Free Printable Pearlspedia Year 9 mathematics

1.

Expand $3x(4+y)$ .

a)

$12x-3xy$

b)

$12x+3xy$

c)

I don’t know 😓

2.

Expand $-4y(2x+3)$ .

a)

$-8xy-12y$

b)

$-8xy+12y$

c)

I don’t know 😓

3.

Expand $x(3x-y)$ .

a)

$3x^2-xy$

b)

$3x^2+xy$

c)

I don’t know 😓

4.

Expand $-3y(2y-3x)$ .

a)

$9xy-6y^2$

b)

$-9xy-6y^2$

c)

I don’t know 😓

5.

Expand $2x(y+z)+3x(2y+z)$ .

a)

$x(8y+5)$

b)

$8yx+6z$

c)

$5xz+8xy$

d)

I don’t know 😓

6.

Expand $3x(3y+2z)+4x(5y+2z)$ .

a)

$x(29y+14z^2)$

b)

$z(14x+29yx)$

c)

$29xy+14xz$

d)

I don’t know 😓

7.

Expand $(x+2y)(x+3y)$ .

a)

$5x^2y^2+x^2+6y^2$

b)

$x^2+6y^2+5x^2y^2$

c)

$x^2+5xy+6y^2$

d)

I don’t know 😓

8.

Expand $(2x+5y)(3x-y)$ .

a)

$6x^2-13xy-5y^2$

b)

$6x^2+13xy-5y^2$

c)

$6x^2+17xy-5y^2$

d)

I don’t know 😓

9.

Expand $(x^2+6)(2x+3)$ .

a)

$5x^2+12x+18$

b)

$2x^3+3x^2+12x+18$

c)

$3x^2+3x^2+12x+18$

d)

I don’t know 😓

10.

Expand $2(2x+1)(3x+2)$ .

a)

$12x^2+14x+4$

b)

$24x^2+28x+8$

c)

$12x^2+2x+4$

d)

I don’t know 😓

11.

Solve the equation
3x = 27.

a)

x = 24

b)

x = 81

c)

x = 9

d)

x = 3

12.

In the equation 4c + 8 = 14, c is the ______________.

a)

constant

b)

coefficient

c)

calculation

d)

variable

13.

5x - 2x =

a)

3 - x

b)

3x

c)

x + 3

d)

3 - x

e)

I'm not sure

14.

How many terms in the following expression:

5x + 3y - 15 + x

a)

1

b)

2

c)

3

d)

4

e)

I'm not sure

15.

Simplify

3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

e)

I'm not sure

16.

If a = 4 and b = 6, what is the value of 3a + 5b?

a)

40

b)

42

c)

44

d)

46

e)

I'm not sure

17.

Which of the following is the correct expansion of:

5(r - 2)?

a)

5r - 2

b)

5r +2

c)

5r + 10

d)

5r - 10

e)

I'm not sure

18.

Expand (x+9)(x-9)

a)

x²-18x-81

b)

x²-81

c)

x²+81

d)

x²+18x-81

e)

I'm not sure

19.

3x - 5 = -26

a)

x=-21

b)

x=21

c)

x=-7

d)

x=61

e)

I'm not sure

20.

Solve for x:

4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

e)

I'm not sure

21.

Expand and simplify 4(x + 2) + 3(x + 5)

a)

7x + 23

b)

7x + 7

c)

7x + 15

d)

7x

22.

Factorise 4x + 8

a)

2(x + 4)

b)

4(x + 2)

c)

4x(x + 2)

d)

12x

23.

What is the highest factor or 12 and 16?

a)

12

b)

16

c)

2

d)

4

24.

Expand -2(x-2)

a)

-2x+4

b)

2x-4

c)

-2x-4

d)

2x-2

25.

Expand and Simplify 3(x+4)+1

a)

3x+13

b)

3x+7

c)

3x+11

d)

3x+15

26.

Expand and Simplify 2(x+2)-2(x+3)

a)

2

b)

4x+8

c)

-2

d)

4x-6

27.

Expand and Simplify 4(x+2)-3(x+1)

a)

x+3

b)

7x+1

c)

x+5

d)

5x+11

28.

Expand and Simplify 4(3x+1)-(x+5)

a)

11x+1

b)

7x+13

c)

11x-1

d)

13x+1

29.

6w - 6w + 6w + 9w

a)

w

b)

15w

c)

9w

d)

6w

30.

Simplify the expression: 7v + 2 + 12 + 2v

a)

23

b)

23v

c)

9 + 14v

d)

9v + 14

31.

w + w + w could be simplified as?

a)

3w

b)

3

c)

w

d)

0

32.

−x²+2−1+6x²−4x²

a)

x ² -1

b)

x² +1

c)

3x² +1

d)

x ²+3

33.

4a + 9 + a

a)

5a + 9

b)

14a

c)

3a + 9

d)

5a - 9

34.

Simplify 6(x + -2)

a)

6x + -2

b)

6x + -12

c)

4x

d)

6x - 2

35.

Simplify the expression: 7+3(1 - 2x)

a)

21 - 6x

b)

10 - 2x

c)

10 - 20x

d)

10 - 6x

36.

-12n - (-13n)

a)

-25n

b)

25n

c)

n

d)

-n

37.

Simplify the expression:
6 + 2(7x - 3)

a)

12 + 7x

b)

14x

c)

14x + 3

d)

9 + 7x

38.

(x - 5)(x + 3)(x + 2)

a)

x³ - 5x² + 11x - 30

b)

x³ + 6x² + 30

c)

x³ +-19x - 30

d)

x³ + 6x² - 30

39.

(3x+2)(2x +3)

a)

6x²+ 6x + 6

b)

5x² + 11x + 6

c)

6x² + 13x + 6

d)

6x²+ 13x + 5

40.

Expand (x + 5)(x - 3)

a)

x² - 15

b)

x² + 2x

c)

x² + 15x - 15

d)

x² + 2x - 15

41.

Factorise: 4x² + 8x

a)

4x(x+2)

b)

4(x²+2x)

c)

2x(2x+4)

d)

2(2x²+4)

42.

Which of the following is the correct expansion of:
3p(4p - 7q)?

a)

7p - 10pq

b)

12pq - 21q²

c)

9q

d)

12p² - 21pq

43.

Expand 4(x+2)

a)

4x+4

b)

4x+2

c)

4x+8

d)

4x+6

44.

Which is a linear equation?

a)

$y=4x+2$

b)

$5$

c)

$mx$

d)

$4s$

45.

Which is a linear equation?

a)

$2x\ +\ 3y$

b)

$y\ =\ \frac{1}{4}x\ +\ 3$

c)

$7x$

d)

$7$

46.

Which is a linear equation?

a)

$2x+3y$

b)

$5x$

c)

$3x+24$

d)

$y=2x-10$

47.

Which is a linear equation?

a)

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

b)

$y\ +\ 3$

c)

$y\ =7x$

d)

$x+3$

48.

Which is not a linear equation?

a)

$y=7x-3$

b)

$y=2x+7$

c)

3x+7y

d)

$y=3x$

49.

Which is a linear equation?

a)

$y=\frac{2}{5}x-13$

b)

$13$

c)

$\frac{1}{9}x$

d)

$3+4$

50.

Which is a linear equation? Check all that apply.

a)

$y=\frac{3}{7}x-\frac{4}{3}$

b)

$2+7$

c)

$3x+7$

d)

$54+x$

51.

13uv - 8 + vu + 7

a)

A) 12uv - 15

b)

B) 5uv + vu + 7

c)

C) 13uv - 1 + vu

d)

D) 14uv - 1

52.

- 9 - rs + 9rs + 9

a)

A) 8rs

b)

B) 18 + 8rs

c)

C) 10rs

d)

D) - 18 - 8rs

53.

20stu - 8u - 12uts - 3 + u

a)

A) 8stu - 7u - 3

b)

B) 8stu - 9u - 3

c)

C) 20stu - 7u - 12uts - 3

d)

D) 20uts - 9u - 12uts - 3

54.

7+7×7−7∕ 7×(7+7)

a)

42

b)

7

c)

14

d)

none of these

55.

3⁷+3⁷+3⁷=⋅⋅⋅⋅⋅⋅⋅

a)

9⁷

b)

3²¹

c)

3⁸

d)

27⁷

56.

IF(x-y)=3 & (x²-y²)=15,THEN(x+y)=......

a)

10

b)

5

c)

45

d)

20

57.

3 + 2³ - 8

a)

8

b)

1

c)

3

d)

-3

58.

-3(x - 3) + 6(x + 1)

a)

3x + 6

b)

3x + 4

c)

-3x + 16

d)

3x + 15

59.

4a + 8 = -20

a)

-6

b)

-7

c)

3

d)

-3

60.

8(x - 1) = 4(x + 4) - 2x

a)

2

b)

6

c)

-2

d)

4

61.

35 is 29% of what?

a)

10.2

b)

1015

c)

120.7

d)

1.2

62.

It takes you 30 minutes to ride 8 miles on your bike, about how long will it take you to ride 10 miles?

a)

34 minutes

b)

38 minutes

c)

32 minutes

d)

40 minutes

63.

(4x⁹)(5x^-5)

a)

20x^-45

b)

9x⁴

c)

9x^-4

d)

20x⁴

64.

(3x² - 5x + 7) - (2x² + 9x - 1)

a)

x² - 4x + 6

b)

5x² - 4x + 8

c)

x² - 14x + 8

d)

x² + 4x + 6

65.

(5a - 4)(3a - 7)

a)

15a² - 23a - 28

b)

15a² - 47a + 28

c)

15a² + 47a - 28

d)

15a² - 23a + 28

66.

Solve the following equation for v

42=6+9v

a)

5.33

b)

39

c)

4

d)

3

67.

Solve the following equation for w

5w + 5 = -90

a)

19

b)

-19

c)

17

d)

-17

68.

Solve for k

-20 = k - 2 + 8k

a)

-2

b)

2

c)

-3

d)

3

69.

Solve for z

2(z + 4) = 20

a)

14

b)

13

c)

7

d)

6

70.

Solve for p

4(p - 2) = 2(p + 5)

a)

1

b)

6

c)

8

d)

9

71.

Solve for x

-130 = -5(4x + 2)

a)

7

b)

6

c)

-6

d)

-7

72.

Solve for v

4(8v - 8) = 192

a)

7

b)

5

c)

-5

d)

-7

73.

Solve for b

-108 = -b - 8(1 + 3b)

a)

-5

b)

4

c)

-4

d)

5

74.

Solve for x

6(x + 2) = 6 + 3x

a)

6

b)

-6

c)

2

d)

-2

75.

Solve for m

-7 + 7m = 1 + 6m

a)

-6

b)

8

c)

-8

d)

6

76.

Simplify by combining like terms:

5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

77.

Simplify d + d + d + d =

a)

d⁴

b)

4d

c)

d4

d)

4 + d

78.

Solve
$3x+y=1$
$x-2y=19$

a)

$x=-4,\ y=3$

b)

$x=3,\ y=-4$

c)

$x=3,\ y=-8$

d)

$x=4,\ y=8$

79.

Solve:

3x - y = 11

x + y = 5

a)

x = 4

y = 1

b)

x = 4

y = -1

c)

x = -4

y = 1

d)

x = -4

y = -1

80.

Solve the Simultaneous Equations: x+y=5; x-y=1

a)

x=2, y=3

b)

x=3, y=2

c)

x=3, y=-2

d)

x=-3, y=2

81.

Solve:

3x - y = 11

x + y = 5

a)

x = 4

y = 1

b)

x = 4

y = -1

c)

x = -4

y = 1

d)

x = -4

y = -1

82.

Two pencils and a ruler cost 49 Naira in total. One pencil and two rulers cost 62 Naira in total. Find the cost of each item.

a)

pencil: 13 Naira

ruler: 23 Naira

b)

pencil: 15 Naira

ruler: 23.50 Naira

c)

pencil: 12 Naira

ruler: 25 Naira

d)

pencil: 18 Naira

ruler: 26 Naira

83.

Cinderella had brochures printed for a new business venture. Cinderella originally ordered 4 boxes of black-and-white brochures and 3 boxes of colour brochures, which cost a total of N134. After those ran out, Cinderella spent N120 on 3 boxes of black-and-white brochures and 3 boxes of colour brochures. Which simultaneous equations represent this situation?

a)

x+y=134

x+y=120

b)

3x+3y=134

4x+3y=120

c)

4x+3y=134

3x+3y=120

d)

7xy=134

6xy=120

84.

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?

a)

3/10

b)

3/9

c)

1/9

d)

1/3

85.

In a drawer, there are 6 white socks, 4 black socks, and 2 brown socks. You pick out a sock, replace it, then pick out a 2nd sock. What is the probability that you will pick a brown, then black sock?

a)

1/11

b)

1/18

c)

1/36

d)

2/33

86.

In a cup are the numbers 1 - 20. Find the theoretical probability of
picking an even number.

a)

10/20

b)

1/2

c)

1/20

d)

20/20

87.

In a cup are the numbers 1 - 20. Find the theoretical probability of
picking a number divisible by 5.

a)

4/20

b)

1/5

c)

5/20

d)

1/4

88.

Find the theoretical probability of NOT landing on yellow if you spin the spinner.

a)

1/8

b)

7/8

c)

1

d)

7

89.

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%

90.

A set of all possible outcomes is known as -

a)

a list

b)

a complement

c)

a sample space

d)

an event

91.

if the experimental probability of the roll of a dice is given below

Roll dice: 1, 3, 3, 4, 4

then the probability of obtaining a 1 is

a)

3/5

b)

1/6

c)

2/5

d)

1/5

92.

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

a)

5/6

b)

1/2

c)

1/3

d)

1/6

93.

What is the probability of choosing a vowel from the alphabet?

a)

21/26

b)

5/26

c)

1/21

d)

7/21

94.

Theoretical Probability is?

a)

What Should happen

b)

What does happen

c)

What Will Happen

d)

What I want to Happen

95.

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

a)

impossible

b)

unlikely

c)

equally likely

d)

likely

96.

The two rectangles are scale drawings. What is the measurement of x?

a)

21

b)

1.25

c)

20

d)

4

97.

The scale drawing car length is 3 cm. If the scale is 1 cm to 4 feet, what is the actual car length?

a)

12 feet

b)

16 feet

c)

10 feet

d)

4 feet

98.

A model of a flagpole has a scale of 1 cm.= 4 m. If the model pole measures 12 cm, how tall is the actual pole?

a)

16 m

b)

3 m

c)

48 m

d)

9 m

99.

Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?

a)

14 in

b)

7 in

c)

42 in

d)

56 in

100.

If the scale factor is greater than one, the new figure will be

a)

a reduction

b)

an enlargement

c)

a scale

d)

not proportional

101.

If the scale factor is less than one, the new figure will be

a)

an enlargement

b)

a reduction

c)

a scale factor

d)

bigger

102.

What is the scale factor from ΔDEF to ΔABC?

a)

1/2

b)

7/3

c)

2

d)

10/3

103.

Jamie made a scale drawing of his apartment building. The building is 300 ft tall. He wants his scale to be 1 inch : 10 ft. How tall should his building be in his scale drawing?

a)

25 inches

b)

60 inches

c)

1/30 inch

d)

30 inches

104.

a)

0.25

b)

0.5

c)

2

d)

1/2

105.

What is the scale factor from the small fry to the large fry?

a)

1/3

b)

48

c)

4

d)

3

106.

A scale factor of 2 is used to enlarge the dimensions of a square. What is the effect of this change on the area of the square?

a)

The area will be half as big.

b)

The area will be twice as large.

c)

The area will be 4 times larger.

d)

The area will be 8 times larger.

e)

The area will not change.

107.

The dimensions of a rectangular photo are 3.5cm. x 5 cm. The dimensions of the photo are enlarged by a scale factor of 2.5. What is the perimeter of the new photo?

a)

17.7 cm²

b)

8.75 cm. X 12.5 cm.

c)

42.5 cm.

d)

There is not enough information.

108.

Solve the proportion:

a)

4

b)

8

c)

14

d)

10

109.

Solve for the following proportion using cross multiplication

a)

b=2

b)

b=5

c)

b=10

d)

b=6

110.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

111.

A model is built to a scale of 1 m ∶ 10 m. If a model airplane is 3 meters long, how long is the actual plane?

a)

13 m

b)

30 m

c)

3 ⅓m

112.

What is 10% of N250

a)

N2.50

b)

N25

c)

N250

d)

N2500

113.

What is 25% of 2 hours?

a)

45 minutes

b)

30 minutes

c)

0.3 hours

d)

0.5 minutes

114.

Convert 0.81 to a percent

a)

0.81%

b)

0.18%

c)

8.1%

d)

81%

115.

What fraction is equivalent to 25%?

a)

1/3

b)

1/4

c)

1/5

d)

1/8

116.

Convert this decimal to a percentage 0.175

a)

17.5%

b)

1750%

c)

175%

d)

1.75%

117.

Susie got a raise. She was making N8.75 an hour. Now she is making N9.50. What is the percent of change?

a)

6% Increase

b)

7% Increase

c)

8% Increase

d)

9% Increase

118.

A Sweet Sensation's cheeseburger cost N0.79 in 1999. Today a cheeseburger costs N1.00. What is the percent change?

a)

21% increase

b)

26.58% increase

c)

26.58% decrease

d)

21% decrease

119.

The average number of shirts sold in the beach shop was 285 on Saturday in the summer. As the temperature went lower, the average number of shirts decreased to 114 every Saturday. What was the percentage decrease of in the average number of shirts sold in the shop?

a)

60%

b)

40%

c)

150%

d)

171%

120.

change .451 to a percent

a)

451%

b)

.451%

c)

.00451%

d)

45.1%

121.

Find the percentage change in the following price increase:

N650 to N728

a)

12%

b)

88%

c)

18%

d)

82%

122.

In a wetland, 400 birds are observed in 2018 and 450 birds are observed in 2019. Find the percentage change of the no. of birds.

a)

decreased by 12.5%

b)

increased by 50

c)

increased by 12.5%

d)

increased by 50%

123.

Original: N350

New: N400

a)

14% increase

b)

25% increase

c)

50% increase

d)

.14% increase

124.

Gabe scored a 70 on his first test. On the retake he scored an 88. What is the percent increase?

a)

25.7%

b)

18%

c)

20.5%

d)

22%

125.

Solve the proportion.

a)

q=2

b)

q=9

c)

q=4.5

d)

q=6

126.

What is 84% of 175?

a)

208.3

b)

48

c)

147

d)

84

127.

A man had a mass of 70 kg. After six months on a diet, his mass was 63 kg. What is the percentage reduction in his mass?

a)

11.1

b)

11

c)

70

d)

10

128.

Ryan Transfers 15% of his pay into saving. If he makes N1850 per month , how much will he save in a YEAR?

a)

N22,200

b)

N277.50

c)

N3330

d)

N1480

129.

MacDaniel sells cars and earns 4% commission on his sales. This month he sold N47,995 worth of cars. What is his commission for the month?

a)

N1,919.80

b)

N11,998.75

c)

N28,797

d)

N9,198.00

130.

Write 57% as a decimal.

a)

5.7

b)

0.057

c)

57

d)

0.57

131.

What is 5/10 in percent form?

a)

0.50

b)

50%

c)

1/2

d)

5.0

132.

What is the percent?

a)

20 %

b)

60%

c)

80%

d)

.60%

133.

Write 0.39 as a percent.

a)

39

b)

3.9%

c)

39%

d)

.0039%

134.

What percent of 15 is 3?

a)

30%

b)

50%

c)

40%

d)

20%

135.

What number is 40% of 40?

a)

14

b)

16

c)

18

d)

40

136.

What fraction is equivalent to 25%?

a)

1/3

b)

1/4

c)

1/5

d)

1/8

137.

What is 1/8 as a percent?

a)

125%

b)

12.5%

c)

1.25%

d)

0.125%

138.

What is 30% of 1200?

a)

300

b)

100

c)

120

d)

360

139.

24 is what percent of 240?

a)

15%

b)

5%

c)

10%

d)

1%

140.

What is the number which 20% of it is 700?

a)

3500

b)

350

c)

35

d)

3.5

141.

Mr. Royal takes his family out to eat and the meal costs N35 before tip. How much would the meal cost including tip if he leaves a 15% tip?

a)

N38.25

b)

N39.25

c)

N40.25

d)

N5.25

142.

What fraction is equivalent to 25%?

a)

1/3

b)

1/4

c)

1/5

d)

1/8

143.

What is 1/8 as a percent?

a)

125%

b)

12.5%

c)

1.25%

d)

0.125%

144.

How much tax would you pay on a new TV that is N899 at Best Buy, if the tax rate is 6.5%?

a)

N957.44

b)

N841

c)

N58.43

145.

A town has a population of 9500 people. Over time the population increases to 16000 people. What is the percentage increase?

a)

68.4%

b)

59.4%

c)

40.6%

d)

50.0%

146.

The movie theater has 250 seats. 225 seats were sold for the current showing. What percent of seats are empty?

a)

10%

b)

20%

c)

80%

d)

90%

147.

Find each percent decrease. Round to the nearest percent. From N80 to N64

a)

35%

b)

10%

c)

20%

d)

25%

148.

Mrs. Ciampa had 27 students in her class last year and this year she had 30 students in her math class. What is the percent of change?

a)

24%

b)

20%

c)

11%

d)

50%

149.

How much tax would you pay on a new TV that is N899 at Best Buy, if the tax rate is 6.5%?

a)

N957.44

b)

N841

c)

N58.43

150.

An original price increases 15% to N48.00. What is the original price?

a)

N55.20

b)

N41.74

c)

N40.80

d)

N7.20

151.

The students measured length during a science experiement, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error?

a)

15.79%

b)

18.75%

c)

2.25%

d)

18%

152.

The students measured length during a science experiement, they got 12 cm. But the actual measurement was 14.25 cm. What was the percent error?

a)

15.79%

b)

18.75%

c)

2.25%

d)

18%

153.

Which of the following expressions is equivalent to x² – 4y²?

a)

(x + 2)(x – 2)

b)

(x – 2y)²

c)

(x + 2y)(x – 2y)

d)

(x + 2y)²

154.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

155.

Factor
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

156.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

157.

The factorization of (x³ - 25 x) is ______

a)

x (x - 5)²

b)

x (x + 5)²

c)

x (x + 5) (x - 5)

d)

None of these

158.

Choose the correct answer:
The factors of a⁴ - b⁴ is _____

a)

(a² + b²) (a + b) (a - b)

b)

(a² + b²) (a² + b²)

c)

(a² - b²) (a² - b²)

d)

None of these

159.

Choose the correct answer:
a² + bc + ab + ac = ______

a)

(a + b) (a + c)

b)

(a + b) (b + c)

c)

(a + c) (b + c)

d)

a (a + b + c)

160.

(x + 1) (x + 1) is a factor of ____

a)

x² + 2x + 1

b)

x² - 2x + 1

c)

x² - 1 + 2x

d)

x² + 1 - 2x

161.

$x^2-x-12=\left(x+p\right)\left(x+q\right)$ . What is the value of $p$ and $q?$

a)

3 , 4

b)

3 , -4

c)

2 , 6

d)

2 , -6

162.

Factorise $64-9k^2$

a)

$\left(8+9k\right)\left(8-9k\right)$

b)

$\left(8-9k\right)\left(8-9k\right)$

c)

$\left(8+3k\right)\left(8-3k\right)$

d)

$\left(8+3k\right)\left(8+3k\right)$

163.

Factorise 3x²+12x

a)

3x(x+4)

b)

3(x²+4)

164.

Difference of squares
Factor x²-16

a)

(x-4)(x+4)

b)

(x-4)(x-4)

c)

(x+4)(x+4)

d)

(x+4){x-(-4)}

165.

Factorise 2x + xy - 6 - 3y

a)

x (2 + y) - 3(2 + y)

b)

(2 + y)(x - 3)

c)

x (2 + y) - 3(2 - y)

d)

(2 + y)(x + 3)

166.

Expand (y+1)(y-2).

a)

y²-2y-2

b)

y²-y-2

c)

y²+y-2

d)

y²+2y-2

167.

Factorise ab+bc+pq+pr.

a)

a(b+c) + p(q+r)

b)

b(a+c) + p(q+r)

c)

b(a+b) + p(q+r)

d)

b(a+c) + q(p+r)

168.

Expand and simplify 4(7x + 3).

a)

28x + 12

b)

28x + 3

c)

47x + 12

d)

47x + 3

169.

Simplify 3x + 2y - 2x + 3y.

a)

x + 5y

b)

5x + 5y

c)

5x + y

d)

5x - 5y

170.

Expand and simplify 3(x + 2) + 4(2x +1).

a)

11x + 10

b)

11x + 7

c)

7x + 10

d)

11x + 3

171.

Factorise x²+4x

a)

x(x+4)

b)

4x(x+1)

172.

Determine the area for the diagrams below using algebraic expressions

a)

10x² - 11x - 6

b)

7x² - 11x - 6

c)

10x² - 19x - 6

d)

10x² + 11x - 6

173.

Factorise $15x+25$

a)

$3\left(5x+5\right)$

b)

$3\left(5x-5\right)$

c)

$5\left(3x+5\right)$

d)

$5\left(3x-5\right)$

174.

Factorise $3x^2-9x$

a)

$3x\left(x-3\right)$

b)

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

c)

$3\left(x^2-3x\right)$

d)

$3\left(x^2+3x\right)$

175.

Factorise $4xy+40x^2$

a)

$4\left(xy+10x^2\right)$

b)

$4x\left(y+10x\right)$

c)

$4x\left(y-10x_{ }\right)$

d)

$x\left(4y+40x\right)$

176.

Factorise $7x^2yz-8y$

a)

$7y\left(x^2z-8\right)$

b)

$x\left(7xyz-8\right)$

c)

$y\left(7x^2z+8\right)$

d)

$y\left(7x^2z-8\right)$

177.

Factorise $9x^2y^2+3xy$

a)

$3xy\left(xy+1\right)$

b)

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

c)

$3xy\left(xy\right)$

d)

$9xy\left(xy+\frac{1}{3}\right)$

178.

Factorise $x+x^2+x^3$

a)

$x\left(x+x^2\right)$

b)

$x\left(1+x+x^2\right)$

c)

$x^3\left(1\right)$

d)

$x\left(x^2+x\right)$

179.

Factorise $2x+3y$

a)

$3\left(x+y\right)$

b)

$x\left(2+3y\right)$

c)

$2\left(x+3y\right)$

d)

Cannot factorization

180.

Factorise $16x^2y^2−8x^2y+9y$

a)

$8xy\left(2xy-x+1\right)$

b)

$8y\left(2x^2y-x^2+1\right)$

c)

$y\left(16x^2y-8x^2+9\right)$

d)

$xy\left(16xy-8x+9\right)$

181.

Factorise 5a+5b

a)

(a+b)

b)

5(a+b)

c)

5a + b

d)

a + 5b

182.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

183.

Which of these are common factors of this expression: 21x²y + 35xy⁷ - 70x²y² ?

a)

7

b)

x

c)

y

d)

x²

184.

Which of these are common factors of this expression: 600a + 25ab² - 75a²b⁵ ?

a)

a

b)

b

c)

25

d)

ab

185.

Factorise 15x-9x² completely

a)

15x(1-3x)

b)

3x(5x-9x)

c)

5x(3-3x)

d)

3x(5-3x)

186.

Factorise completely ax²y - 2ax²z

a)

2ax²(y-2z)

b)

ax²(y-2z)

c)

ax(yx-2xz)

d)

a(xy-2x²z)

187.

Factorise completely: xh + xk + yh + yk

a)

(h + k)(x + y)

b)

(h + x)(y + k)

c)

h(x + y + k)

d)

(hk)(x + y)

188.

Factorise completely ax - ay - bx + by

a)

(a + b)(x + y)

b)

(a - b)(x + y)

c)

(a + b)(x - y)

d)

(a - b)(x - y)

189.

Factorise completely ms + 2mt² - ns - 2nt²

a)

(s+2t²)(m+n)

b)

(s-2t²)(m-n)

c)

(s+2t²)(m-n)

d)

(s+2t)(m-n²)

190.

Factorise completely: 6ax + 2bx + 3ay + by

a)

(3x+b)(2a+y)

b)

(3a+b)(2x+y)

c)

(3a+y)(2x+b)

d)

(3x+y)(2a+b)

191.

In a direct variation, y = 39 when x = 3.

Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

192.

y varies directly with x. When y = 25, x = 125. Find the value of x when y = 20.

a)

3

b)

4

c)

55

d)

100

193.

The amount of money earned on a job is directly proportional to the number of hours worked. If N70 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

N29

b)

N308

c)

N 1.57

d)

N 265

194.

What ordered pair does a direct variation always go through when graphed?

a)

(0, 0)

b)

(1, 0)

c)

(0, 1)

d)

(1, 1)

195.

Is this a direct variation?

y = 2x

a)

yes

b)

no

196.

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

a)

Yes

b)

Yes

c)

Yes

d)

No

197.

Which graph shows a direct variation between x and y?

a)

A

b)

B

c)

C

d)

D

198.

Does this function represent a direct variation?

y = 7x + 3

a)

yes

b)

no

199.

Given that y varies directly as the square of x. Find the relation between y and x.

a)

y α √x

b)

y α 1 ∕ √x

c)

y α x²

d)

y α 1 ∕ x²

200.

Given that Q varies directly as the square root of P. Given that the value of P = 1/4 when Q = 3. Find the value of P if Q = 2.

a)

1 / 9

b)

1 / 3

c)

12

d)

36

201.

R varies directly as cube root of S. The relation between R and S is

a)

R α S^1/3

b)

R α S³

c)

R α 1 / S^1/3

d)

R α 1 / S³

202.

Given that x varies directly as the square root of y and x = 15 when y = 9. Calculate the value of y when x = 30.

a)

A. 36

b)

B. 25

c)

C. 18

d)

D. 5

203.

A type of variation that involves 3 or more quantities that may vary directly.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

204.

This type of variation states that the two quantities increase at the same time or decrease at the same time.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variation

d)

Combined Variation

205.

The cost c varies directly as the number of n pencils is written as

a)

c = kn

b)

k = cn

c)

n = k/c

d)

c = k/n

206.

The speed r of a moving object is inversely proportional to the time t travelled is written as

a)

r = kt

b)

r = k/t

c)

t = kr

d)

t = r/k

207.

Which of the following types of variation states that the decrease of one quantity results to the increase of the other quantity?

a)

Direct Variation

b)

Inverse Variaton

c)

Joint Variation

d)

Combined Variation

208.

If y varies directly as x and y = 24, when x = 3, then what is the value of k?

a)

4

b)

6

c)

8

d)

72

209.

Which of the following phrases illustrate an inverse variation?

a)

The area of the wall to the amount of paint used to cover it

b)

The amount of money raised in a concert to the number of tickets sold

c)

The time a teacher spends in checking papers to the number of students

d)

The age of a used car to its resale value

210.

If s varies directly as t and inversely as v, then which of the following equations describes the relation among the three variables s, t, and v?

a)

s = k / tv

b)

s = kv / t

c)

1/s = kt/ v

d)

s = kt / v

211.

Which of the following is the graph of a direct square variation?

a)

Straight Line

b)

Quadratic Curve

c)

Broken Line

d)

Hyperbola

212.

This is a variation where one quantity varies directly to other quantity and inversely to the other quantity.

a)

Direct Variation

b)

Inverse Variation

c)

Joint Variaiton

d)

Combined Variation

213.

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?

a)

50 kg water

b)

72 kg water

c)

94 kg water

d)

150 kg water

214.

Find the unit rate: N3.60 for 3 pounds of apples. How much does it cost for 1 pound of apples?

a)

N1.00 per pound

b)

N3.60 per pound

c)

N1.20 per pound

d)

N1.10 per pound

215.

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns N187.15, what should she earn if she worked 40 hours?

a)

N394

b)

N440

c)

N472.80

d)

N512.20

216.

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is N123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.

a)

N3813

b)

N620

c)

N190.65

d)

N4.96

217.

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. How many gallons of water would be used to wash 12 loads?

a)

60 gallons

b)

780 gallons

c)

156 gallons

d)

12/13 gallons

218.

In a direct variation, y = 39 when x = 3.
Find the value of y when x = 2.

a)

26

b)

3

c)

58.5

d)

2

219.

What does the Direct Variation Equation look like?

a)

Y= kx

b)

y = mx + b

c)

y = b

d)

y = x

220.

If y vaires directly with x and y= 12 when x= 15. What is the value of x when y= 16?

a)

12.8

b)

20

c)

11.25

d)

19

221.

In a direct variation, y=39 when x=3. Find the value of y when x=2.

a)

26

b)

3

c)

58.5

d)

2

222.

If y varies jointly with the product of x and z, and y = 105 when x = 5 and z = 7, find y when x = 9 and z = 10.

a)

270

b)

180

c)

360

d)

255

223.

If y varies jointly with the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10.

a)

100

b)

200

c)

300

d)

400

224.

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, x is 16. What is the value of x when y = 8 and z =12?

a)

32

b)

64

c)

48

d)

96

225.

A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3. Then what is the value of A when B = 6 and C = 4?

a)

12

b)

24

c)

36

d)

48

226.

If a varies jointly as b and the square root of c, and a = 21 when b = 5 and c = 36, find a when b = 9 and c = 225.

a)

126

b)

196

c)

256

d)

289

227.

z varies jointly with x and y. If x = 2, y = 3 and z = 4, find z when x = -6 and y = 2.

a)

-6

b)

-8

c)

-10

d)

-12

228.

z varies jointly with x and y. If x = 5, y = -1, and z = 10. Find z when x = -1/2 and y = 7.

a)

5

b)

6

c)

7

d)

8

229.

z varies jointly with x and y. If x = 7, y = 3 and z = -14, find y when z = -8 and x = 3.

a)

3

b)

4

c)

5

d)

6

230.

z varies jointly with x and y. If x = 8, y = -3 and z = -6, find x when z = 12 and y = -16.

a)

-3

b)

-4

c)

-6

d)

-9

231.

The equation for a Joint Variation is represented as:

a)

y = kx

b)

y = k/x

c)

y = kxz

d)

y = kx/z

232.

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

233.

if y is directly proportional to x, y is 10 when x is 3. What is the value of y when x is 5?

a)

16 2/3

b)

1.5

c)

6

d)

12

234.

What ordered pair does a direct variation always go through when graphed?

a)

(0, 0)

b)

(1, 0)

c)

(0, 1)

d)

(1, 1)

235.

y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?

a)

y=32x

b)

y=16x

c)

y=2x

d)

y=(1/2)x

236.

Is this a direct variation?

a)

yes

b)

no

237.

Is this a direct variation?

a)

yes

b)

no

238.

Which graph shows a proportional relationship between x and y?

a)

A

b)

B

c)

C

d)

D

239.

If y =4 when x = -4, find y when x =7.

a)

y= x, 7

b)

y= -x; 7

c)

y = -x; -7

d)

y= x; -7

240.

What does the Direct Variation Equation look like?

a)

Y= kx

b)

y = mx + b

c)

y = b

d)

y = x

241.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. What is the equation of variation?

a)

y = 10x

b)

y = 2x

c)

y = 5x

d)

y = 1/5x

242.

If y vaires directly with x and y= 12 when x= 15. What is the value of x when y= 16?

a)

12.8

b)

20

c)

11.25

d)

19

243.

A map of Texas is scaled so that 3 inches represents 90 miles. How far apart are Pecos and Fort Stockton if they are 1.8 inches apart on the map?

a)

54 miles

b)

15 miles

c)

30 miles

d)

50 miles

244.

In a direct variation, y=39 when x=3. Find the value of y when x=2.

a)

26

b)

3

c)

58.5

d)

2

245.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. What is the equation of variation?

a)

y = 10x

b)

y = 2x

c)

y = 5x

d)

y = 1/5x

246.

Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and thunder, about how far away was the lightning?

a)

40 miles

b)

4/5 miles

c)

8 miles

d)

20 miles

247.

A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. What is the equation of variation?

a)

y = 123x

b)

y = 20x

c)

y = 6.15x

d)

y = 0.16x

248.

At top speed, a rabbit can cover 7 miles in 12 minutes. What is the constant of variation?

a)

k = 7

b)

k = 12

c)

k = 12/7

d)

k = 7/12

249.

At top speed, a rabbit can cover 7 miles in 12 minutes. What is the equation of variation?

a)

y = 7x

b)

y = 12x

c)

y = 12/7x

d)

y = 7/12x

250.

At top speed, a rabbit can cover 7 miles in 12 minutes. If a rabbit could continue at this rate indefinitely, how long would it take the rabbit to cross the 220-mile expanse of the Mojave Desert?

a)

31.4 minutes

b)

18.3 minutes

c)

377.1 minutes

d)

128.1 minutes

251.

A dishwasher uses 65 gallons of water to wash 5 loads of dishes. How many gallons of water would be used to wash 12 loads?

a)

60 gallons

b)

780 gallons

c)

156 gallons

d)

12/13 gallons

Pearlspedia Year 9 mathematics

Total questions: 251

Worksheet time: 1hrs 24mins

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