Free Printable A2 Test 7 OPTIONAL Review: Radical Expressions & Functions

1.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

2.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

3.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

Simplify

a)

A

b)

B

c)

C

d)

D

e)

None of the above

7.

Simplify the radical expression

a)

b)

c)

d)

8.

$\sqrt{81\left(x+3\right)^{12}}$

a)

$9\left(x+3\right)^4$

b)

$3\left(x+3\right)^6$

c)

$9\left(x+3\right)^6$

d)

$9\left(x+\sqrt{3}\right)^{2\sqrt{3}}$

9.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

10.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

11.

Simplify the following:

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

14.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

15.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

16.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

17.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

18.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

19.

a)

5x^5/4

b)

5x^-5/4

c)

(5x)^-5/4

d)

(5x)^-4/5

20.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

21.

Re-write the expression in radical form.
x^2/3

a)

∛x²

b)

√x³

c)

(1/x)

d)

∛x

22.

Rewrite the following as a radical. Simplify if possible.

a)

A

b)

B

c)

C

d)

D

23.

Write the expression in radical form.
y^1/2

a)

√y

b)

∛y

c)

√y²

d)

∛y²

24.

a)

a

b)

b

c)

c

d)

d

25.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

26.

Write in exponential form
√x⁵

a)

X¹∕ ⁵

b)

X ²⁄⁵

c)

X⁵⁄ ²

d)

X⁵

27.

$x^{\frac{5}{12}}=$

a)

b)

$\frac{x^{5\ }}{x^{12}\ }$

c)

d)

$\left(x^{12}\right)^{5\ }$

28.

Rewrite the expression in radical form.
$x^{\frac{7}{2}}$

a)

$\sqrt{x^7}$

b)

$7\sqrt{x^2}$

c)

7x²

d)

∛x⁷

29.

Simplify:

a)

2

b)

4

c)

16

d)

64

30.

a)

A

b)

B

c)

C

d)

D

31.

a)

a⁶/ b¹²

b)

b¹²/ a⁴

c)

a¹²/ b⁶

d)

1 / a⁶b¹⁰

32.

Simplify
x²⁄ ³⋅x¹⁄ ³

a)

2x

b)

x²⁄₉

c)

x

d)

x²

33.

Simplify . Your answer should contain only positive exponents. $\left(x^{\frac{5}{3}}y^{-2}\right)^0$

a)

$1$

b)

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

c)

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

d)

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

34.

According to exponent rules, when we divide the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

35.

According to exponent rules, when we raise the power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

a

b)

b

c)

c

d)

d

38.

Simplify. Your final answer should have positive exponents only.

$\left(2x^{\frac{1}{9}}\right)^4$

a)

$2^4x^{\frac{37}{9}}$

b)

$2x^{\frac{4}{9}}$

c)

$2^4x^{\frac{4}{9}}$

39.

Simplify. Your final answer should have positive exponents only.

$\frac{x^{\frac{2}{3}}}{x^{\frac{1}{3}}}$

a)

Cannot be simplified.

b)

$x$

c)

$\frac{1}{x^{\frac{1}{3}}}$

d)

$x^{\frac{1}{3}}$

40.

Simplify the following expression:

a)

16

b)

32

c)

40

d)

64

41.

What is the value of 27^⅓?

a)

27

b)

9

c)

3

d)

1/3

42.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

43.

64^4/3

a)

256

b)

8

c)

8⁴

d)

2

44.

49^1/2

a)

7

b)

98

c)

21

d)

14

45.

What is the X-INTERCEPT of this square root function?

a)

(0,0)

b)

(9,0)

c)

(0,-3)

d)

(1,1)

46.

What is the RANGE of the function?

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

47.

What is the y-intercept of the function

f\left(x\right)=\sqrt{x+4}+1

?

a)

$\left(0,0\right)$

b)

$\left(0,3\right)$

c)

$\left(3,0\right)$

d)

$None$

48.

What is the domain of the function $f(x) = \sqrt{x - 2}$ ?

a)

$\left[2,\infty\right)$

b)

$\left[0,\infty\right)$

c)

$\left(2,\infty\right)$

d)

$\left(0,\infty\right)$

49.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

50.

Which is the graph of the square root parent function?

a)

A

b)

B

c)

C

d)

D

51.

Which describes the graph?

a)

y=√(x+4)+1

b)

y=√(x-4)-1

c)

y=√(x+4)-1

d)

y=√(x-4)+1

52.

Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.

a)

Domain: (-∞, ∞) Range: [-∞, 4]

b)

Domain: [1, ∞) Range: (-∞, 4]

c)

Domain: [-1. ∞) Range: [4, ∞)

d)

Domain: [4, ∞) Range: [-1,∞)

53.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

(-∞, 0)

d)

[ 0, ∞)

54.

Which one means left

a)

x →-∞

b)

x →∞

55.

Which one means up

a)

y →-∞

b)

y →∞

56.

Which one means the function goes up on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

57.

Which one means the function goes down on the left

a)

x →-∞, y→∞

b)

x →-∞, y→-∞

58.

Which function matches the graph?

a)

A

f(x) = − ∛(x + 3) − 1

b)

B

f(x) = − ∛(x - 3) − 1

c)

C

f(x) = ∛(x + 3) − 1

d)

D

f(x) = ∛(x - 1) + 3

59.

What kind of function is represented by the graph?

a)

Cube Root Function

b)

Cubic Function

c)

Polynomial Function

d)

Square Root Function

60.

What is the Domain of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

61.

What is the Range of ALL Cube Root Functions?

a)

(−∞,∞)

b)

[0,∞)

c)

(−∞,0]

d)

All Cube Root Functions are different.

62.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

63.

The graph of a function is shown. What are the domain and range of this function?

a)

Domain: (-∞, ∞)
Range: (-∞, ∞)

b)

Domain: [-7, ∞)
Range: (-∞, ∞)

c)

Domain: (-∞, ∞)
Range: (-∞, 3]

d)

Domain: [-7, ∞)
Range: (-∞, 3]

64.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

65.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

66.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

67.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

68.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

69.

Determine which graph matches the given equation.

a)

b)

c)

d)

e)

70.

Fill in the blank:

When choosing x-values to plot the graph of a cube root function, we choose specific values that will make the ___ a perfect cube.

a)

radicand

b)

radical

c)

index

d)

radical symbol

A2 Test 7 OPTIONAL Review: Radical Expressions & Functions

Total questions: 70

Worksheet time: 18hrs 30mins

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