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Algebra 2 honers math review

Total questions: 100

Worksheet time: 50mins

Name
Class
Date
1.

Simplify the expression: (8 - 7i) - (7i) + 2

a)

8 - 14i + 2

b)

8 - 7i + 2

c)

10 - 7i

d)

10 - 14i

2.

Simplify the expression: (-5 - 5i) + (-1 - 5i)

a)

-6 - 10i

b)

-6 - 5i

c)

-4 - 10i

d)

-4 - 5i

3.

Solve the equation: log_6 4 + log_6 (x + 5) = 1

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = -5

4.

Solve the equation: log_9 5x^2 - log_9 5 = 4

a)

x = 3

b)

x = 5

c)

x = 2

d)

x = 4

5.

Simplify the expression: (-2 + i)^2

a)

4 - 4i + i^2

b)

4 - 4i - 1

c)

4 - 4i + 1

d)

4 + 4i - 1

6.

Solve the equation: log_4 4x^2 - log_4 4 = 4

a)

x = 2

b)

x = 4

c)

x = 1

d)

x = 3

7.

Which of the following inequalities is represented by the graph?

a)

y ≤ x^2 - 2x + 4

b)

y ≥ x^2 - 2x + 4

c)

y < x^2 - 2x + 4

d)

y > x^2 - 2x + 4

8.

Which of the following inequalities is represented by the graph?

a)

y ≤ x^2 + 8x + 15

b)

y ≥ x^2 + 8x + 15

c)

y < x^2 + 8x + 15

d)

y > x^2 + 8x + 15

9.

Which of the following inequalities is represented by the graph?

a)

y ≤ x^2 + 2x

b)

y ≥ x^2 + 2x

c)

y < x^2 + 2x

d)

y > x^2 + 2x

10.

Which of the following inequalities is represented by the graph?

a)

y ≤ x^2 + 6x + 12

b)

y ≥ x^2 + 6x + 12

c)

y < x^2 + 6x + 12

d)

y > x^2 + 6x + 12

11.

Which of the following is the correct graph for the function f(x) = 4/x - 2?

a)

Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -2

b)

Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -1

c)

Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 0

d)

Graph with vertical asymptote at x = 1 and horizontal asymptote at y = -2

12.

Which of the following is the correct graph for the function f(x) = 4/x - 1?

a)

Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -2

b)

Graph with vertical asymptote at x = 0 and horizontal asymptote at y = -1

c)

Graph with vertical asymptote at x = -1 and horizontal asymptote at y = 0

d)

Graph with vertical asymptote at x = 1 and horizontal asymptote at y = -1

13.

Which of the following is the correct graph for the function f(x) = 3/(x + 2)?

a)

Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 0

b)

Graph with vertical asymptote at x = 0 and horizontal asymptote at y = 2

c)

Graph with vertical asymptote at x = 2 and horizontal asymptote at y = 0

d)

Graph with vertical asymptote at x = -2 and horizontal asymptote at y = 3

14.

Divide r^4 - r^3 - 4r^2 - 3r - 1 by r + 1

a)

r^3 - 2r^2 - 2r - 1

b)

r^3 - r^2 - 3r - 1

c)

r^3 - r^2 - 2r - 1

d)

r^3 - 2r^2 - 3r - 1

15.

Divide x^3 + 11x^2 + 23x - 42 by x + 6

a)

x^2 + 5x + 7

b)

x^2 + 5x - 7

c)

x^2 + 6x + 7

d)

x^2 + 6x - 7

16.

Divide 8p^3 - 39p^2 + 29p - 4 by p - 4

a)

8p^2 - 7p + 1

b)

8p^2 - 7p - 1

c)

8p^2 - 8p + 1

d)

8p^2 - 8p - 1

17.

Divide x^3 - 2x^2 - 26x - 8 by x + 4

a)

x^2 - 6x - 2

b)

x^2 - 6x + 2

c)

x^2 - 7x - 2

d)

x^2 - 7x + 2

18.

Divide x^2 + 8x^2 - 10x + 1 by x - 1

a)

x + 9x - 1

b)

x + 9x + 1

c)

x + 8x - 1

d)

x + 8x + 1

19.

Divide x^3 + 4x^2 - 5x - 18 by x + 2

a)

x^2 + 2x - 9

b)

x^2 + 2x + 9

c)

x^2 + 3x - 9

d)

x^2 + 3x + 9

20.

Divide 10p^4 - 108p^3 + 83p^2 - 40p + 100 by p - 10

a)

10p^3 - 8p^2 + 3p - 10

b)

10p^3 - 8p^2 + 3p + 10

c)

10p^3 - 9p^2 + 3p - 10

d)

10p^3 - 9p^2 + 3p + 10

21.

Which of the following equations represents the graph of a circle centered at the origin with a radius of 6?

a)

x^2 + y^2 + 8x - 4y + 19 = 0

b)

x^2 + y^2 - 8x + 4y + 19 = 0

c)

x^2 + y^2 - 36 = 0

d)

x^2 + y^2 - 2x - 2y - 2 = 0

22.

Factor the expression 54u^3 - 2 completely.

a)

2(27u^3 - 1)

b)

2(27u - 1)(u^2 + u + 1)

c)

2(27u - 1)(u^2 - u + 1)

d)

54(u - 1)(u^2 + u + 1)

23.

Factor the expression 2 - 432x^3 completely.

a)

2(1 - 216x^3)

b)

2(1 - 6x)(1 + 6x + 36x^2)

c)

2(1 - 6x)(1 - 6x + 36x^2)

d)

2(1 - 6x)(1 + 6x - 36x^2)

24.

Factor the expression 54a^3 + 16 completely.

a)

2(27a^3 + 8)

b)

2(27a + 2)(a^2 - 2a + 4)

c)

2(27a + 2)(a^2 - 2a + 8)

d)

2(27a + 2)(a^2 - 2a + 16)

25.

Factor the expression -2u^3 + 250 completely.

a)

-2(u^3 - 125)

b)

-2(u - 5)(u^2 + 5u + 25)

c)

-2(u - 5)(u^2 - 5u + 25)

d)

-2(u - 5)(u^2 + 5u - 25)

26.

Factor the expression 108x^3 + 4 completely.

a)

4(27x^3 + 1)

b)

4(27x + 1)(x^2 - x + 1)

c)

4(27x + 1)(x^2 + x + 1)

d)

4(27x + 1)(x^2 - x + 4)

27.

Factor the expression 54x^3 - 128 completely.

a)

2(27x^3 - 64)

b)

2(27x - 4)(x^2 + 4x + 16)

c)

2(27x - 4)(x^2 - 4x + 16)

d)

2(27x - 4)(x^2 + 4x - 16)

28.

Factor the expression 216m^3 + 1 completely.

a)

1(216m^3 + 1)

b)

1(6m + 1)(36m^2 - 6m + 1)

c)

1(6m + 1)(36m^2 + 6m + 1)

d)

1(6m + 1)(36m^2 - 6m + 6)

29.

Factor the expression 8 - 125x^3 completely.

a)

(2 - 5x)(4 + 10x + 25x^2)

b)

(2 - 5x)(4 - 10x + 25x^2)

c)

(2 - 5x)(4 + 10x - 25x^2)

d)

(2 - 5x)(4 - 10x - 25x^2)

30.

Condense the expression ( 30 log_9 x + 6 log_9 y ) to a single logarithm.

a)

log_9 (x^{30} y^6)

b)

log_9 (x^{6} y^{30})

c)

log_9 (x^{36} y)

d)

log_9 (x y^{36})

31.

Condense the expression ( 18 log_7 x + 3 log_7 y ) to a single logarithm.

a)

log_7 (x^{18} y^3)

b)

log_7 (x^{3} y^{18})

c)

log_7 (x^{21} y)

d)

log_7 (x y^{21})

32.

Condense the expression ( 15 log_6 x + 5 log_6 y ) to a single logarithm.

a)

log_6 (x^{15} y^5)

b)

log_6 (x^{5} y^{15})

c)

log_6 (x^{20} y)

d)

log_6 (x y^{20})

33.

Condense the expression ( 3 ln 7 + ln 10 / 3 ) to a single logarithm.

a)

ln (7^3 * 10^(1/3))

b)

ln (7^3 * 10^3)

c)

ln (7 * 10^(1/3))

d)

ln (7^3 * 10)

34.

Expand the logarithm log_8 (10 * 3^2)^6.

a)

6 log_8 (10) + 12 log_8 (3)

b)

6 log_8 (10) + 6 log_8 (3^2)

c)

6 log_8 (10) + 2 log_8 (3^6)

d)

6 log_8 (10) + 6 log_8 (3)

35.

Expand the logarithm log_4 (7 * 8^4)^6.

a)

6 log_4 (7) + 24 log_4 (8)

b)

6 log_4 (7) + 6 log_4 (8^4)

c)

6 log_4 (7) + 4 log_4 (8^6)

d)

6 log_4 (7) + 6 log_4 (8)

36.

Expand the logarithm log_7 (6 * 5 * 11^2).

a)

log_7 (6) + log_7 (5) + 2 log_7 (11)

b)

log_7 (6) + log_7 (5) + log_7 (11^2)

c)

log_7 (6) + 2 log_7 (5) + log_7 (11)

d)

log_7 (6) + log_7 (5^2) + log_7 (11)

37.

Expand the logarithm log_7 (11^5 / 2^4).

a)

5 log_7 (11) - 4 log_7 (2)

b)

5 log_7 (11) + 4 log_7 (2)

c)

4 log_7 (11) - 5 log_7 (2)

d)

4 log_7 (11) + 5 log_7 (2)

38.

Expand the logarithm log_6 ( (8 * 3 * 7)^(1/3) ).

a)

(1/3) (log_6 (8) + log_6 (3) + log_6 (7))

b)

(1/3) (log_6 (8) + log_6 (3) - log_6 (7))

c)

(1/3) (log_6 (8) - log_6 (3) + log_6 (7))

d)

(1/3) (log_6 (8) - log_6 (3) - log_6 (7))

39.

Evaluate log_8 (u^6 / v^6).

a)

6 log_8 (u/v)

b)

log_8 (u/v)

c)

0

d)

1

40.

Evaluate log_7 (z^5 / x^(3/2)).

a)

5 log_7 (z) - (3/2) log_7 (x)

b)

log_7 (z) - (3/2) log_7 (x)

c)

5 log_7 (z) + (3/2) log_7 (x)

d)

log_7 (z) + (3/2) log_7 (x)

41.

Evaluate log_2 ((5/6)^2).

a)

2 log_2 (5/6)

b)

log_2 (5/6)

c)

-2 log_2 (5/6)

d)

-log_2 (5/6)

42.

Evaluate log_5 (sqrt(11) * 3 * 10).

a)

log_5 (33 * sqrt(11))

b)

log_5 (330)

c)

log_5 (33)

d)

log_5 (sqrt(330))

43.

Evaluate log_7 (343).

a)

3

b)

2

c)

1

d)

0

44.

Evaluate log_3 (243).

a)

5

b)

4

c)

3

d)

2

45.

Evaluate log_3 (27).

a)

3

b)

2

c)

1

d)

0

46.

Evaluate log_5 (125).

a)

3

b)

2

c)

1

d)

0

47.

Evaluate log_5 (1/25).

a)

-2

b)

-1

c)

0

d)

1

48.

Evaluate log_3 (9).

a)

2

b)

1

c)

0

d)

-1

49.

Evaluate log_6 (216).

a)

3

b)

2

c)

1

d)

0

50.

Evaluate log_4 (64).

a)

3

b)

2

c)

1

d)

0

51.

Evaluate log_2 (1).

a)

0

b)

1

c)

2

d)

-1

52.

Evaluate log_4 (16).

a)

2

b)

1

c)

0

d)

-1

53.

Solve the quadratic equation: 2n^2 - 4n = 23.

(a)  

54.

Solve the quadratic equation: 2x^2 + 5 = -12x.

(a)  

55.

Solve the quadratic equation: 8n^2 - 4n = 5.

(a)  

56.

Solve the quadratic equation: 5x^2 = 4 - x.

(a)  

57.

Solve the quadratic equation: 10n^2 - 2n = 7.

(a)  

58.

Solve the quadratic equation: 5a^2 - 13 = -8a.

(a)  

59.

Solve the quadratic equation: x^2 = 12x + 20.

(a)  

60.

Solve the quadratic equation: 8r^2 - 13 = -7r.

(a)  

61.

Solve the quadratic equation: 3x^2 + 2x = 9.

(a)  

62.

Solve the quadratic equation: 11p^2 = -3p + 11.

(a)  

63.

Convert -75° to radians.

a)

-5π/12

b)

-5π/6

c)

-π/4

d)

-π/3

64.

Convert 4π/3 radians to degrees.

a)

120°

b)

180°

c)

240°

d)

270°

65.

Convert -220° to radians.

a)

-11π/9

b)

-11π/6

c)

-5π/6

d)

-7π/6

66.

Convert -π/3 radians to degrees.

a)

-45°

b)

-60°

c)

-90°

d)

-120°

67.

Convert 135° to radians.

a)

3π/4

b)

5π/6

c)

2π/3

d)

7π/6

68.

Convert 210° to radians.

a)

5π/6

b)

7π/6

c)

11π/6

d)

4π/3

69.

Convert 700° to radians.

a)

35π/9

b)

35π/18

c)

25π/9

d)

25π/18

70.

Convert 11π/36 radians to degrees.

a)

55°

b)

60°

c)

70°

d)

90°

71.

Convert 7π/6 radians to degrees.

a)

180°

b)

210°

c)

240°

d)

270°

72.

Convert 60° to radians.

a)

π/6

b)

π/3

c)

π/4

d)

π/2

73.

Find (g ∘ h)(x) if g(x) = x² - 2x and h(x) = -x - 4.

a)

(x + 4)² - 2(x + 4)

b)

(x - 4)² - 2(x - 4)

c)

(-x - 4)² - 2(-x - 4)

d)

(x + 4)² + 2(x + 4)

74.

Find (f ∘ g)(x) if f(x) = -2x + 2 and g(x) = -2x³ - 4x.

a)

-2(-2x³ - 4x) + 2

b)

-2(-2x³ - 4x) - 2

c)

-2(-2x³ + 4x) + 2

d)

-2(-2x³ + 4x) - 2

75.

Find (f ∘ g)(t) if f(t) = 3t - 3 and g(t) = -2t² + t.

a)

3(-2t² + t) - 3

b)

3(-2t² + t) + 3

c)

3(-2t² - t) - 3

d)

3(-2t² - t) + 3

76.

Find (g ∘ h)(a) if g(a) = a - 1 and h(a) = a² - 4a.

a)

(a² - 4a) - 1

b)

(a² - 4a) + 1

c)

(a² + 4a) - 1

d)

(a² + 4a) + 1

77.

Find (f ∘ g)(x) if f(x) = 3x + 2 and g(x) = x³ + 2x².

a)

3(x³ + 2x²) + 2

b)

3(x³ + 2x²) - 2

c)

3(x³ - 2x²) + 2

d)

3(x³ - 2x²) - 2

78.

Find (g ∘ h)(t) if g(t) = 4t + 5 and h(t) = -2t.

a)

4(-2t) + 5

b)

4(-2t) - 5

c)

4(2t) + 5

d)

4(2t) - 5

79.

Find (h ∘ g)(t) if h(t) = 3t - 1 and g(t) = t + 2.

a)

3(t + 2) - 1

b)

3(t + 2) + 1

c)

3(t - 2) - 1

d)

3(t - 2) + 1

80.

Find (g ∘ f)(n) if g(n) = 2n - 4 and f(n) = 4n + 4.

a)

2(4n + 4) - 4

b)

2(4n + 4) + 4

c)

2(4n - 4) - 4

d)

2(4n - 4) + 4

81.

Find (g ∘ h)(n) if g(n) = n - 5 and h(n) = n² + 2n.

a)

(n² + 2n) - 5

b)

(n² + 2n) + 5

c)

(n² - 2n) - 5

d)

(n² - 2n) + 5

82.

Find (h ∘ g)(x) if h(x) = -x and g(x) = 2x - 3.

a)

-(2x - 3)

b)

-(2x + 3)

c)

(2x - 3)

d)

(2x + 3)

83.

Which of the following equations represents a parabola that opens downwards?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

84.

Which of the following equations has a vertex at the point (4, -4)?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

85.

Which of the following equations represents a parabola with a minimum value?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

86.

Which of the following equations represents a parabola that opens upwards?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

87.

Which of the following equations has a vertex at the point (-1, -2)?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

88.

Which of the following equations has a vertex at the point (4, 1)?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

89.

Which of the following equations represents a parabola with a maximum value?

a)

y = -2x^2 - 8x - 12

b)

y = 3x^2 - 24x + 44

c)

y = 3x^2 + 6x + 1

d)

y = 2x^2 - 16x + 33

90.

Identify the vertex and axis of symmetry of the quadratic function y = -2x^2 + 8x - 6. Then sketch the graph.

a)

Vertex: (2, 2), Axis of symmetry: x = 2

b)

Vertex: (1, 0), Axis of symmetry: x = 1

c)

Vertex: (3, -1), Axis of symmetry: x = 3

d)

Vertex: (4, 4), Axis of symmetry: x = 4

91.

Identify the vertex and axis of symmetry of the quadratic function y = x^2 + 6x + 7. Then sketch the graph.

a)

Vertex: (-3, -2), Axis of symmetry: x = -3

b)

Vertex: (-2, -1), Axis of symmetry: x = -2

c)

Vertex: (-1, 0), Axis of symmetry: x = -1

d)

Vertex: (0, 1), Axis of symmetry: x = 0

92.

Identify the vertex and axis of symmetry of the quadratic function x = -2y^2 + 4y + 4. Then sketch the graph.

a)

Vertex: (3, 1), Axis of symmetry: y = 1

b)

Vertex: (2, 2), Axis of symmetry: y = 2

c)

Vertex: (1, 1), Axis of symmetry: y = 1

d)

Vertex: (0, 0), Axis of symmetry: y = 0

93.

Identify the vertex and axis of symmetry of the quadratic function x = y^2 - 10y + 28. Then sketch the graph.

a)

Vertex: (3, 5), Axis of symmetry: y = 5

b)

Vertex: (2, 4), Axis of symmetry: y = 4

c)

Vertex: (1, 3), Axis of symmetry: y = 3

d)

Vertex: (0, 2), Axis of symmetry: y = 2

94.

Which of the following is the inverse of the function f(x) = sqrt((-x + 3) / 2)?

a)

A) f^-1(x) = 2x^2 - 3

b)

B) f^-1(x) = -2x^2 + 3

c)

C) f^-1(x) = 2x^2 + 3

d)

D) f^-1(x) = -2x^2 - 3

95.

Which of the following is the inverse of the function f(x) = -3 / x - 2?

a)

A) f^-1(x) = -3 / (x + 2)

b)

B) f^-1(x) = 3 / (x + 2)

c)

C) f^-1(x) = -3 / (x - 2)

d)

D) f^-1(x) = 3 / (x - 2)

96.

Which of the following is the inverse of the function g(x) = (4 - sqrt(16x)) / 2?

a)

A) g^-1(x) = (4 - 2x) / 16

b)

B) g^-1(x) = (4 - 2x^2) / 16

c)

C) g^-1(x) = (4 - 4x) / 16

d)

D) g^-1(x) = (4 - 4x^2) / 16

97.

Which of the following is the inverse of the function f(x) = -4 / (x + 1) - 3?

a)

A) f^-1(x) = -4 / (x + 3) - 1

b)

B) f^-1(x) = -4 / (x - 3) - 1

c)

C) f^-1(x) = -4 / (x + 3) + 1

d)

D) f^-1(x) = -4 / (x - 3) + 1

98.

Which of the following is the inverse of the function f(x) = (-15 + 3x) / 5?

a)

A) f^-1(x) = (5x + 15) / 3

b)

B) f^-1(x) = (5x - 15) / 3

c)

C) f^-1(x) = (3x + 15) / 5

d)

D) f^-1(x) = (3x - 15) / 5

99.

Which of the following is the inverse of the function h(x) = 1 / (-x - 3) + 2?

a)

A) h^-1(x) = 1 / (-x + 2) - 3

b)

B) h^-1(x) = 1 / (-x - 2) + 3

c)

C) h^-1(x) = 1 / (-x + 2) + 3

d)

D) h^-1(x) = 1 / (-x - 2) - 3

100.

Which of the following is the inverse of the function g(x) = -x - 1?

a)

A) g^-1(x) = -x + 1

b)

B) g^-1(x) = -x - 1

c)

C) g^-1(x) = x - 1

d)

D) g^-1(x) = x + 1