Free Printable Algebra 2 Exam Review

1.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

2.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

3.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

4.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

5.

For division, what # is in the left
box?

a)

0

b)

1

c)

2

d)

3

6.

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

a)

0

b)

10

c)

15

d)

-7

7.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor!

b)

No, it is not a factor!

8.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

9.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

10.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

11.

Select all the identities which are incorrect.

a)

(x + y)(x - y) = x² - y²

b)

(u + v)² = u² +2uv + v²

c)

(x + y)(x - y) = x² + y²

d)

(u - v)² = u² - v²

e)

(u + v)² = u² + v²

12.

Is the following a polynomial identity

x² + (a + b)x + ab = (x + a)(x + b).

a)

Yes, they are equal

b)

No, they are not equal

13.

Is the following a polynomial identity

m³ + n³ = (m + n)(m² + mn + n²).

a)

Yes, they are equal

b)

No, they are not equal

14.

Find the product:
(5n-8)(5n+8)

a)

25n²-64

b)

10n²

c)

5n²+16

d)

16

15.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

16.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

17.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

18.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

19.

Multiply.
(b+3)(b²+2b+1)

a)

b³+6b²+6b+3

b)

b³+5b²+7b+3

c)

4b³+8b²+3b

d)

3b³+6b²+3b

20.

What is the degree of the polynomial:
7x³ – 8x² + 9

a)

5

b)

2

c)

6

d)

3

21.

(5x⁴- 4x³- 2x² + x - 19) - (x⁴+ 5x³ + 8x² + x + 5)

a)

4x⁴- 9x³- 10x²- 24

b)

4x⁴- 9x³ - 10x²- 2x - 24

c)

4x⁴ - 9x³ - 10x² + 2x - 24

d)

-4x⁴ - 9x³ - 10x² - 24

22.

(4x+1)(5x−2)

a)

20x² + 3x − 2

b)

20x² − 11x + 5

c)

20x² − 18x + 2

d)

20x² − 3x − 2

23.

Simplify the following expression:
-8 (5b + 2) -7 (b - 5)

a)

-33b + 19

b)

-47b² + 21

c)

33b - 19

d)

-47b +19

24.

$\frac{\text{3}x^2-2xy}{\text{2x}}$

a)

$1.5x^{3\ }-x^2y$

b)

$1.5x\ -\ y$

c)

$1.5x\ +\ y$

d)

$1.5x\ -\ 2y$

25.

$\frac{4ab\ -\ 8b}{2b}$

a)

2a + 4

b)

2ab - 4

c)

2a - 4

d)

2a - 4b

26.

$\frac{6a^3b^2c^{4\ }-\ 8a^2b^2c}{2a^2bc}$

a)

$3abc\ -\ 4abc$

b)

$3abc^{3\ }-\ 4b$

c)

$3a^3b^2c^{4\ }-\ 4b$

d)

$3abc\ +4b$

27.

$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$

a)

$6y^2\ +3y^2\ -4y^2$

b)

$15y^{4\ }+6y^2\ -\ 9$

c)

$6y^{4\ }+3y^2-4$

d)

$6y^{3\ }-3y^2\ +4y$

28.

a)

x+7

b)

x+2

c)

X-10

d)

X-7

29.

a)

2

b)

2a

c)

3a+1

d)

x+7

30.

a)

2x² + 3x + 8 + -57/x-4

b)

2x² - 13x - 56

c)

2x² + 3x + 8 +7/x-4

d)

2x² - 3x - 16 + -89/x-4

31.

√24

a)

4√6

b)

2√6

c)

6√2

d)

2√12

32.

√28

a)

7√2

b)

7√4

c)

4√7

d)

2√7

33.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

34.

In simplest radical form,
√75 is equivalent to

a)

25√3

b)

25√3

c)

5√3

d)

3√5

35.

Simplify √18

a)

3√2

b)

9√2

c)

3√9

d)

2√3

36.

√675

a)

225√3

b)

15√5

c)

3√15

d)

15√3

37.

What is the median of this data set?

3 , 17 , 17 , 11 , 8 , 13 , 5 , 18

a)

11

b)

12

c)

13

d)

17

38.

What is the median of this data set?
20 , 1 , 7 , 19 , 11 , 19

a)

11

b)

15

c)

19

d)

20

39.

Calculate the mean of Shelly's test scores if she has scored 75, 97, and 92 so far this semester.

a)

92

b)

88

c)

132

d)

123

40.

What is the mode of the following data set?

5, 7, 7, 8, 12 , 12, 5, 6, 13, 12

a)

5

b)

7

c)

12

d)

no mode

41.

What is the range in a set of data?

a)

average

b)

biggest minus smallest

c)

the middle number

d)

the number happening the most

42.

3, 4, 5, 5, 5, 6, 7

The range of these numbers is

a)

15

b)

4

c)

2

d)

5

43.

What is the mode in this set of numbers:
7, 14, 20, 3, 7, 14, 2, 14, 7

a)

7

b)

20

c)

7 & 14

d)

none of the above

44.

Find the mean of these numbers:
4,2,5,6,3

a)

2

b)

5

c)

4

d)

6

45.

Barry Bonds has a career batting average of .298. What is the probability that he will get on base 6 times in 10 at bats?

a)

3.58%

b)

5.46%

c)

22.67%

d)

100%

46.

If you were to flip a coin 20 times, what is the probability you would get exactly 10 heads?

a)

50%

b)

17.62%

c)

.58.81%

d)

41.19%

47.

4. When rolling two dice, the probability of rolling doubles is ⅙. Suppose that a game player rolls the dice four times, hoping to roll doubles. Find the probability that the player gets doubles twice in 4 attempts.

a)

88.4%

b)

11.6%

c)

98.4%

d)

1.6%

48.

What is the probability of flipping a coin and getting heads?

a)

1/2

b)

1/3

c)

1/4

d)

Never, Tails never fails.

49.

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a quarter?

a)

5/11

b)

5/6

c)

1/3

d)

5

50.

The probability of it raining today is 30%. What is the probability that it will NOT rain?

a)

30%

b)

70%

c)

100%

d)

0%

51.

What is the probability of spinning an even number?

a)

16 2/3%

b)

33 1/3%

c)

50%

d)

75%

52.

What is the probability of pulling a red marble out of a jar of marbles that have 10 green marbles, 7 red marbles and 3 blue marbles?

a)

1/7

b)

7/20

c)

7/10

d)

3/10

53.

What is the probability that the person picked will be a boy given they speak german?

a)

.7273

b)

.4

c)

.16

d)

.22

54.

What is the probability that a student does play a sport given they do not play an instrument?

a)

.2

b)

.2222

c)

.10

d)

.5

55.

The probability that a women likes the color blue is 10%. The probability of being a women is 40%. What is the probability that the a women is chose given they liked the color blue?

a)

4

b)

.4

c)

.1

d)

.25

56.

P(Sandals|Pants):

a)

4/20

b)

6/15

c)

1/2

d)

2/7

57.

Simplify.

a)

$\frac{xy}{2}$

b)

$2xy^2$

c)

$\frac{x^2y^2}{2}$

58.

Simplify.

a)

$z-2$

b)

$\frac{1}{z-2}$

c)

$z-5$

d)

$\left(z-5\right)\left(z-2\right)$

59.

Simplify.

a)

$\frac{3}{x+5}$

b)

$\frac{3x-3}{x^2-5}$

c)

$\frac{0}{x-5}$

d)

Already Simplified

60.

Multiply.

a)

$\frac{5x\left(x+5\right)}{x^3}$

b)

$\frac{5\left(x+5\right)}{x^2}$

c)

$\frac{5x^2+25}{x^3}$

61.

Multiply.

a)

$1$

b)

$0$

c)

$No\ Solution$

d)

$Already\ Simplified$

62.

Multiply.

a)

$\frac{1}{m^2}$

b)

$m^2$

c)

$\frac{1}{m\left(m+1\right)}$

d)

$Already\ Simplified$

63.

Divide.

a)

$\frac{x^5}{y^3}$

b)

$\frac{x^3}{y}$

c)

$\frac{x}{y}$

d)

$\frac{x^2}{y^2}$

64.

Divide.

a)

$Already\ Simplified$

b)

$\frac{4\left(x-2\right)}{3\left(x+3\right)}$

c)

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

d)

$\frac{2}{3}$

65.

Divide.

a)

$\frac{x+4}{x-5}$

b)

$\frac{2}{\left(x-5\right)\left(x-3\right)}$

c)

$\frac{2\left(x+4\right)}{\left(x-5\right)\left(x-3\right)}$

d)

$Already\ Simplified$

66.

Solve.

a)

$n=5$

b)

$n=\frac{1}{8}$

c)

$n=8$

d)

$No\ Solution$

67.

Solve.

a)

$g=\frac{2}{3}$

b)

$g=1\ \frac{1}{2}$

c)

$g=2$

d)

$No\ Solution$

68.

Simplify: $\frac{8x\left(3x+5\right)\left(x+7\right)^2}{32x\left(x+7\right)\left(3x-5\right)}$

a)

$\frac{\left(3x+5\right)\left(x+7\right)}{4\left(3x-5\right)}$

b)

$\frac{x+7}{4}$

c)

$\frac{3x+5}{4\left(3x-5\right)}$

d)

$\frac{1}{4}$

69.

Identify the excluded values of: $\frac{8x}{3x-30}$

a)

$x\ne\frac{10}{3}$

b)

$x\ne0$

c)

$x\ne10$

d)

$x\ne-10$

70.

What are the restricted values of: $\frac{x+5}{x^2-x-30}$

a)

$x\ne-5$

b)

$x\ne6$

c)

$x\ne5\ and\ x\ne6$

d)

$x\ne6\ and\ x\ne-5$

71.

Solve for x. $\frac{-8}{x+6}=\frac{3}{2x}$

a)

$x=-\frac{6}{19}$

b)

$x=\frac{19}{18}$

c)

$x=-\frac{18}{13}$

d)

$x=-\frac{18}{19}$

72.

Solve for x. $\frac{8}{x^2-2x}+\frac{2}{x}=\frac{4}{x-2}$

a)

No Solution

b)

$x=0\ and\ 2$

c)

$x=0$

d)

$x=2$

73.

Solve for x. $\frac{x}{x-3}+\frac{x}{x+3}=\frac{x+15}{x^2-9}$

a)

$x=-12$

b)

$x=-12\ and\ x=3$

c)

$x=12$

d)

$x=-3$

74.

Find the inverse of f(x) = -4x - 12

a)

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

b)

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

c)

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

d)

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

75.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

76.

What is the inverse of this function?

a)

A

b)

B

c)

C

d)

D

77.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

78.

a)

A

b)

B

c)

C

d)

D

79.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

80.

Which is f ^-1(x)?

a)

f^-1(x) = 5x + 3

b)

f^-1(x) = 5x - 3

c)

f^-1(x) = 5x - 15

d)

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

81.

Which is f ^-1(x)?

a)

f^-1(x) = 3x + 5

b)

f^-1(x) = 3x - 5

c)

f^-1(x) = 3x - 15

d)

f^-1(x) = 3x + 15

82.

a)

A

b)

B

c)

C

d)

D

83.

a)

A

b)

B

c)

C

d)

D

84.

a)

A

b)

B

c)

C

d)

D

85.

a)

A

b)

B

c)

C

d)

D

86.

a)

A

b)

B

c)

C

d)

D

87.

a)

A

b)

B

c)

C

d)

D

88.

a)

A

b)

B

c)

C

d)

D

89.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

90.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

91.

Which formula is used to find the explicit equation for geometric sequences?

a)

a_n = a_n-1 + d

b)

a_n = a_n-1 * r

c)

a_n = a₁ + d(n-1)

d)

a_n = a₁ * r^n-1

92.

Find the general rule for: 64, -32, 16, -8, …

a)

64(1/2)^n-1

b)

(-32)^n-1

c)

64(-1/2)^n-1

d)

(32)^n-1

93.

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

a)

a_n = a_n-1 x 3

b)

a_n = 5(3)^n-1

c)

a_n = 3(5)^n-1

d)

a_n = 5 + (n-1)3

94.

Find the 11^th term for: 64, -32, 16, -8, …

a)

-.0625

b)

.0625

c)

-.03125

d)

.03125

95.

You have $10 in you bank account. It doubles every month. How much money will you have after 5 months?

a)

$50

b)

$35

c)

$320

d)

$250

96.

Which sequence is represented by the equation 2(7)^n-1 ?

a)

7, 14, 28, 56...

b)

2, 14, 98, 686...

c)

2, 9, 16, 23...

d)

7,9,11,13...

Algebra 2 Exam Review

Total questions: 96

Worksheet time: 24hrs 0mins

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