Free Printable ALIYAAH LUNA'S MATH

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Worksheets

ALIYAAH LUNA'S MATH

Total questions: 146

Worksheet time: 2hrs 50mins

Name

Class

Date

1.

$\sqrt{45}$ Simplify:

a)

$9\sqrt{5}$

b)

$3\sqrt{5}$

c)

$5\sqrt{9}$

d)

$15\sqrt{3}$

2.

$\sqrt{75x^2}$

a)

$5x^2\sqrt{3}$

b)

$5x$

c)

$5x\sqrt{3x}$

d)

$5x\sqrt{3}$

3.

Simplify... $4\sqrt{75}$

a)

$4\sqrt{5}$

b)

$12\sqrt{5}$

c)

$20\sqrt{3}$

d)

$7\sqrt{3}$

4.

Simplify $\sqrt{50x^4}$

a)

$25x^2\sqrt{2}$

b)

$5x\sqrt{2}$

c)

$25x^2$

d)

$5x^2\sqrt{2}$

5.

$\sqrt{45x^4y^7}$

a)

$3x²y³\sqrt{5}$

b)

$9x²y³\sqrt{5y}$

c)

$3x²y³\sqrt{5y}$

d)

$3x⁴y⁷$

6.

a)

30

b)

43

c)

46

d)

54

7.

Solve the equation:
2x - (3x + 1) = 2(x + 4)

a)

x=-3

b)

x=3

c)

x=-7/3

d)

x=7/3

8.

Write the improper fraction as a mixed number

²³/₅

a)

4 ³/₅

b)

4 ⁵/₃

c)

5 ³/₄

d)

4 ³/₄

9.

Write the improper fraction as a mixed number

³⁶/₄

a)

9 ¹/₄

b)

9 ³/₄

c)

8 ⁴/₄

d)

9

10.

Write the improper fraction as a mixed number

²²/₃

a)

7 ²/₃

b)

7 ¹/₃

c)

7 ¹/₄

d)

7 ³/₄

11.

Write the improper fraction as a mixed number

²⁷/₈

a)

3 ²/₈

b)

4 ³/₈

c)

8 ³/₄

d)

3 ³/₈

12.

Write the improper fraction as a mixed number in simplest form

a)

3 ²/₉

b)

3 ³/₉

c)

9 ³/₉

d)

3 ¹/₃

13.

Write the mixed number as an improper fraction

2 ¹/₄

(a)

14.

Write the mixed number as an improper fraction

5 ⁶/₇

(a)

15.

Write the mixed number as an improper fraction

3 ⁴/₉

(a)

16.

Write the mixed number as an improper fraction

4 ⁵/₈

(a)

17.

Write the mixed number as an improper fraction

7 ⁵/₁₁

(a)

18.

Write the mixed number as an improper fraction

2 ³/₅

(a)

19.

Carl said that ⁹/₄ and 1 ¹/₄ are equal, is he correct?

a)

yes

b)

no

20.

What fractions corresponds with point A

a)

⁴/₂

b)

1 ³/₈

c)

⁹/₄

d)

¹/₂

e)

3³/₄

21.

a)

3/4

b)

4/3

c)

160/75

d)

75/160

22.

a)

-3

b)

1/3

c)

3

d)

-1/3

23.

a)

1/6

b)

-6

c)

6

d)

-1/6

24.

a)

1/18

b)

18

c)

-18

d)

-1/18

25.

a)

1/6

b)

-6/25

c)

-24

d)

6/25

26.

a)

-6

b)

3/32

c)

-2/3

d)

-3/32

27.

a)

-25/12

b)

-1/3

c)

-3

d)

-12/25

28.

Mr. Gomez had 3/4 of a cake to divide amongst 6 guests. What part of the cake will each guest receive?

a)

1/8

b)

8

c)

9/2

d)

3/4

29.

Karen has 12 1/2 yards of material. A cape for play takes 3 5/6 yards. How many capes can Karen make with the material?

a)

4

b)

36

c)

9

d)

3

30.

The club members hiked 3 kilometers north and 4 kilometers east, but then went directly home as shown by the dotted line. How far did they travel to get home?

a)

4 km

b)

5 km

c)

6 km

d)

7 km

31.

Triangle XYZ is a right triangle with legs measuring 8 cm and 15 cm. What is the length of XZ?

a)

23 cm

b)

21 cm

c)

19 cm

d)

17 cm

32.

Jamie and Fred are meeting Sarita at her house. Jamie must use the crosswalk in front of Fred’s house to cross the street.

a)

66 ft

b)

130 ft

c)

178 ft

d)

199 ft

33.

Which statement about the length of the hypotenuse of a right triangle whose legs are 7.5 inches and 8.5 inches is true?

a)

The hypotenuse is between 8 and 9 inches.

b)

The hypotenuse is between 9 and 10 inches.

c)

The hypotenuse is between 10 and 11 inches.

d)

The hypotenuse is between 11 and 12 inches.

34.

A rectangular piece of paper measures 10 centimeters wide by 17 centimeters long. What is the length of the paper’s diagonal to the nearest centimeter?

a)

14 centimeters

b)

17 centimeters

c)

20 centimeters

d)

27 centimeters

35.

What is the length of a diagonal of the field?

a)

120 ft.

b)

200 ft.

c)

394 ft.

d)

520 ft.

36.

Based on the measurements in the diagram, what is k?

a)

A. 8 ft.

b)

B. 11 ft.

c)

C. 12 ft.

d)

D. 18 ft.

37.

Alex is building a ramp for a bike competition. He has two rectangular boards. One board is 6 meters long and the other is 5 meters long. If the ramp has to form a right triangle, what should its height be?

a)

3 meters

b)

4 meters

c)

3.3 meters

d)

7.8 meters

38.

A right angle is made where the top of a ladder meets the top of a slide as shown in the picture below. What is the length of the slide?

a)

√8 meters

b)

8 meters

c)

12 meters

d)

√194 meters

39.

The ladder needs to lean against the house at a height of 24 feet. How far should Cheri place the base of the ladder from her house?

a)

1 foot

b)

7 feet

c)

35 feet

d)

49 feet

40.

What is the value of x in the right triangle shown below?

a)

8 feet

b)

12 feet

c)

18 feet

d)

23 feet

41.

If the television screen shown above is 20 inches wide, what is the height, in inches, of the screen?

a)

√45

b)

√90

c)

10

d)

15

42.

A triangle is a right triangle if the lengths, a, b, and c, of its three sides satisfy the following equation: $a^2 + b^2 = c^2$ Which of the following is a right triangle?

a)

A. a triangle with sides measuring 13, 15, and 19

b)

B. a triangle with sides measuring 17, 25, and 36

c)

C. a triangle with sides measuring 20, 21, and 29

d)

D. a triangle with sides measuring 18, 23, and 41

43.

A window washer leans a 13–foot ladder against a house. The bottom of the ladder is 5 feet from the house. How high is the second-floor window off the ground?

a)

12 feet

b)

8 feet

c)

18 feet

d)

√194

44.

In the figure below, D is the midpoint of AC, and BD is perpendicular to AC. What is the length of BD?

a)

15 centimeters

b)

16 centimeters

c)

18 centimeters

d)

20 centimeters

45.

The legs of a right triangle measure 20 centimeters and 21 centimeters. How long is the hypotenuse in centimeters?

a)

22

b)

25

c)

29

d)

35

46.

The lengths of the sides of △MNO are 40 centimeters, 50 centimeters, and 30 centimeters. Which formula could be used to show that △MNO is a right triangle?

a)

$30^2 + 40^2 = 50^2$

b)

$30^2 + 50^2 = 40^2$

c)

$40^2 + 50^2 = 30^2$

d)

$40^2 - 30^2 = 50^2$

47.

Mike leans a 10-foot ladder against a wall. He puts the bottom of the ladder 3 feet away from the wall. Approximately how far up the wall does the ladder go?

a)

7.0 feet

b)

9.5 feet

c)

10.4 feet

d)

13.0 feet

48.

What is the approximate area of the shaded region?

a)

70 cm²

b)

12 cm²

c)

82 cm²

d)

58 cm²

49.

Find the area of this shape

a)

60 units squared

b)

45 units squared

c)

65 units squared

d)

30 units squared

50.

Find the area of the shape. Give your answer to 1 decimal place...

a)

63.6cm²

b)

254.5cm²

c)

127.2cm²

d)

56.5cm²

51.

Find the area of the shape. Give your answer to 1 decimal place...

a)

39.3cm²

b)

78.5cm²

c)

15.7cm²

d)

31.4cm²

52.

Find the area of the shape. Give your answer to 1 decimal place...

a)

56.5cm²

b)

226.2cm²

c)

113.1cm²

d)

37.7cm²

53.

a)

54 cm2

b)

45 cm2

c)

63 cm2

d)

36 cm2

54.

Find the area of the figure

a)

43 sq inches

b)

102 sq inches

c)

37 inches

d)

90 sq inches

55.

What is the area of the composite figure?

a)

144 m²

b)

111 m²

c)

45 m²

d)

70 m²

56.

Find the area

a)

150m²

b)

120m²

c)

126m²

d)

200m²

57.

What is the area of the composite figure?

a)

80 cm²

b)

16 cm²

c)

96 cm²

d)

32 cm²

58.

_{Find the area.}

a)

28 square cm

b)

36 square cm

c)

40 square cm

d)

36 square feet

59.

What is the area of the composite shape?

a)

40ft²

b)

9ft²

c)

49ft²

d)

61ft²

60.

Identify the a, b, and c in this quadratic expression

4x² - 10x + 3

a)

a = 3, b = -10, c = 4

b)

a = 3, b = 4, c = -10

c)

a = -10, b = 3, c = 4

d)

a = 4, b = -10, c = 3

61.

Identify the a, b, and c in this quadratic expression

7 + 13x - 19x²

a)

a = 7, b = 13, c = -19

b)

a = 13, b = 7, c = -19

c)

a = -19, b = 13, c = 7

d)

a = 7, b = -19, c = 13

62.

4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

63.

Solve: 5x - 14 = 8x + 4

a)

6

b)

-6

c)

-18/13

d)

10/3

64.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

65.

Solve the following equations
4 (x + 3) = 2x + 5

a)

7/2

b)

- 7/2

c)

2

d)

7

66.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

67.

What operation would you perform first and then second when solving for m in the following equation?
10 + 7m = 17

a)

subtract 10, divide by 7

b)

divide by 7, subtract 10

c)

multiply by 7, add 10

d)

add 10, multiply by 7

68.

Solve the equation.
14 − 4(2k + 4) = -2(4 − 3k)

a)

k = -³⁄₇

b)

k = ³⁄₇

c)

k = ⁵⁄₇

d)

k = ⁷⁄₃

69.

Solve for x:

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

a)

x = 20

b)

x = 7

c)

x = 10

d)

x = 3

70.

Solve for x:

$8x-4\left(x+8\right)=8$

a)

x = 2

b)

x = 10

c)

x = 4

d)

x = -4

71.

Solve for x:

3(3x - 6) = 18

a)

x = 4

b)

x = -4

c)

no solution

d)

infinite solutions

72.

2(4x - 3) - 8 = 4 + 2x

a)

x = 1

b)

x = 3

c)

x = 5/6

d)

x = -3

73.

Solve:
2(2x + 3) = -6(x + 9)

a)

1.2

b)

6

c)

-6

d)

7.5

74.

Solve for x.

\frac{2\ }{3}x=4

a)

3

b)

4

c)

5

d)

6

75.

Solve for x.

\frac{3}{7}x-8=1

a)

-16

b)

21

c)

-3

d)

9

76.

-14 + 6b + 7 - 2b = 1 + 5b

a)

no solution

b)

-8

c)

45

d)

-35

77.

3(x - 5) - x = 1

a)

x = 4

b)

x = 8

c)

x = 3

d)

x = 2

78.

S = 3F - 24 Solve for F

a)

F = (S + 24)/3

b)

F = S/3 + 24

c)

F = 3S + 24

d)

F = 3(S + 24)

79.

Solve m - n = 5 for m.

a)

m = 5 + n

b)

m = -5 - n

c)

m = -5 + n

d)

m = 5 - n

80.

Solve for t.
D= rt

a)

D/r = t

b)

Dr = t

c)

D/t = r

d)

Dt = r

81.

What should we do first to solve for x?
y=mx+b

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

82.

$\frac{m+4}{2}-\frac{2\left(1-3m\right)}{3}$

a)

$\frac{2-5m}{6}$

b)

$\frac{7m+2}{6}$

c)

$\frac{15m+8}{6}$

d)

$\frac{8-9m}{6}$

83.

$\frac{p}{3m}-\frac{1-p}{m}$

a)

$\frac{pm-3m-p}{3m^2}$

b)

$\frac{pm-3m+p}{3m^2}$

c)

$\frac{4p-3}{3m}$

d)

$\frac{-2p-3}{3m}$

84.

$\frac{m}{n}+\frac{1-2m}{2n}$

a)

$\frac{1+m}{2n}$

b)

$\frac{n+m}{2n}$

c)

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

d)

$\frac{1}{3n}$

85.

Simplify the algebraic fraction.

a)

1/a

b)

8a/9

c)

9/8a

d)

9a/8

86.

a)

10a/10b

b)

10a/5b

c)

2a/b

d)

a/b

87.

a)

(2k-6l )/12

b)

(4k-12l )/24

c)

(k-3l)/6

d)

(3d-2l)/24

88.

a)

2a/0

b)

2a/5

c)

2a/10

d)

2a

89.

Given that p = 2q + 4, express q in terms of p.

Diberi p = 2q + 4, ungkapkan q dalam sebutan p.

a)

$2q\ =\ p\ -\ 4$

b)

$2q\ =\ p\ +\ 4$

c)

$q\ =\ \frac{p\ -\ 4}{2}$

d)

$q\ =\ \frac{p\ +\ 4}{2}$

90.

Given,
Diberi,
$m\ =\ \sqrt{n}\ -\ 1$
State n, as the subject of formula.
Ungkapkan n sebagai perkara rumus.

a)

$n\ =\ \left(m\ -1\ \right)^2$

b)

$n\ =\ \left(m\ +1\ \right)^2$

c)

$n\ =\ \sqrt{m\ -1}$

d)

$n\ =\ \sqrt{m\ +\ 1}$

91.

Given that,
Diberi,
$y\ =\ 5x^2$
express x in terms of y.
ungkapkan x dalam sebutan y.

a)

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

b)

$x\ =\ \sqrt{y-5}$

c)

$x=\ \sqrt{5y}$

d)

$x\ =\ \sqrt{\frac{y}{5}}$

92.

Given that,
Diberi,
$m\ =\ \frac{a\ -\ b}{c\ -\ d}$
find the value of m when a = 2, b = 8, c = 5 and d = 1.
cari nilai v apabila a = 2, b = 8, c = 5 dan d = 1.

a)

$-\frac{3}{2}$

b)

$\frac{3}{2}$

c)

$\frac{5}{2}$

d)

$-\frac{5}{2}$

93.

The area of the trapezium below is 36 cm². If x + y = 11 cm, calculate the value of x and y.

Luas trapezium di bawah ialah 36 cm². Jika x + y = 11 cm, hitung nilai x dan y.

a)

x = 5, y = 4

b)

x = 5, y = 7

c)

x = 4, y = 7

d)

x = 4, y = 5

94.

Mark ( √ ) if x is the subject of the formula.

Tandakan ( √ ) jika x ialah perkara rumus.

a)

2x = 4y² + 3

b)

x = 3y -4z

c)

x =9px - y

d)

y = x + 5

95.

p = r + 8.

Express r in terms of p.

a)

p - 8

b)

8 - p

c)

p + 8

96.

p = 2m - n

Express m in terms of n.

a)

(p + n)/2

b)

(p - n)/2

c)

(n - p)/2

d)

2(p + n)

97.

Given that k = 4s + 5t, find the value of t when k= 30 and s = 5.

Diberi k = 4s + 5t, cari nilai t apabila k= 30 dan s = 5.

a)

-10

b)

10

c)

-2

d)

2

98.

The area, A of trapezium ABCD is given by the formula A = ½ h (a + b).
Which of the following is true?

a)

h is the length of AB

b)

h is the length of DC

c)

a is the length of AB

d)

b is the length of DC

99.

Diagram shows a trapezium. state the formula of the area of the trapezium.

a)

$\frac{1}{2}\times\left(p+r\right)\times9$

b)

$9\times r$

c)

$9\times r\times p$

d)

$\frac{1}{2}\times9\times p\times r$

100.

Simplify the algebraic fraction.

a)

1/a

b)

8a/9

c)

9/8a

d)

9a/8

101.

a)

2a/0

b)

2a/5

c)

2a/10

d)

2a

102.

a)

4a/2

b)

2a

c)

3a/2

d)

4a/4

103.

a)

10a/10b

b)

10a/5b

c)

2a/b

d)

a/b

104.

a)

a/2

b)

3a/6

c)

8a/6

d)

7a/6

105.

a)

(2k-6l )/12

b)

(4k-12l )/24

c)

(k-3l)/6

d)

(3d-2l)/24

106.

a)

8m²/8n²

b)

13m/4n

c)

13m²/4n²

d)

8m/8n

107.

$\frac{8}{5d+4}-\frac{1}{2d-3}=$

a)

$\frac{11d-20}{\left(5d+4\right)\left(2d-3\right)}$

b)

$\frac{21d-28}{\left(5d+4\right)\left(2d-3\right)}$

c)

$\frac{11d-28}{\left(5d+4\right)\left(2d-3\right)}$

d)

$\frac{21d+20}{\left(5d+4\right)\left(2d-3\right)}$

108.

a)

A

b)

B

c)

C

d)

D

109.

a)

A

b)

B

c)

C

d)

D

110.

a)

A

b)

B

c)

C

d)

D

111.

$\frac{3}{x-4}+\frac{x}{2x+7}$

a)

$\frac{x^2+2x+21}{\left(x-4\right)\left(2x+7\right)}$

b)

$\frac{x^2+6x+21}{\left(x-4\right)\left(2x+7\right)}$

c)

$\frac{x^2+6x+7}{\left(x-4\right)\left(2x+7\right)}$

d)

$\frac{x^2+2x+7}{\left(x-4\right)\left(2x+7\right)}$

112.

What is the probability that the sun will rise tomorrow?

a)

Likely

b)

Unlikely

c)

Impossible

d)

Certain

113.

The numbers 1 to 20 are each written on a card. The 20 cards are mixed together. Find the probability that the number on the the card is a factor of 24

a)

1/20

b)

5/20

c)

1/2

d)

7/20

114.

The numbers 1 to 20 are each written on a card. The 20 cards are mixed together. Find the probability that the number on the the card prime

a)

2/5

b)

3/5

c)

5/7

d)

3/7

115.

A fair die is thrown once. Find the probability of obtaining an odd number

a)

1/3

b)

1/2

c)

3/5

d)

1/6

116.

a fair coin is tossed and a fair die is rolled. Find the probability of obtaining a 'head' and a 'six'

a)

1/2 x 1/6 = 1/12

b)

1/2 + 1/6 = 4/6

c)

1/8

d)

1/7

117.

A bag contains 8 red marbles, 4 blue marbles and 2 yellow marbles. What is the probability of randomly taking a yellow marble out of the bag?

a)

1/6

b)

1/7

c)

1/2

d)

2/13

118.

What is the probability of rolling an even number on a dice?

a)

1/3

b)

2/3

c)

1/2

d)

1/6

119.

The probability of rolling a prime number on a dice is:

a)

1/3

b)

2/3

c)

1/2

d)

1/6

120.

An unlikely chance event is closer to what number?

a)

0

b)

1

c)

0.5

d)

100

121.

The probability of it raining today is 30%. What is the probability that it will NOT rain?

a)

30%

b)

70%

c)

100&

d)

0%

122.

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then without putting the first card back, he picks a second card at random.

a)

Independent

b)

Dependent

123.

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced. P(purple then black)

a)

1/18

b)

2/5

c)

3/7

d)

4/9

124.

There are six nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. Both times the coin is a nickel.

a)

2/7

b)

6/13

c)

5/16

d)

3/19

125.

Sue will randomly select from a treat bag containing 6 lollipops and 4 gum balls. Sue will select a treat, not replace it, and then select a second treat.

a)

Independent

b)

Dependent

126.

A bag contains 5 red balls and 3 green balls. A ball is drawn at random and then replaced. Another ball is drawn. What the probability that both ball are green?

a)

3/8

b)

1/2

c)

9/64

d)

6/8

127.

Total number of outcomes when tossing a single coin

(a)

128.

Total outcomes when tossing a single die.

(a)

129.

How many red face cards are there in a deck of 52 playing cards?

(a)

130.

How many black ace cards are there in a deck of 52 playing cards ?

(a)

131.

Find the number of heart jack in a deck of 52 cards

(a)

132.

Probability can never be more than ?

(a)

133.

Find the probability of having exactly one head while tossing two coins simultaneously

a)

2/4

b)

1/4

c)

3/4

d)

1

134.

Find the total possible outcomes of throwing two dice simultaneously

a)

6

b)

12

c)

36

d)

None of these

135.

If i have numbers from 1 to 100.i have to select one number at random.What is the probaility that selected number is a perfect square?

a)

0.1

b)

0.01

c)

1

d)

0.8

136.

In a deck of 52 cards ,if one card is selected at random. What is the probability that the card drawn is a red card?

a)

0.5

b)

0 4

c)

0.3

d)

0.2

137.

What is sample space?

a)

All of the Outcomes

b)

What Will Happen

c)

What Can Happen

d)

What I want to Happen

138.

Which of the following situations is represented by this tree diagram?

a)

3 shirt options, 6 pants options, and 12 shoe options

b)

3 shirt options, 2 pants options, and 2 shoe options

c)

2 shirt options, 3 pants options, and 1 shoe option

139.

Which shows the sample space for flipping two coins?

a)

H, T

b)

HH, HT, TH, TT

c)

HH, TT

d)

Dime, Nickel

140.

The possible results of an experiment

a)

outcomes

b)

event

c)

experiment

d)

probability

141.

If I flip 3 coins, how many outcomes are there?

a)

3

b)

6

c)

8

d)

12

142.

If I flip a coin and role a dice, how many outcomes are there?

a)

4

b)

6

c)

9

d)

12

143.

Tree Diagram

a)

A written list of all possible outcomes

b)

A description of all possible outcomes

c)

A drawing with branches of all possible outcomes

144.

What is the probability of rolling 15 with a pair of dice?

a)

impossible

b)

unlikely

c)

equally likely

d)

likely

145.

100% chance of something happening

a)

Uncertain

b)

Impossible

c)

Possible

d)

Certain

146.

You spin the spinner. How many possible outcomes are there?

(Color does not matter)

a)

4

b)

8

c)

1

d)

6

100 %

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