Free Printable Semester 2 Final Review- Algebra

1.

Factor Completely: x²-17x+72

a)

(x-9)(x+8)

b)

(x-9)(x-8)

c)

x(x-3)

d)

(x+9)(x+8)

2.

Factor Completely: x²-7x-8

a)

(x+1)(x-8)

b)

(x+1)(x+8)

c)

5(x+4)(x+5)

d)

(x-1)(x+8)

3.

Factor Completely: 2k²-14k-60

a)

2(k-10)(k-3)

b)

Not Factorable

c)

(k-5)(k+9)

d)

2(k-10)(k+3)

4.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

5.

Factor Completely: x²+13x+40

a)

(x+5)(x+8)

b)

5x(x+3)

c)

3x(x+6)

d)

x(x-4)

6.

Factor Completely: 3x²+15x-72

a)

x(x+5)

b)

3(x+8)(x-3)

c)

(3x+24)(x-3)

d)

3(x-8)(x+3)

7.

Factor Completely: 16q³-48q²+36q

a)

4q(2q-3)²

b)

4q(2q+3)²

c)

4(4q³-12q²+9q)

d)

4q(2q-3)(2q+3)

8.

Factor Completely: 4k²+24k+36

a)

(2k+6)²

b)

(2k-6)²

c)

(2k-6)(2k+6)

d)

4(k+3)²

9.

Factor Completely: 5x²-11x+6

a)

(5x+6)(x-1)

b)

(5x-6)(x-1)

c)

(2x-7)(x-3)

d)

(5x-6)(x+1)

10.

Factor Completely: 14p²-24p-8

a)

(5p+3)(p-4)

b)

(3p-2)(p+10)

c)

2(7p-2)(p+2)

d)

2(7p+2)(p-2)

11.

Does this graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

12.

Does this question have a maximum or a minimum?

a)

Maximum

b)

Minimum

13.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

14.

Where is the axis of symmetry for this parabola?

a)

x = −1

b)

x = 0

c)

y = 3

d)

x = −3

15.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

16.

What is the y-intercept of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

17.

What are the zeros of the parabola?

a)

1, 5

b)

3, -5

c)

3, 0

d)

-6, 1

18.

What is the vertex of y= x²- 8x + 14 ?

a)

(2, 4)

b)

(-4, -2)

c)

(4, -2)

d)

(-2, 4)

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

a)

A

b)

B

c)

C

d)

D

22.

a)

A

b)

B

c)

C

d)

D

23.

What is the equation that best represents the graph?

a)

y=2^y

b)

y=2^x

c)

y=2^-x

d)

y=x²

24.

Which of the following best represents the graph?

a)

y=2^x

b)

x=2^y

c)

y=x²

d)

y=2^-x

25.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: −∞<x<∞
Range: y>0

b)

Domain: −∞<x<∞
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

26.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

a)

Horizontal shift left one unit!

b)

Horizontal shift right one unit!

c)

Vertical shift up one unit!

d)

Vertical shift down one unit!

27.

Write the function for the following table:

a)

f(x)= 1(2)^x

b)

f(x)= 2(1)^x

c)

f(x) = 2x+1

d)

f(x)= x+2

28.

Write the function for the following table:

a)

f(x) = 1(3)^x

b)

f(x) = 3(3)^x

c)

f(x) = 3x+3

d)

f(x)= 6x+1

29.

Write the function for the following table:

a)

f(x) = 5x + .08

b)

f(x)= 5x + 2

c)

f(x) = .08(5)^x

d)

f(x)= 2(5)^x

30.

The temperature in Springfield on this date in the last ten years were: 68, 68, 69, 70, 72, 70, 68, 75, 55, 67. What is the average temperature on this date over the last ten years? (Round to nearest whole number)

a)

60

b)

61

c)

68

d)

69

31.

Jessica has five grades from assessments and quizzes. They are all weighted equally. If her grades are 50, 70, 88, 70, and 88, what is her current average grade?

a)

71

b)

72

c)

73

d)

74

32.

The mean of six numbers is 5.

Five of the numbers are 6, 6, 5, 3 and 1.

Work out the sixth number.

a)

4

b)

9

c)

4.2

d)

7

33.

Simplify the radical expression:
$\sqrt{2x^2y^3}$

a)

$2y\sqrt{xy}$

b)

$2x\sqrt{y^2}$

c)

$y\sqrt{2xy}$

d)

$xy\sqrt{2y}$

34.

Simplify the radical expression:
$\sqrt{128a^3b^4}$

a)

$8ab^2\sqrt{2a}$

b)

$2a\sqrt{8ab^2}$

c)

$2ab\sqrt{64ab}$

d)

$64ab^2\sqrt{2a}$

35.

Simplify the radical:
$\sqrt{98}$

a)

$2\sqrt{7}$

b)

$7\sqrt{2}$

c)

$14\sqrt{2}$

d)

$49\sqrt{2}$

36.

Simplify the radical:
$\sqrt{180}$

a)

$5\sqrt{6}$

b)

$5\sqrt{5}$

c)

$13\sqrt{5}$

d)

$6\sqrt{5}$

37.

Simplify the radical expression:
$\sqrt{27m^7p^{4\ }}$

a)

$3m\sqrt{3m^3p^2}$

b)

$3m^3p^2\sqrt{3m}$

c)

$9mp\sqrt{3m}$

d)

$9m^3p^2\sqrt{3m}$

38.

Simplify the radical expression:
$\sqrt{x^3y^5z^2}$

a)

$xy^2z$

b)

$x^2y^4z^2\sqrt{xy}$

c)

$xy^2z\sqrt{xy}$

d)

$xyz\sqrt{xy}$

39.

Simplify the radical expression:
$\sqrt{151r^2s^3}$

a)

$rs\sqrt{151s}$

b)

$151rs\sqrt{s}$

c)

$10rs\sqrt{15s}$

d)

$r^2s^2\sqrt{151s}$

40.

Simplify the radical expression:
$2\sqrt{48}$

a)

$4\sqrt{3}$

b)

$8\sqrt{3}$

c)

$2\sqrt{3}$

d)

$3\sqrt{8}$

41.

Simplify the radical expression:
$\sqrt{92a^2b^3}$

a)

$23ab\sqrt{2b}$

b)

$2ab\sqrt{23b}$

c)

$4ab\sqrt{23b}$

d)

$4a^2b^2\sqrt{23b}$

42.

√5 + √20

a)

5

b)

25

c)

3√5

d)

2√3

43.

Simplify:

a)

2√3√14

b)

4√42

c)

2√42

d)

4√3√14

44.

√98 + 5√2

a)

8√3

b)

12√2

c)

7√2

d)

7√3

45.

√300 + √75

a)

15√3

b)

√375

c)

20√5

d)

16√5

46.

√300 + √75

a)

15√3

b)

√375

c)

20√5

d)

16√5

47.

a)

0

b)

√5

c)

1

d)

-2√15

48.

Simplfiy

a)

5√2

b)

0

c)

2√2

d)

-3√2

49.

Simplify

a)

√5

b)

-3√6

c)

√6

d)

6

50.

Simplify

a)

9

b)

5√2 + 2

c)

10√2

d)

2√2 + 3√30

51.

a)

A

b)

B

c)

C

d)

D

52.

a)

3√3x

b)

3√x

c)

2√3x

d)

2√x

53.

1)

a)

A

b)

B

c)

C

d)

D

54.

Simplify: √(28xy²)

a)

2y√(7x)

b)

√(28xy²)

c)

y√(28x)

d)

7x√(2y)

55.

Simplify:

a)

2

b)

4√3

c)

2√3

d)

4

56.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

57.

Rationalize the denominator:
$\frac{\sqrt{5}}{2\sqrt{3}}$

a)

$\frac{\sqrt{15}}{6}$

b)

$\frac{\sqrt{15}}{18}$

c)

$\frac{5\sqrt{3}}{6}$

d)

$\frac{5\sqrt{3}}{18}$

58.

Rationalize the denominator:
$\frac{2\sqrt{8}}{\sqrt{12}}$

a)

$\frac{\sqrt{96}}{6}$

b)

$\frac{2\sqrt{6}}{3}$

c)

$\frac{2\sqrt{96}}{12}$

d)

$\frac{4\sqrt{2}}{2\sqrt{3}}$

59.

4r^-3 * 2r²

a)

8r

b)

4
--
r⁶

c)

16x⁶

d)

8
--
r

60.

(2/5)^-2

a)

25/4

b)

4/25

c)

25

d)

4

61.

(x²)⁰

a)

1

b)

2

c)

x²⁰

d)

x²

62.

(3x⁴y³z⁵)³

a)

12x¹²y⁹z¹⁵

b)

9x¹²y⁹z¹⁵

c)

3x¹²y⁹z¹⁵

d)

27x¹²y⁹z¹⁵

63.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

64.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

65.

What is the value of x?
3^{16 =}(3⁸)(3^x)

a)

2

b)

8

c)

4

d)

1

66.

a³b(ab)²=

a)

a⁵b³

b)

a⁶b⁴

c)

a²b²

d)

a⁹b⁶

67.

Simplify the expression.
1/w^-5

a)

1/w⁵

b)

w⁵

c)

w^-5

d)

1/w^-5

68.

Simplify
(x^-²)¹^/²

a)

1∕ (x³^/²)

b)

1∕ (x²)

c)

1∕ x

d)

x

69.

Simplify
(4x³-3x² + 6x - 4) - (-2x³ + x² -20)

a)

4x² - 6x³- 2x + 6

b)

3x + 5x²+ 1

c)

6x³ -4x² + 6x +16

d)

3x + 2

70.

Is the following table a quadartic function?

a)

YES

b)

NO

71.

Does this table represent a quadratic function?

a)

NAH.

b)

YAS.

72.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

73.

Find the length of the missing side.

a)

20 in.

b)

68 in.

c)

16 in.

d)

80 in.

74.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

75.

Does the set of numbers represent a Pythagorean Triple.
15, 20, 25

a)

Yes

b)

No

76.

Find h

a)

35.60

b)

35.00

c)

35.71

d)

61.03

77.

The Pythagorean Theorem ONLY works on which triangle?

a)

obtuse

b)

scalene

c)

isosceles

d)

right

78.

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

a)

25 feet

b)

26 feet

c)

27 feet

d)

28 feet

79.

What is the median of this data set?
7.3, 2.9, 1.5, 0.6, 3.8

a)

2.9

b)

3

c)

3.5

d)

4.3

80.

When finding the median, what do you do if there are two middle numbers?

a)

Add them together and divide by 2

b)

Write them both as the answer

c)

Give up

d)

Pick one

81.

In a music academy, 24 students learn to play music in the Guitar, 25 in the Piano,16 in the Saxophone, 22 in drums, 32 in the Trumpet, 15 in the Violin and 32 in the Woodwind. Find the median.

a)

24

b)

16

c)

25

d)

24.5

82.

The science scores of nine students in a class are 72, 94, 56, 71, 88, 95, 59, 98 and 60. What is the median of the scores?

a)

72

b)

73

c)

56

d)

75.5

83.

What is the MEDIAN of this data

a)

95

b)

90

c)

100

d)

40

84.

Rewrite using a positive exponent.
7^-10

a)

¹/_7¹⁰

b)

7¹⁰

c)

¹/_7^-10

d)

-70

85.

Rewrite using a positive exponent.
(-5)^-4

a)

(-5)⁴

b)

¹/_(-5)^-4

c)

¹/_(-5)⁴

d)

-625

86.

Write with positive exponents:

a)

a^-2

b)

a²

c)

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

d)

2a

87.

Evaluate

a)

1/10

b)

-1/32

c)

1/32

d)

32

88.

Evaluate

a)

-1/14

b)

1/14

c)

-1/49

d)

1/49

89.

Write using only positive Exponents. SIMPLIFY

\frac{1}{\left(2\right)^{-2}}

a)

-4

b)

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

c)

$2^2$

d)

4

90.

Evaluate when x=3 and y=1

x^{-2}y

a)

9

b)

1/6

c)

1/9

d)

6

91.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

92.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

93.

Which of the following is equivalent to the expression $\frac{1}{2x^7}$ ?

a)

$\left(2x\right)^{-7}$

b)

$\frac{1}{2}x^7$

c)

$\frac{1}{2}x^{-7}$

d)

$2x^{-7}$

94.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

95.

Choose the correct answer.

a)

A

b)

B

c)

C

d)

D

96.

Solve by taking square roots.

2x² - 8 =100

a)

x = ±√54

b)

x = ±3√6

c)

x = ± 9√6

d)

x = ±2√27

97.

Solve the equation by factoring.

a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

98.

Solve the equation by factoring.
x² - 35x - 36

a)

-1, 36

b)

1, -36

c)

-6, 6

d)

-6

99.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

100.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

101.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

102.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

103.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

104.

An object is launched directly upward at 64 feet per second (ft/s) from an elevated platform. The height of the object represented by the equation

h(t) = –16t² + 64t + 80.

What is the height of the platform where the object was launched?

a)

64 ft.

b)

80 ft.

c)

128 ft.

d)

144 ft.

105.

An object is launched directly upward at 64 feet per second (ft/s) from an elevated platform. The height of the object represented by the equation

h(t) = –16t² + 64t + 80.

After 1 second, how high is the object?

a)

64 ft.

b)

80 ft.

c)

128 ft.

d)

144 ft.

106.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^.08

b)

^1.08

c)

.92

d)

8

107.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

108.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

109.

7.82 x 10^-⁶ is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

a)

Large

b)

Small

c)

Basic

110.

Change from standard form to scientific notation: 12,000,000

a)

12.0 x 10⁷

b)

0.12 x 10⁷

c)

1.2 x 10⁶

d)

1.2 x 10⁷

111.

Change from standard form to scientific notation: 0.000398

a)

39.8 x 10^-5

b)

3.98 x 10^-5

c)

3.98 x 10^-4

d)

39.8 x 10^-6

112.

125,678,000: Change to scientific notation

a)

1.25678 x 10¹²

b)

.125678 x 10^-9

c)

12.5678 x 10⁸

d)

1.25678 x 10⁸

113.

Try to change the number back to standard form: 3.97 x 10^-2

a)

0.000397

b)

0.0397

c)

0.0000397

d)

0.397

114.

a)

A. Mean

b)

B. Median

c)

C. Mode

d)

D. Range

115.

a)

A. 8

b)

B. 12

c)

C. 15

d)

D. 19

116.

a)

A. 6

b)

B. 12

c)

C. 13

d)

D. 19

117.

a)

A. 6 and 8

b)

B. 8 and 12

c)

C. 12 and 15

d)

D. 15 and 19

118.

The equation y = x² + 3x - 18 is graphed. Based on this graph, what are the roots (x-intercepts) of the equation x² + 3x - 18 = 0?

a)

-3 and 6

b)

0 and -18

c)

3 and -6

d)

3 and -18

119.

The equation y = x² is graphed. Based on this graph, what are the roots of the equation x² = 0?

a)

0

b)

-1 and 1

c)

2 and 0

d)

y

120.

How many solutions (roots) does this graph have?

a)

one

b)

two

c)

no solutions

d)

cannot be determined

Semester 2 Final Review- Algebra

Total questions: 120

Worksheet time: 5hrs 57mins

Similar Resources on Wayground