2

6x y = 3

A) (1, 3)B) (1, 3)C) Infinite number of solutions

D) (1, 3)

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14/17

Sketch the solution to each system of inequalities.

79) y > x + 3

y > x 2

A)

4 2 0 2 4

4

2

2

4

B)

4 2 0 2 4

4

2

2

4

C)

4 2 0 2 4

4

2

2

4

D)

4 2 0 2 4

4

2

2

4

80) y 4

3x 1

y 1

3x + 2

A)

4 2 0 2 4

4

2

2

4

B)

4 2 0 2 4

4

2

2

4

C)

4 2 0 2 4

4

2

2

4

D)

4 2 0 2 4

4

2

2

4

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15/17

81) y 1

3x 2

y >2

3x + 1

A)

4 2 0 2 4

4

2

2

4

B)

4 2 0 2 4

4

2

2

4

C)

4 2 0 2 4

4

2

2

4

D)

4 2 0 2 4

4

2

2

4

82) y 1

3x + 1

y >4

3x 2

A)

4 2 0 2 4

4

2

2

4

B)

4 2 0 2 4

4

2

2

4

C)

4 2 0 2 4

4

2

2

4

D)

4 2 0 2 4

4

2

2

4

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16/17

Write the slope-intercept form of the equation of each line.

83)

5 4 3 2 1 0 1 2 3 4 5

4

2

2

4

A) y = 2

5x + 2

B) y =2

5x + 2

C) y =4

5x + 2

D) y=x

+ 2

84)

5 4 3 2 1 0 1 2 3 4 5

4

2

2

4

A) y =3

2x + 4

B) y = 3

2x + 4

C) y = 4x 3

2

D) y = 4x +3

2

85) 4x 7y = 3

A) y =5

7

x +3

7

B) y =4

7x +

3

7

C) y = 4

7x +

3

7

D) y =2

7x +

3

7

86) 7x 5y = 51

A) y =51

5

x +4

5

B) y = 51

5x +

4

5

C) y =7

5x

51

5

D) y =4

5x

51

5

Write the slope-intercept form of the equation of the line through the given point with the given slope.

87) through: (4, 4), slope = 2

A) y = 2x + 2 B) y = 4x + 2

C) y = 2x + 2 D) y = 2x + 4

88) through: (3, 4), slope = 0

A) x = 4 B) x = 1

C) y = 4 D) x = 4

Write the slope-intercept form of the equation of the line through the given points.

89) through: (0, 5) and (5, 5)

A) y = 2x + 5 B) y = 5x 2

C) y = 2x + 5 D) y = x 2

90) through: (0, 5) and (2, 0)

A) y =5

2x + 5

B) y = 5

2x + 5

C) y = 5x + 5

2

D) y = x +5

2

Write the slope-intercept form of the equation of the line described.

91) through: (5, 5), parallel to y = 1

5x 3

A) y = x 4 B) y = 1

5x 4

C) y =1

5x 4 D) y = 4x 4

92) through: (5, 4), parallel to y = 8

5x + 5

A) y = 8

5x 4 B) y = 4x

1

5

C) y = 1

5x 4 D) y = 4x

1

5

-16-


17/17

93) through: (4, 5), perp. to y = 1

2x + 5

A) y = 3x + 2 B) y = 3x + 2

C) y = 2x 3 D) y = 2x 3

94) through: (1, 4), perp. to y = x + 1

A) y = 2x 5 B) y = x 5

C) y = 5x + 1 D) y = x 5

Simplify each expression.

95) (1 + b4 + b2) + (7b4 7b2 + 7)

A) 3b4 7b2 + 8

B) 3b4 8b2 + 8

C) 3b4 6b2 + 8

D) 8b4 6b2 + 8

96) (7 + 2x3 4x2) (3x4 3x3 + x2)

A) 3x4 + 11x3 5x2 + 7

B) 3x4 + 11x3 + x2 + 3

C) 3x4 + 5x3 5x2 + 7

D) 3x4 + 11x3 5x2 + 3

97) Wilbur and Ndiba each improved their yards by planting rose bushes and ornamental grass. They

bought their supplies from the same store. Wilbur spent $78 on 3 rose bushes and 6 bunches of

ornamental grass. Ndiba spent $136 on 12 rose bushes and 2 bunches of ornamental grass. What is the

cost of one rose bush and the cost of one bunch of ornamental grass?

A) rose bush: $5, bunch of ornamental grass: $7 B) rose bush: $10, bunch of ornamental grass: $8

C) rose bush: $8, bunch of ornamental grass: $10 D) rose bush: $12, bunch of ornamental grass: $4

98) Lisa and Shayna each improved their yards by planting hostas and ivy. They bought their supplies from

the same store. Lisa spent $46 on 2 hostas and 4 pots of ivy. Shayna spent $78 on 4 hostas and 6 pots

of ivy. What is the cost of one hosta and the cost of one pot of ivy?

A) hosta: $5, pot of ivy: $10 B) hosta: $4, pot of ivy: $3

C) hosta: $7, pot of ivy: $9 D) hosta: $9, pot of ivy: $7

99) The water park is a popular field trip destination. This year the senior class at High School A and the

senior class at High School B both planned trips there. The senior class at High School A rented and

filled 8 vans and 7 buses with 251 students. High School B rented and filled 9 vans and 14 buses with

411 students. Each van and each bus carried the same number of students. How many students can a

van carry? How many students can a bus carry?

A) Van: 13, Bus: 21 B) Van: 18, Bus: 13C) Van: 21, Bus: 13 D) Van: 5, Bus: 10

100) Amy and Jennifer each improved their yards by planting daylilies and ornamental grass. They bought

their supplies from the same store. Amy spent $108 on 8 daylilies and 14 bunches of ornamental grass.

Jennifer spent $78 on 12 daylilies and 7 bunches of ornamental grass. What is the cost of one daylily

and the cost of one bunch of ornamental grass?

A) daylily: $6, bunch of ornamental grass: $3 B) daylily: $4, bunch of ornamental grass: $3

C) daylily: $3, bunch of ornamental grass: $6 D) daylily: $2, bunch of ornamental grass: $7

algebra 2 - semester review packet no answers

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