Free Printable Edgenuity Unit 3 review Radical and Rational Functions

1.

What is the missing factor?

a)

3

b)

5

c)

6

d)

7

2.

Use a factor tree to find prime factorization of 24.

a)

2 x 3 x 2 x 3

b)

2 x 3 x 2 x 2

c)

6 x 2 x 2

d)

2 x 3 x 4

3.

13² = ______

a)

225

b)

196

c)

169

d)

166

4.

√196 = ______

a)

14

b)

14²

c)

15

d)

15²

5.

125

a)

Is a perfect square.

b)

Is not a perfect square.

6.

Which equation is shown graphed? Use Desmos and pay attention to parenthesis.

a)

y = 2√(x)

b)

y = −2√(x)

c)

y = −½√(x)

d)

y = ½√(x)

7.

Name the parent function.

a)

cube root

b)

quadratic

c)

cubic

d)

square root

e)

linear

8.

What is the domain of the function in this graph?

a)

x ≤ 3

b)

x ≥ 3

c)

x ≤ 0

d)

x ≥ 0

9.

What is the range of the function in this graph?

a)

y ≤ 3

b)

y ≥ 3

c)

y ≤ 0

d)

y ≥ 0

10.

Which of the following is the function shown in the graph?

a)

b)

c)

d)

11.

a)

4

b)

-4

c)

2

d)

-2

12.

Which of the following represents direct variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

13.

Which of the following represents indirect variation?

a)

y = kx

b)

y = k/x

c)

y = x/k

d)

y = mx + b

14.

Y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?

a)

y=2x

b)

y=2/x

c)

y=4x

d)

y=x/2

15.

y varies directly with the square of x. If y=40 when x=4, find y when x = 7. Plug the numbers into the direct variation equation to find k, then find y when x=7.

a)

17.5

b)

70

c)

122.5

16.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

17.

Is the given table a direct variation? If so, what is the constant of variation?

a)

Yes; 1/3

b)

Yes; 3

c)

Yes; 5

d)

No

18.

Which of the given graphs is a direct variation?

a)

A

b)

B

c)

C

d)

D

19.

Is the given table a direct variation? If so, what is the constant?

a)

Yes; 1/4

b)

Yes; 4

c)

Yes; 2

d)

No

20.

Determine the type of variation:

a)

Direct

b)

Inverse

c)

Neither

21.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

22.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours (x) and earns $187.15 (y), what should she earn if she worked 40 hours?

a)

$394

b)

$443.25

c)

$472.80

d)

$512.20

23.

y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?

a)

y = 2x

b)

y = 2/x

c)

y = 4x

d)

y = x/2

24.

Which number is irrational?

a)

$\sqrt{25}$

b)

$\sqrt{9}$

c)

-34

d)

$\sqrt{2}$

25.

Solve the radical equation and check for extraneous solutions:

a)

A

b)

B

c)

C

d)

D

26.

What is the first step when solving the radical equation $4\sqrt{x-7}+\ 12\ =\ 28$

a)

Divide both sides of the equation by 4

b)

Square both sides of the equation

c)

Subtract 12 from both sides of the equation

d)

Add 7 to both sides of the equation

e)

Check your solution

27.

a)

-5√1

b)

8√2 + 13√3

c)

21√5

d)

20√5

28.

a)

8√6

b)

8√12

c)

12√6

d)

12√12

29.

Simplify.

a)

b)

c)

d)

30.

.141414141414...

a)

Rational

b)

Irrational

31.

pi - 3.141592....

a)

Rational

b)

Irrational

32.

5

a)

Rational

b)

Irrational

33.

√7

a)

Rational

b)

Irrational

34.

√25

a)

Rational

b)

Irrational

35.

When you add two rational numbers, the sum is...

a)

always rational

b)

sometimes rational, sometimes irrational

c)

always irrational

d)

never rational

36.

When you multiply two rational numbers, the sum is...

a)

always rational

b)

sometimes rational, sometimes irrational

c)

always irrational

d)

never rational

37.

When you add a rational number and irrational number, the sum is...

a)

always rational

b)

sometimes rational, sometimes irrational

c)

always irrational

d)

mostly irrational

38.

When you multiply a rational number and irrational number, the product is...

a)

always rational

b)

sometimes rational, sometimes irrational

c)

always irrational

d)

mostly irrational

39.

Use Desmos.

a)

-0.32

b)

0.32

c)

3.2

d)

-3.2

40.

What is the ∛125 ? Use Desmos.

a)

41.6

b)

-5

c)

5

41.

a)

11√5

b)

11√10

c)

5√5

d)

12√10

42.

a)

0

b)

3∛1

c)

3∛7

d)

3

43.

a)

13√3

b)

10√30

c)

13√6

d)

11√3

44.

Simplify the radical...

√20a²b⁴

a)

2ab²√5

b)

4ab²√5

c)

5ab²√2

d)

2a²b²√5

45.

Simplify:

a)

1/5

b)

20/100

c)

2/10

d)

1/√25

46.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

47.

Simplify:
√6 ⋅√6

a)

√36

b)

2√3

c)

12

d)

6

48.

Simplify 2√5(3√3+6√2)

a)

6√15+12√10

b)

15√6+30√10

c)

90

d)

6√10+12√6

49.

The number under the radical sign or square root sign is called the ______.

a)

radical sign

b)

radicand

c)

factor

d)

exponent

50.

Simplify

a)

x²y√xy

b)

xy

c)

x²y²

d)

Can't Simplify

51.

Evaluate: √54p⁶k⁵

a)

3p³k²√6k

b)

6pk√3p⁴k³

c)

3p²k²√6pk

d)

9p³k²√6k

52.

Simplify

\frac{\sqrt{5}}{\sqrt{3}}

a)

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

b)

$\frac{\sqrt{15}}{3}$

c)

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

d)

$\frac{\sqrt{5}}{9}$

e)

None of these

53.

Simplify

\frac{\sqrt{5}}{\sqrt{2}}

a)

$\frac{\sqrt{10}}{4}$

b)

$\frac{\sqrt{5}}{2}$

c)

$\frac{\sqrt{10}}{2}$

d)

$\frac{\sqrt{5}}{4}$

e)

None of these

54.

Simplify:

a)

A

b)

B

c)

C

d)

D

55.

Simplify
$\sqrt{6}\left(\sqrt{6}+\sqrt{10}\right)$

a)

$6+2\sqrt{15}$

b)

$8\sqrt{15}$

c)

$\sqrt{96}$

d)

$6\sqrt{6}+2\sqrt{15}$

56.

Simplify
$\sqrt{30}\left(\sqrt{3}-\sqrt{12}\right)$

a)

$-3\sqrt{10}$

b)

$3\sqrt{10}$

c)

$10\sqrt{3}$

d)

$-10\sqrt{3}$

57.

Simplify 2³

a)

6

b)

9

c)

8

d)

16

58.

What is the exponent form for the factors
5 x 5 x 5?

a)

3⁵

b)

5³

59.

Which number is the BASE?
2³= 8

a)

2

b)

3

c)

8

60.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

61.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

62.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

63.

Write the following expression in exponential form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

64.

Simplify using Desmos.

a)

2

b)

8

c)

16

d)

32

65.

The square root of 36x² is __________

a)

6

b)

6x

c)

4x

d)

6x²

66.

Simplify . Your answer should contain only positive exponents. $\left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1}$

a)

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

b)

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

c)

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

d)

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

67.

Exponent Rules: Product Rule

a^x\cdot a^y=

a)

$a^{x\cdot y}$

b)

$a^{x+y}$

c)

$a^x+a^y$

68.

Exponent Rules: Quotient Rule

\frac{a^x}{a^y}=

a)

$a^{x-y}$

b)

$a^{\frac{x}{y}}$

c)

$a^{x+y}$

69.

Exponent Rules: Power of a Power Rule

a^{x^y}\ or\ \left(a^x\right)^y\ =

a)

$a^{x+y}$

b)

$a^{x\cdot y}$

c)

$a^xa^y$

70.

Exponent Rules: Power of a Product

\left(ab\right)^x=

a)

$a^x+b^x$

b)

$a^{bx}$

c)

$a^xb^x$

71.

Exponent Rules: Negative Exponent

a^{-x}=

a)

$-a^{-x}$

b)

$-a^x$

c)

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

d)

$-\frac{1}{a^x}$

72.

Exponent Rules: RATIONAL EXPONENT

a^{\frac{x}{y}}=

a)

$\ ^y\sqrt{a^x}$

b)

$a^x-a^y$

c)

$\frac{a^x}{a^y}$

73.

Simplify the following:
$\left(x^3y\right)^2$

a)

$x^5y^2$

b)

$x^6y^2$

c)

$x^1y^{-1}$

d)

$2x^3y$

74.

x^-3

a)

-3x

b)

x³

c)

1/ x^-3

d)

1/ x³

75.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

Edgenuity Unit 3 review Radical and Rational Functions

Total questions: 75

Worksheet time: 19hrs 45mins

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