Free Printable Aisha Quiz

1.

$2\sqrt{3}+\ \sqrt{3}$ is equal to

a)

$2\sqrt{6}$

b)

6

c)

$3\sqrt{3}$

d)

$4\sqrt{6}$

2.

$\sqrt{10}\ \times\sqrt{5}$ is equal to

a)

$\sqrt{15}$

b)

$\sqrt{150}$

c)

$\sqrt{50}$

d)

5

3.

The number obtained on rationalizing the denominator of $\frac{1}{\sqrt{7}-2}$ is

a)

$\frac{\sqrt{7}+2}{3}$

b)

$\frac{\sqrt{7}-2}{3}$

c)

$\frac{\sqrt{7}+2}{5}$

d)

$\frac{\sqrt{7}-2}{5}$

4.

$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to

a)

$\sqrt{9}-\sqrt{8}$

b)

$\frac{\sqrt{9}-\sqrt{8}}{1}$

c)

$3-\sqrt{8}$

d)

$3+\sqrt{8}$

5.

After rationalize the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}}$ , we get the denominator as

a)

13

b)

19

c)

5

d)

37

6.

The number obtained on rationalizing the denominator of $\frac{3}{\sqrt{3}}$ is

a)

3

b)

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

c)

$\sqrt{3}$

d)

$3\sqrt{3}$

7.

$64^{\frac{1}{3}}$ is equal to

a)

8

b)

4

c)

12

d)

6

8.

$2^{\frac{1}{3}}\times\ 2^{\frac{1}{6}}$ is equal to

a)

2

b)

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

c)

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

d)

3

9.

$a^{-1}$ is equal to

a)

a

b)

1

c)

0

d)

$\frac{1}{a}$

10.

$\left(3^{\frac{1}{2}}\right)^{\frac{1}{3}}$ is equal to

a)

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

b)

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

c)

$3^{\frac{1}{5}}$

d)

$3^{\frac{1}{6}}$

11.

Write 2 x 2 x 2 x 2 in index form

a)

2³

b)

2⁵

c)

16

d)

2⁴

12.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

13.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

14.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

15.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

16.

Simplify 4⁰

a)

1

b)

4

c)

0

17.

Simplify 4⁷ ÷ 4³

a)

4¹⁰

b)

4

c)

4²¹

d)

4⁴

18.

Write (4⁷ x 4³) ∕ 4⁴ as a single power

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

19.

Evaluate 1² + 2² + 3²

a)

6

b)

12

c)

14

d)

11

20.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

21.

Simplify

a)

A

b)

B

c)

C

d)

D

22.

Simplify

a)

A

b)

B

c)

C

d)

D

23.

a×a×a

a)

3a

b)

3a³

c)

a³

d)

3a²

24.

a³×a⁴

a)

7a

b)

12a

c)

a¹²

d)

a⁷

25.

9a+a

a)

9a²

b)

9a

c)

10a

d)

11a

26.

a×a×a×a

a)

4a

b)

a⁴

c)

4a⁴

d)

2a²

27.

a²×a⁴

a)

6a

b)

6a²

c)

a⁶

d)

8a²

28.

5a×3a

a)

15a²

b)

30a

c)

15a

d)

a³⁰

29.

a×a⁸

a)

a⁸

b)

2a⁸

c)

a⁹

d)

2a⁹

30.

7a+3a

a)

21a²

b)

10a²

c)

21a

d)

10a

31.

If 8^x = 32^1.5, What is the value of x?

a)

1.5

b)

2.5

c)

3

d)

4

32.

If 8^x = 32^1.5, What is the value of x?

a)

1.5

b)

2.5

c)

3

d)

4

33.

Evaluate 8^1/3* 4^-1/2

a)

8

b)

4

c)

2

d)

1

34.

Evaluate 27^-1/3 * 49^-1/2* 125⁰

a)

210

b)

21

c)

1/21

d)

1

35.

If 5ⁿ= 125 find n.

a)

25

b)

1/3

c)

-3

d)

3

36.

Simplify 9^-1/2 * 81^3/4 - 9^1/2

a)

3

b)

1/9

c)

1/3

d)

9

37.

Evaluate 8^1/3 * 25^1/2 * 25⁰

a)

10

b)

125

c)

1/25

d)

1/10

38.

Evaluate 27^2/3 * 64^-1/2 - 32^-2/5

a)

2/9

b)

1.5

c)

4.5

d)

6

39.

Simplify 27^1/3- 16 ^-1/4

a)

6

b)

5

c)

4

d)

3

40.

Evaluate 16^-5/4* 2³* 10⁰

a)

40

b)

1/4

c)

1/40

d)

4

41.

Solve 16^{2x - 1}= 64

a)

1.5

b)

1.25

c)

4/5

d)

-1.25

42.

Write 6²x 6³as a single power

a)

7776

b)

6⁶

c)

6⁵

d)

36⁵

43.

Write 9⁵ ÷ 9³ as a single power

a)

9²

b)

9⁸

c)

9¹⁵

44.

Which is greater, 2654⁰ or 5⁰?

a)

2654⁰

b)

5⁰

c)

They are the same

d)

Zero is greater

45.

a⁷×a⁴÷a⁵

a)

a⁷

b)

a⁶

c)

a⁴

d)

a¹¹

46.

Write (4⁷ x 4³) ∕ 4⁴ as a single power

a)

4¹⁴

b)

4¹

c)

4⁸

d)

4⁶

47.

a³×a⁴

a)

7a

b)

12a

c)

a¹²

d)

a⁷

48.

(3x²y³)²

a)

9x⁴y⁶

b)

3x⁴y⁵

c)

6x⁴y⁶

d)

9xy

49.

What is the area of a rectangle with dimensions listed below:

length = 10x⁷

width = 7x⁵

a)

70x¹²

b)

70x³⁵

c)

17x¹²

d)

17x³⁵

50.

What is the value of (-2)^3?

a)

-8

b)

-6

c)

6

d)

8

51.

Simplify 5^-2

a)

-10

b)

1/25

c)

1/(5)²

d)

-1/10

52.

a)

z¹

b)

1

c)

0

d)

z^-1

53.

a)

12

b)

8

c)

4

d)

2

54.

a)

1/4

b)

2/3

c)

2

d)

0.5

55.

a)

1/7

b)

7

c)

24.5

d)

-7

56.

a)

3

b)

9

c)

12

d)

6

57.

a)

1/16

b)

1/9

c)

1/3

d)

1/27

58.

a)

1

b)

1/x

c)

x

d)

x^-11

59.

a)

25

b)

5

c)

2

d)

3

60.

a)

$125\sqrt{x}$

b)

$125x^{-2}$

c)

$5x^{4.5}$

d)

$125x^{4.5}$

61.

$\left(6a^8b\right)\left(10a^3b^4\right)$

a)

$60a^5b^{-3}$

b)

$60a^{24}b^4$

c)

$16a^{11}b^5$

d)

$60a^{11}b^5$

62.

Simplify by rationalizing the denominator:

(Hint: rewrite without a surd on the denominator)

a)

b)

c)

d)

63.

Simplify by rationalising the denominator:

(Hint: Rewrite without surds in the denominator)

a)

b)

c)

d)

64.

Expand and simplify ...

(2 + √3)(3 + √3)

a)

9 + 5√3

b)

6 + 6√3

c)

9 + √3

d)

15 + 5√3

65.

Expand and simplify ...

(3 + 2√2)(1 + 3√2)

a)

15 + 11√2

b)

15 + 5√2

c)

5 + 11√2

d)

5 + 5√2

66.

To rationalize the denominator of this expression you need to multiply by

a)

$\frac{4}{4}$

b)

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

c)

$\frac{4}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{4}$

67.

Rationalize the denominator:
$\frac{1}{4\sqrt{10}}$

a)

$\frac{\sqrt{1}}{4}$

b)

$\frac{\sqrt{10}}{40}$

c)

$\frac{1}{4}$

d)

$\frac{\sqrt{10}}{400}$

68.

Express the following division without any surds in the denominator.

a)

$\frac{\sqrt{7}}{2}$

b)

$\sqrt{2}$

c)

$\frac{\sqrt{14}}{2}$

d)

$\frac{\sqrt{14}}{7}$

e)

cannot be done

69.

Rationalize the denominator:
$\frac{\sqrt{5}}{2\sqrt{3}}$

a)

$\frac{\sqrt{15}}{6}$

b)

$\frac{\sqrt{15}}{18}$

c)

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

d)

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

70.

$\frac{10+8\sqrt{7}}{\sqrt{31}}$

a)

$\frac{3\sqrt{221}}{16}$

b)

$\frac{8\sqrt{31}+11\sqrt{217}}{31}$

c)

$\frac{10\sqrt{31}+8\sqrt{217}}{31}$

d)

$\frac{10\sqrt{33}+8\sqrt{231}}{33}$

71.

Fully simplify...

a)

b)

c)

d)

72.

Find $\sqrt{2}-4$ multiplied with its conjugate.

(a)

73.

Choose two expressions with correct rationalizing the denominator process.

a)

$\frac{8}{3\sqrt{5}}\times\frac{-3\sqrt{5}}{-3\sqrt{5}}$

b)

$\frac{4+\sqrt{3}}{\sqrt{3}-2}\times\frac{4-\sqrt{3}}{4-\sqrt{3}}$

c)

$\frac{5}{1-\sqrt{3}}\times\frac{5}{1+\sqrt{3}}$

d)

$\frac{2\sqrt{2}+3}{\sqrt{2}+1}\times\frac{\sqrt{2}-1}{\sqrt{2}-1}$

74.

Do you think

\sqrt{\left(3\right)\left(4\right)}

is equal to

\sqrt{3}\times\sqrt{4}

?

a)

Yes

b)

No

75.

Do you think $\sqrt{4+5}$ is equivalent to $\sqrt{4}+\sqrt{5}$ ?

a)

Yes

b)

No

76.

Rationalize the denominator for $\frac{12}{\sqrt{2}}$ .

a)

$6\sqrt{2}$

b)

$-6\sqrt{2}$

c)

$122$

d)

$-\sqrt{2}$

77.

Simplify by rationalizing the denominator:

(Hint: rewrite without a surd on the denominator)

a)

b)

c)

d)

78.

Simplify by rationalising the denominator:

(Hint: Rewrite without surds in the denominator)

a)

b)

c)

d)

79.

Expand and simplify ...

(2 + √3)(3 + √3)

a)

9 + 5√3

b)

6 + 6√3

c)

9 + √3

d)

15 + 5√3

80.

Expand and simplify ...

(3 + 2√2)(1 + 3√2)

a)

15 + 11√2

b)

15 + 5√2

c)

5 + 11√2

d)

5 + 5√2

81.

To rationalize the denominator of this expression you need to multiply by

a)

$\frac{4}{4}$

b)

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

c)

$\frac{4}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{4}$

82.

Rationalize the denominator:
$\frac{1}{4\sqrt{10}}$

a)

$\frac{\sqrt{1}}{4}$

b)

$\frac{\sqrt{10}}{40}$

c)

$\frac{1}{4}$

d)

$\frac{\sqrt{10}}{400}$

83.

Express the following division without any surds in the denominator.

a)

$\frac{\sqrt{7}}{2}$

b)

$\sqrt{2}$

c)

$\frac{\sqrt{14}}{2}$

d)

$\frac{\sqrt{14}}{7}$

e)

cannot be done

84.

Rationalize the denominator:
$\frac{\sqrt{5}}{2\sqrt{3}}$

a)

$\frac{\sqrt{15}}{6}$

b)

$\frac{\sqrt{15}}{18}$

c)

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

d)

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

85.

$\frac{10+8\sqrt{7}}{\sqrt{31}}$

a)

$\frac{3\sqrt{221}}{16}$

b)

$\frac{8\sqrt{31}+11\sqrt{217}}{31}$

c)

$\frac{10\sqrt{31}+8\sqrt{217}}{31}$

d)

$\frac{10\sqrt{33}+8\sqrt{231}}{33}$

86.

Fully simplify...

a)

b)

c)

d)

87.

Find $\sqrt{2}-4$ multiplied with its conjugate.

(a)

88.

Choose two expressions with correct rationalizing the denominator process.

a)

$\frac{8}{3\sqrt{5}}\times\frac{-3\sqrt{5}}{-3\sqrt{5}}$

b)

$\frac{4+\sqrt{3}}{\sqrt{3}-2}\times\frac{4-\sqrt{3}}{4-\sqrt{3}}$

c)

$\frac{5}{1-\sqrt{3}}\times\frac{5}{1+\sqrt{3}}$

d)

$\frac{2\sqrt{2}+3}{\sqrt{2}+1}\times\frac{\sqrt{2}-1}{\sqrt{2}-1}$

89.

Do you think

\sqrt{\left(3\right)\left(4\right)}

is equal to

\sqrt{3}\times\sqrt{4}

?

a)

Yes

b)

No

90.

Do you think $\sqrt{4+5}$ is equivalent to $\sqrt{4}+\sqrt{5}$ ?

a)

Yes

b)

No

91.

Rationalize the denominator for $\frac{12}{\sqrt{2}}$ .

a)

$6\sqrt{2}$

b)

$-6\sqrt{2}$

c)

$122$

d)

$-\sqrt{2}$

92.

$2\sqrt{3}+\sqrt{3}$ is equal to

a)

$2\sqrt{6}$

b)

6

c)

$3\sqrt{3}$

d)

$4\sqrt{6}$

93.

The number obtained on rationalising the denominator of $\frac{1}{\sqrt{7}-2}$ is

a)

$\frac{\sqrt{7}+2}{3}$

b)

$\frac{\sqrt{7}-2}{3}$

c)

$\frac{\sqrt{7}+2}{5}$

d)

$\frac{\sqrt{7}+2}{45}$

94.

Which of the following is irrational?

a)

\sqrt{\frac{4}{9}}

b)

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

c)

$\sqrt{7}$

d)

$\sqrt{81}$

95.

$Multiply\ 6\sqrt{5}by\ 2\sqrt{5}$

a)

70

b)

60

c)

80

d)

50

96.

$Add\ 2\sqrt{2}+\ 5\sqrt{3}\ \ and\ \sqrt{2}-3\sqrt{3}$

a)

$\sqrt{2\ \ }-\sqrt{3}$

b)

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

c)

$3\sqrt{2}-2\sqrt{3}$

d)

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

97.

Simplify $\sqrt{125}\ \times\sqrt{5}$

a)

5

b)

25

c)

35

d)

50

98.

$On\ simplifying\ \left(\sqrt{5\ }+\sqrt{7}\right)²,\ we\ get$

a)

12

b)

$\sqrt{35}$

c)

$\sqrt{5}+\sqrt{7}$

d)

$12+2\sqrt{35}$

99.

After rationalising the denominator of

\frac{7}{3\sqrt{3}-2\sqrt{2}}

, we get the denominator as

a)

13

b)

19

c)

5

d)

35

100.

What is the $\frac{p}{q}$ form of 0.252525... ?

(a)

101.

The number obtained on rationalizing the denominator of $\frac{3}{\sqrt{3}}$ is

a)

3

b)

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

c)

$\sqrt{3}$

d)

$3\sqrt{3}$

102.

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

a)

$y+6=\frac{1}{2}\left(x+6\right)$

b)

$x-2y=16$

c)

$y=\frac{1}{2}x-8$

d)

$y=\frac{1}{2}x-11$

103.

Write a line equation in standard form given the point and slope: (3, -8); slope = -3

a)

$3x+y=1$

b)

$y=-3x+9$

c)

$y+8=-3\left(x-3\right)$

d)

$y=-3x+1$

104.

Write a linear equation in point-slope form given the point and slope: (5, -9), slope = -2/5

a)

$y+5=-\frac{2}{5}\left(x-9\right)$

b)

$y-5=-\frac{2}{5}\left(x+9\right)$

c)

$y-9=-\frac{2}{5}\left(x+5\right)$

d)

$y+9=-\frac{2}{5}\left(x-5\right)$

105.

Write an equation in slope-intercept form given the point and slope: (-4, -7); slope = 1

a)

$y+7=x+4$

b)

$y=x-3$

c)

$y=x-7$

d)

$x-y=3$

106.

Starting at sunrise, the temperature rose 2.5⁰ every hour. After 8 hours, the temperature was 67⁰. Write an equation in point-slope form to model the temperature, y, after x hours after sunrise. If sunrise was at 6:00 AM, what is the temperature at noon?

a)

y+67=2.5(x+8) ; the temperature was 62⁰ at noon

b)

y−67=2.5(x−8); the temperature was 62⁰ at noon

c)

y−67=2.5(x−8); the temperature was 77⁰ at noon

d)

y−8=2.5(x−67); the temperature was 77⁰ at noon

107.

The aquarium is draining a large fish tank. The pump they are using can drain 24 gallons per hour. After 3 hours, there are 78 gallons left in the tank. Write an equation in slope-intercept form to model the water left in the tank, y, after x hours of draining. How many gallons were originally in the tank?

a)

$y=-24x+78$ ; there was 78 gal in the tank initially

b)

$y=24x-150$ ; there was 150 gal in the tank initially

c)

$y=150x-24$ ; there was 24 gal in the tank initially

d)

$y=-24x+150$ ; there was 150 gal in the tank initially

108.

Ben and Julia rented a truck from the same company to move to college. Ben drive 150 miles and paid $64.95 while Julia drove 84 miles and paid $45.15. What is the slope and what does it represent in context to the situation.

a)

m = 0.30; it represents the cost per mile.

b)

m = 0.30; it represents the initial fee for the moving truck

c)

m = 19.95; it represents the initial fee for the moving truck

d)

m = 3.33; it represents the cost per mile.

109.

Allie orders candles from an online company that offers flat rate shipping. She placed an order for 4 candles for $35. A few months later, she placed an order for 12 candles for $95. Write an equation in point-slope form to model the total cost, y, for ordering x candles. How much is shipping?

a)

$y+35=7.5\left(x+4\right)$ ; shipping is $7.50

b)

$y-95=7.5\left(x-12\right)$ ; shipping is $7.50

c)

$y-35=7.5\left(x-4\right)$ ; shipping is $5

d)

$y+95=7.5\left(x+12\right)$ ; shipping is $5

110.

Which equations form a linear function?

a)

$y=2x-5$

b)

$y=x^2+2$

c)

$y=-x$

d)

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

111.

If g(x) represents a vertical shift of f(x) = -x up 4 units followed by a vertical stretch (steepness) by a factor of 3. What is the rule of g(x)?

a)

$g\left(x\right)=-3x+12$

b)

$g\left(x\right)=-4x+12$

c)

$g\left(x\right)=-x+4$

d)

$g\left(x\right)=-3x+4$

112.

Which equation represents the graph of the function with point (-2, 5) and slope of 3?

a)

$y=3x+5$

b)

$y-5=3\left(x+2\right)$

c)

$3x-y=11$

d)

$y-5=3\left(x-2\right)$

113.

What is the equation and slope of the line shown on the grid?

a)

y = 6; slope is -1

b)

x = 6; slope is zero

c)

y = 6; slope is 6

d)

x = 6; slope is undefined

114.

Which equation represents y = -3x + 5 in point-slope form?

a)

$y+7=-3\left(x-4\right)$

b)

$y+1=-3\left(x+2\right)$

c)

$y-4=3\left(x+7\right)$

d)

$y-2=3\left(x-1\right)$

Aisha Quiz

Total questions: 114

Worksheet time: 3hrs 3mins

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