Free Printable 2022-23 Algebra 2 Exam Review

1.

1) Distribute (2x - 3)²

a)

4x² - 9

b)

4x² + 9

c)

4x² - 12x + 9

d)

4x² - 12x - 9

2.

Evaluate -3²

a)

-9

b)

9

c)

-6

d)

6

3.

Evaluate (-3)²

a)

-9

b)

9

c)

-6

d)

6

4.

What is the/are the y-intercepts of
f(x)=3x² - 8x + 2

a)

(0, 2)

b)

(0, -2)

c)

(2, 0)

d)

(-2, 0)

5.

Simplify Completey: x⁵ ⋅ x^-3⋅ x¹²

a)

x^-180

b)

x¹⁴

c)

x¹⁸⁰

d)

x^-14

6.

Rewrite the exponential equation as a logarithmic equation.
2^x = 8

a)

log₂x = 8

b)

log_x2 = 8

c)

log₂8 = x

d)

log₂2 = 8

7.

Rewrite the logarithmic equation as an exponent.
log₄25 = x

a)

4^x = log

b)

4²⁵ = x

c)

4^x =25

d)

log = 4

8.

Which of the following is the factored form of x³ – 125?

a)

(x - 5)³

b)

(x - 5)(x² + 25)

c)

(x - 5)(x² + 5x + 25)

d)

(x - 5)(x² - 5x + 25)

9.

What is the solution set to x² = 2x – 5?

a)

{±i}

b)

{2 ± 2i}

c)

{1 ± 2i}

d)

{1, 2}

10.

Which is a factor of 3x² + 10x – 8 = 0?

a)

(x - 4)

b)

(2x - 3)

c)

(x + 6)

d)

(3x - 2)

11.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

12.

Simplify the rational function

a)

1/(3x)

b)

3x(x + 1)

c)

3x

d)

(x + 1)

13.

Divide

a)

A

b)

B

c)

C

d)

D

14.

Solve

a)

A

b)

B

c)

C

d)

D

15.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

16.

a)

36

b)

18

c)

-18

d)

27

17.

a)

x = 2

b)

x = 4

c)

x = 7

d)

x = 9

18.

Simplify the expression:

a)

25x²y³

b)

-5xy² ∛5x

c)

5ixy² ∛5x

d)

-125x³y⁶ ∛5x

19.

a)

A

b)

B

c)

C

d)

D

20.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

21.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

22.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

23.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

24.

Identify the 'c' value: y = 16x² -8x -24

a)

16

b)

-8

c)

24

d)

-24

25.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

26.

Solve the equation by factoring:
5x² - 35x + 60 = 0

a)

3, -4

b)

-3, 4

c)

3, 4

d)

-3, -4

27.

Solve by using the quadratic formula:
15x²+22x=-8

a)

-2/3, 4/5

b)

2/3, -4/5

c)

2/3, 4/5

d)

-2/3, -4/5

28.

Use the quadratic formula to find the solutions for
y = 3x³ + 8x - 1

a)

0.1167 and -2.7833

b)

.7 and -16.7

c)

.35 and -8.35

d)

0.2358 and -1.236

29.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

30.

find x for
x²+2x-8=0

a)

x= -4, 2

b)

x= -4, -2

c)

x= 4, 2

d)

x= -2, 4

31.

Factor
10x² + 15x-5

a)

25(10x³+45x-15)

b)

5(2x³ + 3x²-x)

c)

x(10x³+15x-5)

d)

5(2x²+3x-1)

32.

Factor Completely:
x² - 36

a)

(x + 9)(x - 4)

b)

(x - 6)(x - 6)

c)

(x - 9)(x + 4)

d)

(x + 6)(x - 6)

33.

Factor x²-6x+8

a)

(x-4)(x-2)

b)

(x+4)(x+2)

c)

(x-4)(x+2)

d)

(x+4)(x-2)

34.

a)

A

b)

B

c)

C

d)

D

35.

What form is this quadratic equation written in: $y=-2\left(x-1\right)\left(x-5\right)$

a)

Intercept

b)

Standard

c)

Vertex

d)

Slope-Intercept

36.

What form is this quadratic equation written in: $y=3x^2-12x-5$

a)

Intercept

b)

Standard

c)

Vertex

d)

Slope-Intercept

37.

Does the quadratic $y=-2\left(x-1\right)\left(x-5\right)$ have a minimum or maximum?

a)

Minimum

b)

Maximum

c)

Neither

d)

Cannot Determine

38.

Does the quadratic $y=3x^2-12x-5$ have a minimum or maximum?

a)

Minimum

b)

Maximum

c)

Neither

d)

Cannot Determine

39.

What is the axis of symmetry of $y=3x^2-12x-5$

a)

y=2

b)

y=-2

c)

x=-2

d)

x=2

40.

Which equation has the narrowest graph?

a)

$y=x^2$

b)

$y=\frac{1}{8}x^2$

c)

$y=-3x^2$

d)

$y=2x^2$

41.

Which equation has the widest graph?

a)

$y=x^2$

b)

$y=\frac{1}{8}x^2$

c)

$y=-3x^2$

d)

$y=2x^2$

42.

Write $y=-\left(x-2\right)^2-5$ in standard form.

a)

$y=-x^2+4x-9$

b)

$y=-x^2-9$

c)

$y=x^2-4x-1$

d)

$y=-x^2+4x+9$

43.

Find the roots of the following quadratic: $y=2x^2+12x+6$

a)

$x=\pm6$

b)

$x=-3\pm\sqrt[]{6}$

c)

$x=-6,\ 0$

d)

$3\pm\sqrt[]{6}$

44.

Frustrated Algebra 2 students stapped their teacher to a rocket. The rocket was launched from an initial height of 2 feet, with an initial velocity of 200 feet per second. The height of the rocket (in feet) with respect to time is given by: $h\left(t\right)=-16t^2+200t+2$

What is the height of the rocket after 2 seconds?

a)

6.25

b)

627

c)

12.5

d)

338

45.

Frustrated Algebra 2 students stapped their teacher to a rocket. The rocket was launched from an initial height of 2 feet, with an initial velocity of 200 feet per second. The height of the rocket (in feet) with respect to time is given by: $h\left(t\right)=-16t^2+200t+2$

When does the rocket hit the ground?

a)

6.25

b)

627

c)

12.5

d)

338

46.

Frustrated Algebra 2 students stapped their teacher to a rocket. The rocket was launched from an initial height of 2 feet, with an initial velocity of 200 feet per second. The height of the rocket (in feet) with respect to time is given by: $h\left(t\right)=-16t^2+200t+2$

When does the rocket hit its maximum height?

a)

6.25

b)

627

c)

12.5

d)

338

47.

If a quadratic has a discriminant of zero, how many solutions will it have?

a)

2 Real Solutions

b)

No Solutions

c)

1 Real Solution

d)

2 Complex Solutions

48.

If a quadratic has a negative discriminant, how many solutions will it have?

a)

2 Real Solutions

b)

No Solutions

c)

1 Real Solution

d)

2 Complex Solutions

49.

If a quadratic has a positive discriminant, how many solutions will it have?

a)

2 Real Solutions

b)

No Solutions

c)

1 Real Solution

d)

2 Complex Solutions

50.

Samantha simplified $\sqrt[]{32}$ as $2\sqrt[]{8}$ . Is this simplified completely?

a)

Yes

b)

No

c)

Bacon

d)

Pizza

51.

Simplify: $\left(6+2i\right)+\left(-10+7i\right)$

a)

-4+9i

b)

16-5i

c)

-16+9i

d)

5i-16

52.

Simplify: $\left(5+6i\right)\left(2+3i\right)$

a)

$10+32i+18i^2$

b)

10+12i

c)

-8+27i

d)

28+27i

53.

The following Real Number Venn diagram correctly shows each set and subset:

a)

True

b)

False

54.

All natural (counting) numbers are..

a)

Whole numbers

b)

Whole numbers, integers

c)

Whole numbers, integers, rational numbers

d)

Whole numbers, integers, rational numbers and irrational numbers

55.

Which of the following is rational?

a)

.211232112421125. . . .

b)

π

c)

√25

d)

√12

56.

(1 + 3) + 4 = 1 + ( 3 + 4)

a)

Commutative Property of Multiplication

b)

Commutative Property of Addition

c)

Associative Property of Multiplication

d)

Associative Property of Addition

57.

9 ^_x 2 = 2 ^_x 9

a)

Commutative Property of Multiplication

b)

Associative Property of Multiplication

c)

Multiplicative Inverse Property

d)

Distributive Property

58.

5(8 + 7) = (5 ^_x 8) + (5 ^_x 7)

a)

Multiplicative Inverse

b)

Distributive Property

c)

Additive Identity

d)

Associative Property of Multiplication

59.

1 ^_x 12 =12

a)

Identity Property of Multiplication

b)

Commutative Property of Multiplication

c)

Multiplication Property of One

d)

Distributive Property

60.

Find and explain the error.
5 - 3 + 2
5 - 5
0

a)

There is no error.

b)

Addition was done first and you should have subtracted first

c)

There is a subtraction error

61.

evaluate bc + 5a
when a = 3, b = 4, and c = -6

a)

9

b)

38

c)

-38

d)

-9

62.

x² - xy if x = 8 and y = -3

a)

88

b)

40

c)

-8

d)

-24

63.

Solve the equation.

a)

x = 0.6

b)

x = 2.3

c)

x = 4

d)

x = -1

64.

What is the first step in solving this equation?

a)

add 4 to both sides

b)

distribute the 4

c)

subtract 4 to both sides

d)

subtract 12 to both sides

65.

3y+6+4y-7=-8

a)

y=-1

b)

y=-8

c)

y=1

d)

y=7

66.

a)

x = 24

b)

x = 12

c)

x = 17.5

d)

x = 19.5

67.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

68.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

69.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

70.

a)

Function

b)

Not a Function

71.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

72.

Find the inverse function

a)

b)

c)

d)

73.

Find the inverse function

a)

b)

c)

d)

74.

given f(x) = $\frac{3x+2}{x-1}$ , What is f(1)?

a)

-5

b)

5

c)

0

d)

f(1) is undefined

75.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

76.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

77.

(3i)(-2+4i)

a)

-6+12i

b)

-12-6i

c)

-2+7i

d)

12+6i

78.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

79.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

80.

w³ + 3w

a)

3w(1)

b)

w(w² + 3)

c)

w³(w + 3)

81.

Factor completely:

3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

82.

Factor the polynomial.
x²-4x-32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

x+2)(x+5)

83.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

84.

Factor
2x² - 13x - 70

a)

(2x-7)(x+10)

b)

(7x+5)(x+2)

c)

(2x+7)(x-10)

d)

2(x+7)(x+10)

85.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

86.

Factor: 27x³ + 8

a)

(3x + 2)(9x² - 6x + 4)

b)

(9x + 2)(3x² + 18x + 4)

c)

(3x²+4)(9x + 2)

d)

(27x + 8)(x² - 216x + 64)

87.

$w^2+7w+4=0$

a)

$\frac{-7\pm\sqrt{33}}{2}$

b)

$\frac{-7\pm\sqrt{65}}{2}$

c)

$\frac{7\pm\sqrt{33}}{2}$

d)

$\frac{-7\pm3\sqrt{11}}{2}$

88.

$5x^2+3x-3=0$

a)

$\frac{-3\pm i\sqrt{51}}{10}$

b)

$\frac{-3\pm\sqrt{69}}{10}$

c)

$\frac{3\pm\sqrt{69}}{2}$

d)

$\frac{-3\pm3\sqrt{23}}{10}$

89.

a)

A

b)

B

c)

C

d)

D

90.

a)

A

b)

B

c)

C

d)

D

91.

a)

A

b)

B

c)

C

d)

D

92.

a)

A

b)

B

c)

C

d)

D

93.

Simplify.

a)

y¹⁵

b)

y⁵

c)

y²

d)

2y⁵

94.

Let f(x) = 3x² - 9x +2.
Is k = -3 a zero of the function?

a)

yes

b)

no

95.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

96.

a)

x = 49

b)

x = 53

c)

x = 45

d)

x = 18

97.

a)

x = -6

b)

x = 3

c)

x = -3

d)

x = 5±

98.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

99.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

100.

Expand

a)

A

b)

B

c)

C

d)

D

101.

Expand

a)

log₈x + log₈y + log₈z

b)

5log₈x + 5log₈y + 5log₈z

c)

log₈xy + 5log₈z

d)

log₈x + log₈y + 5log₈z

102.

Rewrite e^x = 9 using a logarithm

a)

ln x = 9

b)

ln 9 = x

c)

log_x e = 9

d)

log₉ x = e

103.

Solve for x:
8^x+1= 3

a)

0.528

b)

0.893

c)

-0.472

d)

1.893

104.

Solve log(x) + log(x-1) = log(3x+12)

a)

x = -3, 4

b)

x = -2, 6

c)

x = -4, 3

d)

x = -6, 2

105.

Simplify $\frac{7n}{3n-18}+\frac{n+3}{3}$

a)

$\frac{8n+3}{3n-15}$

b)

$\frac{n^2+4n-18}{3\left(n-6\right)}$

c)

$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$

d)

$\frac{7n+n+3}{3n-18+3}$

106.

$\frac{4x}{x-5}-\frac{3}{x-6}$ Simplify

a)

$\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$

b)

$\frac{4x-3}{2x+1}$

c)

$\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}$

d)

$\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}$

107.

Simplify $\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}$

a)

$\frac{n-3}{n-8}$

b)

$\frac{n-3}{\left(n+5\right)\left(n-8\right)}$

c)

$\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}$

d)

$\frac{n^2+2n-14}{2n-3}$

108.

$\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}$ Simplify

a)

$\frac{m-5}{m-2}$

b)

$\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}$

c)

$\frac{m^2+2m-32}{m^2+14m+49}$

d)

$\frac{-5}{2m^2}$

109.

Solve for x

a)

6

b)

17/5

c)

19/2

d)

- 6

110.

Solve for v

a)

- 7/6

b)

- 9/5

c)

9/5

d)

-3

111.

Which one is the same as fοg(x)

a)

g(f(x))

b)

f(g(x))

112.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

113.

Given f(x) = 2x and
g(x) = x²+3 , find f(g(x)).

a)

x²+2x+3

b)

4x²+3

c)

2x²+3

d)

2x²+6

114.

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)).

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

115.

An object flies through the air and follows a parabolic path. Which of these typically represents the x-axis?

a)

time

b)

height from the ground

116.

An object flies through the air and follows a parabolic path. What does the y-axis represent?

a)

time

b)

height from the ground

c)

horizontal distance

d)

money

117.

What is the initial (starting) height of an object following this path? h(t) = -16t² +20t + 6

a)

-16 feet

b)

0 feet

c)

20 feet

d)

6 feet

118.

Simplify √-23

a)

-√23

b)

23i

c)

23

d)

i√23

119.

Simplify √-4

a)

2i

b)

-2i

c)

2

d)

4i

120.

Simplify -√-48

a)

4i√3

b)

-4i√3

c)

i√48

d)

-48i

121.

$\ \ \sqrt{-3}\cdot\sqrt{-15}$

a)

$-3i\sqrt{5}$

b)

$3i\sqrt{5}$

c)

$3\sqrt{5}$

d)

$-3\sqrt{5}$

122.

$\left(5+4i\right)\ +\ \left(6\ -\ 5i\right)$

a)

$11\ +\ 9i$

b)

$11\ -\ i$

c)

$50-\ i$

d)

$10\ -i$

123.

$\left(7+4i\right)\left(-2+5i\right)$

a)

$-34+27i$

b)

$6+27i$

c)

$-14+27i+20i^2$

d)

$-34+42i$

124.

$b^2+8b-33=0$

a)

$\left\{8,-33\right\}$

b)

$\left\{3,-11\right\}$

c)

$\left\{3,11\right\}$

d)

$\left\{-11,-3\right\}$

125.

Factor the greatest monomial 6x²-27x

a)

(6x+1)(x+3)

b)

3x(2x-9)

c)

6x(x-9)

d)

(3x-9)(2x+3)

126.

x² -4 = 77

a)

9

b)

-9

c)

No Real Solutions

d)

±9

127.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

2022-23 Algebra 2 Exam Review

Total questions: 127

Worksheet time: 7hrs 32mins

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