Free Printable Algebra revision

1.

a)

x²

b)

x⁶

c)

x⁵

d)

x^-6

2.

a)

y⁴

b)

y⁵

c)

y⁶

d)

6^y

3.

a)

z¹

b)

1

c)

0

d)

z^-1

4.

a)

a⁷

b)

a¹

c)

1/a¹²

d)

a¹²

5.

a)

t²⁴

b)

t¹²

c)

t¹⁸

d)

t^-12

6.

a)

12

b)

8

c)

4

d)

2

7.

a)

x^-4

b)

1/x²

c)

x¹⁰

d)

x⁴

8.

a)

x⁴

b)

4x³

c)

3x³

d)

4x²

9.

a)

3a¹⁵

b)

9a¹⁵

c)

9a⁸

d)

27a¹⁵

10.

a)

3y⁶

b)

6y³

c)

4y⁶

d)

3y⁴

11.

a)

1/4

b)

2/3

c)

2

d)

0.5

12.

a)

1/7

b)

7

c)

24.5

d)

-7

13.

a)

3

b)

9

c)

12

d)

6

14.

a)

1/16

b)

1/9

c)

1/3

d)

1/27

15.

a)

1

b)

1/x

c)

x

d)

x^-11

16.

Simplify the algebraic fraction.

a)

2pq

b)

2/pq

c)

pq/2

d)

p/2q

17.

Simplify the algebraic fraction.

a)

-3/b

b)

-b/3

c)

3b

d)

-3b

18.

Simplify the following.

$\frac{15}{5\left(3-a\right)}$

a)

$\frac{3}{3-a\ }$

b)

$3-a$

c)

$\frac{3-a}{3}$

d)

$\frac{3}{a-3}$

19.

Simplify the following.

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

a)

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

b)

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

c)

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

d)

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

20.

a)

10a/10b

b)

10a/5b

c)

2a/b

d)

a/b

21.

a)

a/2

b)

3a/6

c)

8a/6

d)

7a/6

22.

a)

8m²/8n²

b)

13m/4n

c)

13m²/4n²

d)

8m/8n

23.

a)

4/p

b)

5/p

c)

14/p²

d)

4/p²

24.

a)

6am/10a

b)

9

c)

9ma/3a

d)

6m

25.

a)

2by/c

b)

4xb/ac

c)

2xb/ac

d)

ac/dc

26.

a)

a²/6

b)

2a/3a

c)

3a/2a

d)

3/2

27.

a)

3c

b)

9b/4a

c)

4a

d)

2c/b

28.

Simplify the algebraic fraction.

a)

-m

b)

-1/m

c)

m/n

d)

1/mn

29.

Simplify the following.

$\frac{6t}{5}\div\frac{3}{4t}$

a)

$\frac{8t^2}{5}$

b)

$\frac{18t}{20t}$

c)

$\frac{9t}{10t}$

d)

$\frac{10t}{8}$

30.

Simplify the following.

$\frac{5q}{7}\div\frac{9q}{8}$

a)

$\frac{40}{63}$

b)

$\frac{14q}{15}$

c)

$\frac{103q}{56}$

d)

$\frac{45q}{56}$

31.

Simplify the following.

$\frac{5}{9e}\div\frac{8}{3e}$

a)

$\frac{87e}{27e^2}$

b)

$\frac{13}{12e}$

c)

$\frac{40}{27e^2}$

d)

$\frac{5}{24}$

32.

a)

2

b)

4

c)

6

d)

8

33.

a)

1

b)

2

c)

3

d)

4

34.

a)

5

b)

6

c)

7

d)

8

35.

a)

2

b)

3

c)

4

d)

5

36.

a)

32

b)

30

c)

29

d)

20

37.

a)

24

b)

25

c)

26

d)

28

38.

a)

35

b)

40

c)

42

d)

45

39.

a)

1

b)

2

c)

3

d)

4

40.

a)

5

b)

-5

c)

7

d)

-7

41.

a)

2

b)

-1

c)

-2

d)

1

42.

a)

2

b)

1

c)

-1

d)

-2

43.

a)

1

b)

2

c)

3

d)

4

44.

a)

7

b)

8

c)

9

d)

10

45.

a)

6

b)

8

c)

2

d)

4

46.

a)

7

b)

8

c)

9

d)

10

47.

a)

7

b)

6

c)

5

d)

8

48.

a)

4

b)

5

c)

6

d)

10

49.

a)

-5

b)

-2

c)

2

d)

5

50.

a)

1

b)

2

c)

3

d)

4

51.

a)

3

b)

5

c)

7

d)

9

52.

Solve for the values of x:
(x - 3)(x + 6) = 0

a)

{ -3, -6 }

b)

{ 3, -6 }

c)

{ -3, -6 }

d)

{ 3, 6 }

53.

Solve using Zero-Product Property.
(x+4)(x-3) = 0

a)

x = 4 and x = -3

b)

x = 2 and x = 1

c)

x = -4 and x = 3

d)

x = -2 and x = 1

54.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

55.

Solve
x² + 9x + 20 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

56.

Solve
x² + 7x + 12 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

57.

Solve
x² + 13x + 12 = 0

a)

x = -1, x = -12

b)

x = -1, x = -24

c)

x = -2, x = -6

d)

x = -2, x = -12

58.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

59.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

60.

x² + 15x + 44 = 0

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

61.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

62.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

63.

Solve for a by factoring.

a² + 2a - 24 = 0

a)

a = -6 and a = 4

b)

a = 6 and a = -4

c)

a = 12 and a = -2

d)

a = 8 and a = -3

64.

Solve by factoring:
x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

65.

Solve by factoring:
x² - 6x + 5 = 0

a)

-6, -1

b)

-5, -1

c)

1, 6

d)

5, 1

66.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

67.

Solve by factoring.
z² - 6z - 27 = 0

a)

z = 3 or z = 9

b)

z = 3 or z = -9

c)

z = -3 or z = 9

d)

z = -3 or z = -9

68.

Solve by factoring.
z² - 18z + 81 = 0

a)

z = 9

b)

z = -9

c)

z = 9 or z = -9

69.

Solve:

k² - 2k - 24 = 0

a)

k = -4, 6

b)

k = -4, -6

c)

k = -6, 1

d)

k = 4, -6

70.

Determine the values of

a, b, and c:

x² – 2x – 3 = 0

a)

a = x², b = -2, c = -3

b)

a = 1, b = -2, c = -3

c)

a = 1, b = 2, c = 3

d)

a =1, b = -2, c = 3

71.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

72.

What are the roots of the quadratic equation below?

2x^2+7x\ +6\ =\ 0

a)

4, -3

b)

-3, 2

c)

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

d)

-2, $-\frac{3}{2}$

e)

-6, $-\frac{3}{4}$

73.

Solve using the Quadratic Formula:

2x²− x − 3 = 0

a)

$x=-\frac{3}{2},\ 1$

b)

$x=\frac{3}{2},\ -1$

c)

$x=-\frac{3}{2},\ -1$

d)

$x=\frac{3}{2},\ 1$

74.

What are the roots of the quadratic equation below?

4x^2-8x\ +3=\ 0

a)

$\frac{3}{4},\ \ \frac{1}{4}$

b)

-\frac{3}{4},\ -\frac{1}{4}

c)

$-\frac{3}{2},\ \frac{1}{2}$

d)

$\frac{3}{2},\ \frac{1}{2}$

e)

No solution

75.

Solve the following quadratic equation using Quadratic Formula

2x² - 3x - 5 = 0

a)

x = -1

x = 5/2

b)

x = 5

x = 2

c)

x = -1/2

x = 5

d)

x = 1/2

x = -5/2

e)

No solution

76.

Solve using the Quadratic Formula:

x² + 5x + 6 = 0

a)

x = 2 and x = 3

b)

x = 6 and x = -5

c)

x = -2 and x = -3

d)

x = -6, and -5

77.

Solve using the Quadratic Formula:

4x²− 4x + 1= 0

a)

$x=-\frac{1}{2},\ \ \frac{1}{2}$

b)

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

c)

$x=-\frac{1}{2}$

d)

$x=\frac{1}{4},\ \ -\frac{1}{4}$

e)

$x=\frac{1}{4}$

78.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

79.

Solve using the Quadratic Formula:

2x^2-3x-4=0

a)

$x=\frac{3+\sqrt{41}}{4}\ or\ \ x=\frac{3-\sqrt{41}}{4}$

b)

$x=\frac{-3+\sqrt{41}}{4}\ or\ \ x=\frac{-3-\sqrt{41}}{4}$

c)

$x=\frac{3+\sqrt{23}}{4}\ or\ \ x=\frac{3-\sqrt{23}}{4}$

d)

$x=\frac{-3+\sqrt{23}}{4}\ or\ \ x=\frac{-3-\sqrt{23}}{4}$

e)

$x=\frac{3+\sqrt{-23}}{4}\ or\ \ x=\frac{3-\sqrt{-23}}{4}$

80.

-13t > 26

a)

t > -2

b)

t > 2

c)

t < 2

d)

t < -2

81.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

82.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

83.

X + 6 > 10

a)

X > 16

b)

X > -4

c)

X < -4

d)

X > 4

84.

-7x + 15 ≥ -20

a)

x ≥ -5

b)

x ≤ -5

c)

x ≥ 5

d)

x ≤ 5

85.

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

a)

x<24

b)

x>-24

c)

x<12

d)

x>18

86.

Which inequality symbol has a graph with an open (empty) circle?

a)

<

b)

≤

87.

Does the sign need to flip when solving?
-2x ≥ 22

a)

YES

b)

NO

88.

a)

A)

b)

B)

c)

C)

d)

D)

89.

a)

A)

b)

B)

c)

C)

d)

D)

90.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

91.

Solve and graph the inequality.
77 ≤ 5 + 8n

a)

A

b)

B

c)

C

d)

D

92.

Translate the following phrase: Jessica must be at least 48 inches to ride the roller coaster.

a)

j > 48

b)

j < 48

c)

j ≤ 48

d)

j ≥ 48

93.

Translate the following phrase: Tom can spend no more than 20 dollars on his mom's birthday present.

a)

t > 20

b)

t < 20

c)

t ≤ 20

d)

t ≥ 20

94.

Translate the following phrase: You and your friends ate more than 8 slices of pizza at the party.

a)

x > 8

b)

x < 8

c)

x ≤ 8

d)

x ≥ 8

95.

Translate the following phrase: Bob spends less than 5 hours on homework each night.

a)

b > 5

b)

b < 5

c)

b ≤ 5

d)

b ≥ 5

96.

Translate the following phrase: Edith must read for a minimum of 20 minutes every night.

a)

e > 20

b)

e < 20

c)

e ≥ 20

d)

e ≤ 20

97.

Translate the following phrase: All students must get at least a 65% for the year in order to pass math.

a)

s = 65

b)

s > 65

c)

s ≥ 65

d)

s ≤ 65

98.

Translate the following phrase: Grace has $45 at most in her purse on a daily basis

a)

g < 45

b)

g > 45

c)

g ≤ 45

d)

g ≥ 45

99.

You need to save a minimum of $1200 to purchase your new laptop. If you already have saved $400 and make 11 per hour, h, at your job, which inequality could be use to solve to determine how many hours you need to work to save enough money.

a)

11h + 1200 ≥ 400

b)

11h + 400 < 1200

c)

11h + 400 > 1200

d)

11h + 400 < 1200

100.

4x + 8y = 20
-4x + 2y = -30
Which variable will be eliminated?

a)

The x

b)

The y

c)

The z

d)

The unknown

101.

Solve by elimination:

4x+9y=28

-4x-2y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

102.

Solve by elimination:

3x+7y=23

-3x-4y=-17

a)

No solution

b)

ARN

c)

(-3,3)

d)

(3,2)

103.

Solve by elimination:
4x+4y=4

3x+4y=10

a)

(7,-6)

b)

(-6,7)

c)

(6,7)

d)

(7,6)

104.

Solve by elimination:
-x+2y=17

2x+2y=-10

a)

ARN

b)

(-9,4)

c)

(-9,-4)

d)

(9,-4)

105.

Solve by elimination:

7x-9y=29

7x+2y=-15

a)

(-4,-1)

b)

(-1,-4)

c)

(-1,4)

d)

(-1,6)

106.

Solve by elimination:

7x + y = -9

-3x - y = 5

a)

No solution

b)

(1,8)

c)

(-2,-3)

d)

(-1,-2)

107.

Solve by elimination:
x + 9y = 8
-6x - 9y = -3

a)

(1,-1)

b)

(1,1)

c)

(-1,1)

d)

(-1,-1)

108.

What is the value of the y-coordinate of the solution to the system of equations
x-2y=1
x+4y=7

a)

1

b)

-1

c)

3

d)

4

109.

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

a)

d + c = 174

4d + 2c = 50

b)

d + c = 50

4d + 2c = 174

c)

d + c = 50

2d + 4c = 174

d)

d + c = 174

2d + 4c = 50

110.

Which variable will be eliminated from the system:

2x + 3y = 5

x + 3y = 7

a)

y

b)

x

111.

12 subtracted from a number gives us 8. Find the number

a)

20

b)

4

c)

12

d)

8

112.

The perimeter of the parallelogram is 24 cm. Work out the value of x.

a)

7

b)

5

c)

3

d)

1

113.

The length (l) of a rectangle is three times the width (w). Find an equation for the perimeter of the rectangle.

a)

P = 2(3w) + 2(w)

b)

p = 2l + 2w

c)

P= 3w + 3w + w + 3w

d)

P = lw

114.

The perimeter of the rectangle is 52 cm. Write an equation in terms of x.

a)

(x - 11 ) + (x + 7) = 52

b)

2(x-11) + 2(x + 7) = 52

c)

(x-11)(x+7) = 52

d)

x-11+x+7=52

115.

The perimeter of the triangle is 29 cm. What is x?

a)

x= 5

b)

x=6

c)

x=7

d)

x=8

Algebra revision

Total questions: 115

Worksheet time: 8hrs 23mins

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