Free Printable Algebra Prerequisite Skills

1.

Simplify:

$\sqrt{24}$

2.

Simplify: $\sqrt[]{28}$

3.

Simplify: $\sqrt[]{48}$

4.

Simplify: $\sqrt{56}$

a)

$2\sqrt{14}$

b)

$4\sqrt{14}$

c)

$2\sqrt{28}$

d)

$2\sqrt{9}$

5.

Simplify: $\sqrt{72}$

a)

$2\sqrt{6}$

b)

$4\sqrt{6}$

c)

$6\sqrt{2}$

d)

$3\sqrt{4}$

6.

Simplify: $\sqrt[]{80}$

7.

Simplify:

\sqrt{98}

a)

$7\sqrt{2}$

b)

$2\sqrt{7}$

c)

$49\sqrt{2}$

d)

$2\sqrt{49}$

8.

Simplify: $\sqrt[]{192}$

a)

$8\ \sqrt[]{5}$

b)

$3\ \sqrt[]{3}$

c)

$8\ \sqrt[]{3}$

d)

$4\ \sqrt[]{2}$

9.

Simplify:

10\sqrt{96}

a)

$40\sqrt{6}$

b)

$160\sqrt{6}$

c)

$96\sqrt{10}$

d)

$60\sqrt{16}$

10.

Simplify:

3\sqrt{125}

a)

$75\sqrt{3}$

b)

$8\sqrt{5}$

c)

$15\sqrt{5}$

d)

$15\sqrt{25}$

11.

Multiply: $\sqrt[]{10}\cdot\sqrt[]{10}$

a)

10

b)

$4\ \sqrt[]{30}$

c)

100

d)

$2\ \sqrt[]{5}$

12.

Multiply: $\sqrt[]{15}\cdot4\ \sqrt[]{3}$

a)

$12\ \sqrt[]{5}$

b)

$3\ \sqrt[]{5}$

c)

45

d)

$3\ \sqrt[]{2}$

13.

Multiply:

3\sqrt{8}\times4\sqrt{10}

a)

$12\sqrt{80}$

b)

$7\sqrt{80}$

c)

$24\sqrt{20}$

d)

$48\sqrt{5}$

14.

Multiply

$\left(2\sqrt{12}\right)\left(3\sqrt{7}\right)$ *Remember to simplify*

15.

Multiply and simplify: $3\sqrt{7}\cdot\sqrt{14}$

a)

$3\sqrt{98}$

b)

$10\sqrt{2}$

c)

$21\sqrt{2}$

d)

$2\sqrt{21}$

16.

$\left(2\ \sqrt[]{6}\right)^2$

17.

Simplify:

2\sqrt{24}+5\sqrt{54}

a)

$7\sqrt{78}$

b)

$19\sqrt{6}$

c)

$7\sqrt{6}$

18.

Add

$\sqrt{2}+3\sqrt{2}$

19.

Add

\sqrt{27}+2\sqrt{12}

a)

$3\sqrt{3}+4\sqrt{6}$

b)

$7\sqrt{3}$

c)

$12\sqrt{3}$

d)

$7\sqrt{6}$

20.

Add

21.

Add

22.

Simplify: $\frac{2}{\sqrt[]{2}}$

23.

Simplify: $\frac{\sqrt[]{2}}{4\ \sqrt[]{3}}$

a)

$\frac{\sqrt[]{15}}{9}$

b)

$\frac{2\sqrt[]{3}}{3}$

c)

$\frac{\sqrt[]{6}}{12}$

d)

$2\sqrt[]{6}$

24.

a)

A

b)

B

c)

C

d)

D

25.

a)

A

b)

B

c)

C

d)

D

26.

a)

A

b)

B

c)

C

d)

D

27.

Which of the following in NOT a perfect square?

a)

49

b)

81

c)

111

d)

144

28.

Which of the following is a perfect square?

a)

12

b)

90

c)

40

d)

64

29.

Simplify: $4\ \sqrt[]{75}$

30.

Simplify: $2\ \sqrt[]{24}$

31.

Simplify: 5√80

a)

20√5

b)

-4√5

c)

5√20

d)

4√5

32.

Simplify:
3√16

a)

12

b)

48

c)

√12

d)

3√4

33.

a)

A

b)

B

c)

C

d)

D

34.

a)

A

b)

B

c)

C

d)

D

35.

Multiply and simplify: $\sqrt{3}\cdot\sqrt{15}$

a)

$\sqrt{45}$

b)

$3\sqrt{5}$

c)

$5\sqrt{3}$

d)

$15\sqrt{3}$

36.

Multiply and simplify: $2\sqrt{12}\cdot\sqrt{5}$

a)

$2\sqrt{60}$

b)

$2\sqrt{15}$

c)

$4\sqrt{15}$

d)

$15\sqrt{4}$

37.

Multiply and simplify: $-2\sqrt{3}\cdot4\sqrt{18}$

a)

$24\sqrt{6}$

b)

$-24\sqrt{6}$

c)

$24\sqrt{3}$

d)

$-24\sqrt{3}$

38.

Simplify.

$\frac{3\sqrt{12}}{\sqrt{25}}$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$\frac{5}{2}$

39.

Simplify $\frac{\sqrt{200}}{\sqrt{2}}$

40.

What is a solution to a system of linear equations?

a)

The point where both lines intersect

b)

The point where the y-axis and x-axis meet

c)

An ordered pair that both lines share

d)

A salt dissolved in water

41.

What would the solution be to this system of linear equations?

a)

(1, -3)

b)

(-3, 1)

c)

(0, -3)

d)

(1, 0)

42.

What would the solution be to this system of linear equations?

a)

(0,0)

b)

(2,2)

c)

(6,0)

d)

(0,4)

43.

When will we get "no solutions" from a system of equations?

a)

The two lines cross once

b)

The two lines are the same and overlap

c)

The two lines are parallel and never touch

d)

The two lines cross at 2 points

44.

Which of the following graphs would fit the system of equations?

$y=2x-4$

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

a)

b)

c)

45.

Match the following graphs to the systems of equations

a)

1.

$y=\frac{2}{3}x+1$

$y=\frac{2}{3}x-2$

b)

2.

$y=-x+7$ $y=2x+1$

c)

3.

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

46.

What is the solution to the system?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

47.

Give the solution to the system.

a)

(3,1)

b)

(1,3)

c)

(-1,3)

d)

(1, -3)

48.

Solve the system of equations.
y = 4x+1
3x + 2y = 13

a)

(1, 5)

b)

(5, 1)

c)

(0.25, 2)

d)

∅

49.

Solve the following system
x + 9y = 8
-6x - 9y = -3

a)

(1,-1)

b)

(1,1)

c)

(-1,1)

d)

(-1,-1)

50.

Solve the system of equations:

5x - 4y = =-16
x+ 2y = -6

a)

(-4,-1)

b)

(5,-1)

c)

(-5,-1)

d)

(4,1)

51.

Solve the system of equations:

2x - 3y = 6
7x - 3y = -9

a)

(-3,-4)

b)

(3,4)

c)

(-4,-3)

d)

(4,3)

52.

Solve the system of equations:

x = - 3
2x + 3y = 6

a)

(4,3)

b)

(-4,3)

c)

(-3,4)

d)

(3,-4)

53.

Solve the system of equations:

7x+4y =12
x + 2y = -4

a)

(-4,4)

b)

(4,4)

c)

(4,-4)

d)

(-4,-4)

54.

Solve the system of equations:

x + 2y = -4
x - 2y = 8

a)

(2,5)

b)

(2,-3)

c)

(2,-2)

d)

(-3,2)

55.

Solve the system of equations:

7x - 2y = 6
x - 2y = -6

a)

(2,4)

b)

(3,-2)

c)

(1,2)

d)

(-2,-4)

56.

Solve the system of equations:

x-4y = 16
5x + 4y = 8

a)

(4,-3)

b)

(-3,4)

c)

(4,3)

d)

(3,-4)

57.

Solve the system of equations:

5x - 2y = 6
x - 2y = -2

a)

(2,2)

b)

(2,1)

c)

(1,2)

d)

(-2,-2)

58.

Solve the system of equations:

x + y = 3
3x - y = 1

a)

(2,1)

b)

(-1,2)

c)

(1,2)

d)

(-2,-1)

59.

Solve the system of equations:

x -2y = -2
3x - 2y = 6

a)

(4,3)

b)

(-3,4)

c)

(-2,-3)

d)

(-3,-4)

60.

Solve the system of equations:

3x - 2y = -8
5x + 2y = -8

a)

(1,-4)

b)

(-1,-4)

c)

(-4,1)

d)

(-2,1)

61.

Solve the system of equations:

x - 4y = -4
x + 2y = 8

a)

(2,2)

b)

(4,2)

c)

(2,-2)

d)

(4,-2)

62.

Solve the system of equations:

x - 2y = 4
3x +2y = 4

a)

(-2,-1)

b)

(4,-1)

c)

(2,-1)

d)

(4,1)

63.

Solve the system of equations:

x - 2y = 4
2x -y = -1

a)

(-2,-3)

b)

(-3,-2)

c)

(2,3)

d)

(3,2)

64.

Solve the system of equations:

5x + 3y = 6
x - 3y = 12

a)

(3,3)

b)

(-3,-3)

c)

(3,-3)

d)

(3,-2)

65.

Solve the system of equations:

x - y = -2
y = -2

a)

(1,-2)

b)

(-1,-2)

c)

(-4,-2)

d)

(4,-2)

66.

Solve the system of equations:

2x - 3y = 6
7x - 3y = -9

a)

(3,4)

b)

(4,-3)

c)

(-4,-3)

d)

(-3,-4)

67.

Solve the system of equations:

3x + y = 4
x + 2y = -2

a)

(2,2)

b)

(-2,-2)

c)

(2,-2)

d)

(-2,2)

68.

Solve the system of equations:

2x + y = -3
x - 2y = -4

a)

(-2,1)

b)

(1,-2)

c)

(2,1)

d)

(1,2)

69.

Solve the system of equations:

x = - 3
2x + 3y = 6

a)

(4,3)

b)

(-4,3)

c)

(-3,4)

d)

(3,-4)

70.

Solve the system of equations:

x + 4y = -8
5x - 4y = -16

a)

(4,1)

b)

(1,4)

c)

(-4,-1)

d)

(-1,-4)

71.

Solve the system of equations:

2x - 3y = 6
7x - 3y = -9

a)

(-3,-4)

b)

(3,4)

c)

(-4,-3)

d)

(4,3)

72.

Solve the system of equations:

5x - 4y = =-16
x+ 2y = -6

a)

(-4,-1)

b)

(5,-1)

c)

(-5,-1)

d)

(4,1)

73.

Factor x²-11x+24

a)

(x-3)(x-8)

b)

(x-2)(x-12)

c)

(x+3)(x+8)

d)

(x+2)(x+12)

74.

Solve for the values of x:
(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

75.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

76.

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

77.

Solve by factoring. (Hint: Factor the GCF)

a)

x = 3, x = -6

b)

x = 0, x = 2

c)

x = 2, x = 3

d)

x = -2, x = 1

78.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

79.

Solve the following with the square root method:

$4\left(x-5\right)^2=12$

a)

$\left(4x+20\right)^2=12$

b)

$x=5\pm\sqrt[]{3}$

c)

$x=-5\pm\sqrt[]{3}$

d)

$x=5\pm\frac{1}{2}\sqrt[]{3}$

80.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

81.

Solve by the Square Root method: x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

82.

Solve by the Square Root method:

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

83.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

84.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

85.

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.

86.

Solve by taking the square root: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

87.

Solve.
n² - 5 = -4

a)

n = ±√9

b)

n = ±3

c)

n = ±1

d)

No real solution

88.

Solve.

9k² = 225

a)

4

b)

4, -4

c)

25, -25

d)

-5, 5

89.

Solve by finding square roots and simplify completely:
$2x^2=20$

a)

$x=\pm10$

b)

$x=\sqrt{10}$

c)

$x=\pm\sqrt{10}$

d)

No real solutions

90.

Solve by finding square roots and simplify completely:
$x^2-16=0$

a)

$x=\pm16$

b)

$x=4$

c)

$x=\pm4$

d)

No real solutions

91.

Solve by factoring:
$x^2-36=0$

a)

$x=\pm6$

b)

$x=\pm36$

c)

$x=\pm18$

d)

No real solutions

92.

Solve by factoring:
$x^2+10x+24=0$

a)

$x=6\ or\ x=4$

b)

$x=\pm\sqrt{14}$

c)

$x=-6\ or\ x=-4$

d)

No real solutions

93.

Solve by factoring:
$x^2+2x-15=0$

a)

$x=3\ or\ x=-5$

b)

$x=\pm\sqrt{13}$

c)

$x=-3\ or\ x=5$

d)

No real solutions

94.

Solve by factoring:
$x^2-10x+16=0$

a)

$x=-2\ or\ x=-8$

b)

$x=\pm\sqrt{6}$

c)

$x=2\ or\ x=8$

d)

No real solutions

95.

Solve by factoring:
$x^2-7x+10=0$

a)

$x=2\ or\ x=5$

b)

$x=-2\ or\ x=-5$

c)

$x=4\ or\ x=10$

d)

No real solutions

96.

Solve using the Quadratic Formula:
$5x^2+3x-1=0$

a)

$x=\frac{3\pm\sqrt{29}}{5}$

b)

$x=\frac{8}{5}\ or\ x=-\frac{2}{5}$

c)

$x=\frac{-3\pm\sqrt{29}}{10}$

d)

No real solutions

97.

Solve using the Quadratic Formula:
$2x^2+6x-8=0$

a)

$x=2\ or\ x=-8$

b)

$x=-1\ or\ x=4$

c)

$x=1\ or\ x=-4$

d)

No real solutions

98.

Solve by factoring:
$x^2+10x+9=0$

a)

$x=1\ or\ x=9$

b)

$x=-1\ or\ x=-9$

c)

$x=-2\ or\ x=-18$

d)

No real solutions

99.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

100.

Find the slope:

a)

3/4

b)

4/3

c)

-3/4

d)

-4/3

101.

The slopes of parallel lines are...

a)

the same

b)

opposite

c)

always different

102.

Slope is know as rise/

a)

run

b)

fall

c)

none

d)

rise

103.

Find the slope of the line.

a)

-2

b)

2

c)

-1

d)

1

104.

Find the slope of the line that passes through:
(6,7) and (4,2)

a)

2/5

b)

-5/2

c)

5/2

d)

-1/2

105.

Find the slope of the line that passes through:
(2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

106.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

107.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=-1/3x-1

d)

y= -3x-3

108.

Which equation matches the graph? (Click me to see the image)

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = -2x

109.

Write the equation for the line in slope-intercept form.

a)

y= -1x+3

b)

y= 4x+3

c)

y=1/4x+3

d)

y= -4x+3

110.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

111.

Identify the slope of the following graph.

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

112.

Identify the slope of the following graph.

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

113.

Identify the slope of the following graph.

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

114.

What would the graph of the equation x = -4 look like?

a)

Horizontal line

b)

Vertical line

115.

What would the graph of y = 8 look like?

a)

Horizontal line

b)

Vertical line

116.

Which of the following would be graphed as a horizontal line?

a)

y = -4

b)

x = 7

c)

y = 3x-4

d)

None of the above

117.

Vertical or horizontal?
y = -3

a)

vertical

b)

horizontal

118.

Vertical or horizontal?
x = 10

a)

vertical

b)

horizontal

119.

Vertical or horizontal?
Slope of 0

a)

vertical

b)

horizontal

120.

Vertical or horizontal?
Undefined slope

a)

vertical

b)

horizontal

121.

What is the equation of this line?

a)

x=5

b)

y=5

c)

y=5x

d)

x=-5

122.

What is the equation of the line?

a)

y = 0

b)

y = 1

c)

y = 2

d)

x = 1

123.

Write the equation of the line shown?

a)

y = 6

b)

x = 6

c)

y = 6x

d)

y = 0

e)

x = 0

124.

Write the equation of the line shown?

a)

y = 6

b)

x = 6

c)

y = 6x

d)

x = 0

e)

y = 0

125.

Write the equation of the line shown.

a)

y = 0

b)

y = -3

c)

x = -3

d)

y = -3x

e)

x = 0

126.

Write the equation of the line shown.

a)

x = -7

b)

y = -7

c)

y = -7x

d)

y = 0

e)

x = -7y

127.

Write the equation of the line shown.

a)

y = -5.5

b)

x = -5.5

c)

y = -5.5x

d)

x = -5.5y

e)

y = 0

128.

Write the equation of the line shown.

a)

x = 1.5

b)

y = 1.5

c)

x = 1

d)

y = 2

129.

Which graph represents the equation

x = 5?

a)

b)

c)

d)

130.

Which graph represents the equation

y = 4?

a)

b)

c)

d)

131.

Which graph represents the equation

y = 2?

a)

b)

c)

d)

132.

Complete the Square
x² + 10x + ____

a)

x² + 10x - 100

b)

x² + 10x + 100

c)

x² + 10x - 25

d)

x² + 10x + 25

133.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

134.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

135.

What value of c would complete the square?

x² +8x + c

a)

4

b)

16

c)

64

d)

-16

136.

Complete the Square:

x² + 14x + (a)

137.

6. Complete the square for

x² - 16x + ____

(find the missing value that goes in the blank)

a)

+ 32

b)

- 16

c)

+ 64

d)

+ 8

138.

Complete the Square:

x² - 20x + (a)

139.

Factor the perfect square trinomial
x² + 14x + 49

a)

(x+7)²

b)

(x+7)(x-7)

c)

(x-7)²

d)

(x+14)²

140.

Factor the perfect square trinomial:
x² + 16x + 64

a)

(x+8)²

b)

(x-8)²

c)

(x-4)²

d)

(x+4)²

141.

Match the following

a)

x² + 16x + 64 =

1.

(x + 8)²

b)

x² - 16x + 64 =

2.

(x - 8)²

c)

x² + 8x + 16 =

3.

(x + 4)²

d)

x² + 4x + 4 =

4.

(x + 2)²

e)

x² - 4x + 4 =

5.

(x -2)²

142.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

143.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

144.

whats the slope of the function y=2/3x+6

a)

2/3

b)

3/2

c)

6

d)

-4

145.

What is the slope?

$y=2x-5$

(a)

146.

What is the slope?

$y=x+3$

(a)

147.

What is the slope?

$y=\frac{3}{5}x-1$

(a)

148.

What is the slope?

$y=-\frac{5}{2}x-\frac{1}{3}$

(a)

149.

What is the y-intercept?

$y=2x-5$

(a)

150.

What is the y-intercept?

$y=x+3$

(a)

151.

What is the y-intercept?

$y=\frac{3}{5}x-1$

(a)

152.

What is the y-intercept?

$y=-\frac{5}{2}x-\frac{1}{3}$

a)

$-\frac{1}{3}$

b)

$-\frac{5}{2}$

c)

$\frac{5}{2}$

d)

$\frac{1}{3}$

153.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

154.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

155.

Solve for x:
2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

156.

Solve for x:
7 - 2(10x + 1) = 25

a)

2/5

b)

2

c)

1

d)

-1

157.

Solve for x:
3(5x + 10) + 10 = 6x - (x + 10)

a)

3

b)

-3

c)

-5

d)

5

158.

Solve for x:
8x + 2 + 3x + 5 = x + 12

a)

-1/2

b)

2

c)

-2

d)

1/2

159.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

160.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

161.

Solve the equation:

2(x + 3) = 8

a)

2.5

b)

1

c)

7

d)

5.5

162.

5x - 4 + 2x = 3

a)

1

b)

2

c)

3

d)

4

Algebra Prerequisite Skills

Total questions: 162

Worksheet time: 13hrs 5mins

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