Free Printable Unit 10/11 Test Review

1.

Solve for x.

$\sqrt[]{x-3}+6=2$

a)

-13

b)

4

c)

19

d)

No Solution

(Extraneous)

2.

Solve for x.

$-8+\sqrt[]{5x-5}=-3$

a)

no solution

b)

6

c)

3

d)

4

3.

Match the correct equation with the given graph.

a)

$y=\sqrt[]{x}+2$

b)

$y=\sqrt[]{x}-2$

c)

$y=\sqrt[]{x+2}$

d)

$y=\sqrt[]{x-2}$

4.

Match the correct equation with the given graph.

a)

y $y=\sqrt[]{x-3}$

b)

$y=\sqrt[]{x}+3$

c)

$y=\sqrt[]{x+3}$

d)

$y=\sqrt[]{x}-3$

5.

Match the correct equation with the given graph.

a)

$y=-\sqrt[]{x+1}$

b)

$y=\sqrt[]{x+1}$

c)

$y=-\sqrt[]{x}-1$

d)

$y=-\sqrt[]{x}+1$

6.

Solve for x.

$7=\sqrt[]{x}-4$

(a)

7.

Solve for x.

$52=\sqrt[]{x-24}+43$

(a)

8.

Solve for x.

$\sqrt[]{7x}=\sqrt[]{10+6x}$

(a)

9.

Solve for x.

$\sqrt[]{70x+88}=\sqrt[]{78x}$

(a)

10.

What is the value for y, when x=109?

$y=-7\sqrt[]{x-84}$

(a)

11.

Solve for x.

$\sqrt[]{2x-6}=\sqrt[]{5x-15}$

(a)

12.

Solve for x.

$\sqrt[]{10-13x}=x-4$

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

13.

Solve for x.

$x-4=\sqrt[]{7x-38}$

a)

x=6, 9

b)

6

c)

No Solution

d)

-9

14.

What is the value y when x=4?

$y=\sqrt[]{x+5}$

(a)

15.

What is the domain of the function $y=\sqrt[]{x+5}$

a)

$All\ Real\ Numbers$

b)

$x\ge5$

c)

$x\le-5$

d)

$x\ge-5$

16.

Which function is represented by the graph shown?

a)

$f\left(x\right)\ =\ 2\sqrt{x}\ -\ 4$

b)

$f\left(x\right)\ =2\ \sqrt{x\ -4}$

c)

$f\left(x\right)\ =\ 2\sqrt{x}$

d)

$f\left(x\right)\ =\ 2\sqrt{x}\ +\ 4$

17.

Solve for x.

$-8\sqrt[]{x-5}=-16$

(a)

18.

Find any x-intercept(s).

$y=\sqrt[]{x-1}-2$

a)

$\left(-5,0\right)$

b)

$\left(3,0\right)$

c)

$\left(5,0\right)$

d)

none

19.

Find the y-intercept.

$y=-\ \sqrt[]{x+9}-6$

a)

none

b)

$\left(0,9\right)$

c)

$\left(0,-3\right)$

d)

$\left(0,-9\right)$

20.

Which of the following is the equation of the graph?

a)

$y=4+\sqrt[]{1-x}$

b)

$y=1+2\ \sqrt[]{4-x}$

c)

$y=4-\ \sqrt[]{x-1}$

d)

$y=1+2\ \sqrt[]{x-4}$

21.

What function best describes this graph?

a)

$y=-\sqrt[]{x+4}-2$

b)

$y=\sqrt[]{x-4}-2$

c)

$y=-\sqrt[]{x-4}-2$

d)

$y=\sqrt[]{x+4}-2$

22.

Identify the Range

$y=-\sqrt[]{x}-2$

a)

$y\le-2$

b)

$y\ge-2$

c)

$y\le0$

d)

$y\ge0$

23.

Find the domain and range of the function $y=\sqrt[]{x-9}$

a)

Domain: $y\ge9$ Range: $x\ge0$

b)

Domain: $x\ge9$ Range: $y\ge0$

c)

Domain: $x\ge0$ Range: $y\ge0$

d)

Domain: $x\ge0$ Range: $y\ge9$

24.

What is the domain of this function?

$y=\sqrt{x-1}-3$

a)

x ≥ 1

b)

x ≤ 1

c)

x ≥ -3

d)

x ≥ -1

25.

What is the range of this function?

$y=\sqrt{x-1}-3$

a)

y ≥ 1

b)

y ≥ -1

c)

y ≥ -3

d)

y ≤ -3

26.

Identify the domain and range of $y\ =\sqrt{x-1}$ .

a)

Domain: $x\ge1$
Range: $y\ge0$

b)

Domain: {All real numbers}
Range: {All real numbers}

c)

Domain: $x\ge0$
Range: $y\ge-1$

d)

Domain: $x\le0$
Range: $y\ge1$

27.

Which shows the graph of $y=\sqrt{x+5}$ ?

a)

b)

c)

d)

28.

Which shows the graph of $f\left(x\right)=\sqrt{x}-4$ ?

a)

b)

c)

d)

29.

Which shows the graph of $y=\sqrt{x}+2$ ?

a)

b)

c)

d)

30.

Which shows the graph of $y=\sqrt{x-1}-3$ ?

a)

b)

c)

d)

31.

Identify the domain and range of $y\ =\sqrt{x+2}$ .

a)

Domain: $x\ge-2$
Range: $y\ge0$

b)

Domain: {All real numbers}
Range: {All real numbers}

c)

Domain: $x\ge2$
Range: $y\ge0$

d)

Domain: $x\le0$
Range: $y\ge-2$

32.

Identify the domain and range of $y\ =\sqrt{x}+5$ .

a)

Domain: $x\le5$
Range: $y\ge0$

b)

Domain: $x\ge0$
Range: $y\ge-5$

c)

Domain: $x\ge0$
Range: $y\ge-1$

d)

Domain: $x\ge0$
Range: $y\ge5$

33.

Identify the domain and range of $y\ =\sqrt{x-3}-4$ .

a)

Domain: $x\ge3$
Range: $y\ge4$

b)

Domain: $x\ge-3$
Range: $y\le-4$

c)

Domain: $x\ge-3$
Range: $y\ge-4$

d)

Domain: $x\ge3$
Range: $y\ge-4$

34.

Find any y-intercept(s).

$y=-\sqrt{x+9}-6$

a)

none

b)

(0, 3)

c)

(0,9)

d)

(0,-9)

35.

Find any x-intercept(s).
$y=\sqrt{x-1}-2$

a)

(-5,0)

b)

(3, 0)

c)

(5,0)

d)

none

36.

Which shows the graph of the function $y=-3\sqrt[]{x}$ ?

a)

b)

c)

d)

37.

What is the Range for:

g\left(x\right)=\sqrt{x+5}-3

a)

$y\ge-3$

b)

$y\le-3$

c)

$y\le3$

d)

$y\ge3$

38.

What are the equations of the asymptotes?

a)

x=-3

y=1

b)

x=3

y =1

c)

x=-3

y =-1

d)

x=3

y=-1

39.

What is the domain of the equation $y=\frac{1}{x+3}$ ?

a)

$x\ne0$

b)

All Real numbers

c)

$x\ne-3$

d)

$x\ge-3$

40.

What is the y-intercept?

a)

(0, -1)

b)

(0, 1)

c)

(0, 4)

d)

There isn't one

41.

What is the vertical asymptote of the equation $y=\frac{x-2}{x+5}$ ?

a)

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

b)

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

c)

$x=-5$

d)

$x=2$

42.

What is the Vertical Asymptote of $y=\frac{x+5}{x-6}$ ?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

43.

What is the y-intercept of $y=\frac{2x+6}{x+1}$

a)

(0, 1)

b)

(0, -1)

c)

(0, 6)

d)

(0, -6)

44.

What is the y-intercept of $y=\frac{4x}{x+5}$ ?

a)

(0, 0)

b)

(0, 5)

c)

(0, 1)

d)

There isn't one

45.

What are the asymptotes of the graph shown?

a)

x = -1 y = -3

b)

x = 1 y = -3

c)

x = -1 y = 3

d)

x = 1 y = 3

46.

What is the horizontal asymptote of the graph shown??

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

47.

What is the vertical asymptote of the graph shown?

a)

x =-3

b)

y = -3

c)

x = 3

d)

y = 3

48.

What is the vertical asymptote of $y=\frac{8}{2x-4}$

a)

x=-2

b)

x=2

c)

x=4

d)

x=0

49.

What is the domain and range of the rational function shown in the graph?

a)

$Domain:\ x\ne2$

$Range:\ y\ne1$

b)

$Domain:\ x\ne1$
$Range:\ y\ne2$

c)

$Domain:\ x\ne\frac{1}{2}$
$Range:\ y\ne\frac{1}{2}$

d)

$Domain:\ x\ne-2$
$Range:\ y\ne-1$

50.

What is the domain and range of the function shown in the graph?

a)

Domain : $x\ne-3$
Range: $y\ne1$

b)

Domain : $x\ne1$
Range: $y\ne-3$

c)

Domain : $All\ Real\ Numbers$
Range: $All\ Real\ Numbers$

d)

Domain : $x\ne-1$
Range: $y\ne3$

51.

What is the quotient of $\frac{15}{0}$ ?

a)

undefined

b)

0

c)

15

d)

-0

52.

What is the quotient of $\frac{0}{15}$ ?

a)

undefined

b)

0

c)

15

d)

-0

53.

Solve the inverse variation equation: $y=\frac{8}{x}$ for x when y = 4

a)

1

b)

2

c)

3

d)

4

54.

Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.

a)

300

b)

75

c)

1,875

d)

12

55.

Which of the following represents inverse variation?

a)

$y=kx$

b)

$y=\frac{k}{x}$

c)

$y=\frac{x}{k}$

d)

$y=mx+b$

56.

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

a)

14

b)

10

c)

2

d)

-14

57.

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k?

a)

121

b)

4

c)

100

d)

6

58.

What is the constant (k) in this inverse variation?
$y=\frac{400}{x}$

a)

x

b)

y

c)

400

d)

Not enough information given

59.

x and y vary inversely. Given (5, 20), what is the constant k?

a)

4

b)

5

c)

25

d)

100

60.

Given the following equation showing inverse variation, identify the constant k.
$y=\frac{54}{x}$

a)

There isn't one

b)

x

c)

54

d)

y

61.

The variables x and y vary inversely, and y = 8 when x = 4.

Write an equation that relates x and y.

a)

y = 32 x

b)

y = ³² / _x

c)

y = 2 x

d)

y = ² / _x

62.

If y varies inversely as x and x=5 when y=20, then what is the constant of variation, k?

a)

121

b)

4

c)

100

d)

6

63.

Assume y varies inversely with x. If x=7 when y=4, what is y when x=2 ?

a)

4

b)

14

c)

7

d)

28

64.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

$2$

b)

$\frac{18}{5}$

c)

$\frac{26}{5}$

d)

$6$

65.

Solve for x: $\frac{6x+18}{x^2}+\frac{1}{x}=\frac{3}{x}$

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

66.

Solve for x: $\frac{5}{x+2}=\frac{1}{x-4}$

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

67.

a)

7

b)

-3

c)

12

d)

14

68.

Solve the following proportion:

$\frac{3}{2}=\frac{9}{x-2}$

(a)

69.

Solve the following proportion:

$\frac{y+15}{2}=\frac{10}{4}$

(a)

70.

Solve the following proportion:

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

(a)

71.

Solve for the following proportion:

$\frac{2}{6-2x}=\frac{3}{4x-5}$

(a)

72.

Solve the following proportion:

$\frac{4}{2x+5}=\frac{-8}{3x+4}$

(a)

73.

Solve: $\frac{\left(a-2\right)}{7}=\frac{\left(a-4\right)}{4}$

a)

8

b)

2.7

c)

4

d)

6.67

74.

Solve: $\frac{\left(n-10\right)}{9}=\frac{\left(n+5\right)}{2}$

a)

-9.29

b)

5

c)

-5

d)

-1.8

75.

Solve: $\frac{4}{\left(x-1\right)}=\frac{2}{\left(x-4\right)}$

a)

7

b)

5.6

c)

-1.6

d)

3

76.

Solve: $\frac{\left(n+10\right)}{7}=\frac{\left(n-8\right)}{3}$

a)

7.4

b)

8

c)

21.5

d)

-9.9

77.

Solve: $\frac{\left(m+7\right)}{5}=\frac{\left(m+6\right)}{6}$

a)

-8

b)

-12

c)

6

d)

8.9

78.

Solve: $\frac{7}{9}=\frac{\left(x+2\right)}{\left(x+10\right)}$

a)

4.6

b)

26

c)

-5.9

d)

-2.4

79.

Solve: $\frac{3}{5}=\frac{\left(k+9\right)}{\left(k-9\right)}$

a)

-36

b)

-5.8

c)

4

d)

-6

80.

Given

$\frac{3}{x+2}=\frac{4}{2x-5}$
which of the following should you have after cross-multiplying?

a)

$6x-15=4x+8$

b)

$6x-5=4x+2$

c)

$8x-20=3x+6$

81.

Solve the following proportion:

$\frac{3}{x}=\frac{3}{7-x}$

(a)

82.

Solve the following proportion:

$\frac{3}{2}=\frac{7-4x}{1-3x}$

(a)

83.

Solve the following proportion:

$\frac{2}{2-2x}=\frac{7}{2x-20}$

(a)

84.

Solve the following proportion:

$\frac{4}{1-3x}=\frac{4}{-5-x}$

(a)

85.

Challenge: SELECT ALL THAT APPLY -

Consider the following:

$\sqrt[]{5x+11}-1=x$

After solving, which solution(s) will be solved EXTRANEOUS.

a)

$5$

b)

$-5$

c)

$2$

d)

$-2$

e)

$4$

86.

Challenge: SELECT ALL THAT APPLY -

When solving the following Radical Equations, which equations will have EXTRANEOUS solutions.

a)

$\sqrt[]{9x-1}+1=0$

b)

$-3\sqrt[]{x+6}=27$

c)

$-7\sqrt[]{-x-7}-7=-7$

d)

$-4\sqrt[]{2x-6}+32=0$

e)

$3\sqrt[]{3x+2}=-12$

87.

Solve.

$3\sqrt[]{3x+2}=-12$

a)

$x=\frac{14}{3}$ is the only solution.

b)

There are no solutions.

$x=\frac{14}{3}$ is extraneous

c)

$x=-2$ is the only solution.

d)

There are no solutions. $x=-2$ is extraneous.

88.

Solve.

$-4\sqrt[]{2x-6}+32=0$

a)

$x=35$ is the only solution.

b)

There are no solutions.

$x=35$ is extraneous

c)

$x=6$ is the only solution.

d)

There are no solutions. $x=6$ is extraneous.

89.

Solve.

$-7\sqrt[]{-x-7}-7=-7$

a)

$x=-7$ is the only solution.

b)

There are no solutions.

$x=-7$ is extraneous

c)

$x=7$ is the only solution.

d)

There are no solutions. $x=7$ is extraneous.

90.

Solve.

$\sqrt[]{9x-1}+1=0$

a)

$x=\frac{2}{9}$ is the only solution.

b)

There are no solutions.

$x=\frac{2}{9}$ is extraneous

c)

$x=0$ is the only solution.

d)

There are no solutions. $x=0$ is extraneous.

91.

Solve.

$-3\sqrt[]{x+6}=27$

a)

$x=75$ is the only solution.

b)

There are no solutions.

$x=75$ is extraneous

c)

$x=-6$ is the only solution.

d)

There are no solutions. $x=-6$ is extraneous.

92.

Which of the following is a solution to the equation $\sqrt[]{3x}=\sqrt[]{4x-1}$ ?

a)

No solutions exist.

b)

x=1

c)

x=-1

d)

x=2

Unit 10/11 Test Review

Total questions: 92

Worksheet time: 9hrs 40mins

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