Free Printable IGCSE Math Ch3 Algebra

1.

$\frac{42xyz}{56}$

a)

$\frac{3xyz}{4}$

b)

xyz

c)

$\frac{6}{8}$

d)

$\frac{6xyz}{8}$

2.

$\frac{45ab}{60abc}$

a)

$\frac{3ab}{4abc}$

b)

$\frac{9}{12c}$

c)

$\frac{3}{4c}$

d)

$\frac{9}{12}$

3.

$\frac{40x^2y}{32y}$

a)

$\frac{10x^2}{8}$

b)

$\frac{5x^2}{4}$

c)

$\frac{10x^2}{8y}$

d)

$\frac{5x^2y}{4y}$

4.

$\frac{8x^4}{2x^2}$

a)

$4x^2$

b)

$4$

c)

$4x$

d)

$4x^6$

5.

$\frac{33a^2b^2}{33a^3b}$

a)

$ab$

b)

$\frac{b}{a}$

c)

$\frac{a}{b}$

d)

$\frac{3b}{4a}$

6.

$\frac{6x+8}{2}$

a)

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

b)

$3x+4$

c)

$\frac{14x}{2}$

d)

$7x$

7.

$\frac{35x^2+20}{5}$

a)

$5x^2+4$

b)

$7x^2+4$

c)

$\frac{7x^2+4}{5}$

d)

$\frac{5x^2+4}{5}$

8.

$\frac{\left(7-70m^3\right)}{7}$

a)

$1-10m^3$

b)

$1-10m^2$

c)

$10-m^3$

d)

$1-70m^2$

9.

$\frac{20af}{4a}$

a)

5a

b)

5f

c)

4a

d)

4f

10.

Simplify $\frac{10a}{32ab}$ .

a)

$\frac{5}{16}$

b)

$\frac{5}{16b}$

c)

$\frac{5b}{16}$

d)

$\frac{5}{16a}$

11.

$\frac{48act}{12t}$

a)

6t

b)

6ac

c)

4ac

d)

4t

12.

$\frac{16mn}{18n}$

a)

$\frac{8mn}{9}$

b)

$\frac{8m}{9n}$

c)

$\frac{8m}{9}$

d)

$\frac{8}{9n}$

13.

a + a + a - a

a)

4a

b)

2a

c)

a²

d)

3a

14.

Simplify

3a+a

a)

$4a$

b)

$3a^2$

c)

$3a+a$

d)

$2a$

15.

Simplify: 2x + 6x - 3x

a)

8x

b)

3x

c)

5x

d)

8x - 3x

16.

Simplify: x + x + x + x + n + n

a)

n² + x⁴

b)

x4 + n2

c)

4x + 2n

d)

5xn

17.

a + a + b + b + a

a)

3ab

b)

2a + b

c)

5ab

d)

3a + 2b

18.

5a + 2b + 3a + 4b

a)

5a + 2b

b)

7ab + 7ab

c)

8a + 6b

d)

8a - 6b

19.

Simplify

2a-5b+a+2b

a)

$3a+7b$

b)

$3a-7b$

c)

$3a-3b$

d)

$a+7b$

20.

Simplify: x + x + 7 + 3

a)

2x + 7 + 3

b)

2x + 10

c)

x2 + 10

d)

No clue

21.

Simplify: 2x + 3x + 8 - 3

a)

5x + 5

b)

2x + 5

c)

5x - 5

d)

6x + 5

22.

6a + 2 - 4a - 5

a)

2a + 3

b)

10a - 7

c)

2a - 3

d)

10a + 7

23.

Simplify: 10x - 3x + 2x + 5 - 7

a)

7x - 2

b)

9x - 2

c)

7x + 2

d)

9x - 2

24.

b² + b²

a)

2b²

b)

b⁴

c)

b²b²

d)

4b

25.

5a² - 3a²

a)

8a²

b)

2a²

c)

2a⁴

d)

8a⁴

26.

Simplify

2a^2+4a-3-7a+a^2

a)

$3a^2-3a-3$

b)

$-6a^2$

c)

$3a^2+11a-3$

d)

$a^2-3a-3$

27.

a x 3

a)

a3

b)

a³

c)

3a

d)

aaa

28.

2 x t x s

a)

ts2

b)

4ts

c)

2st

d)

ts²

29.

3b x 5a

a)

3b5a

b)

35ab

c)

ba15

d)

15ab

30.

Simplify

3a\times a

a)

$3a$

b)

$4a$

c)

$3a^2$

d)

$3$

31.

5c x 2c

a)

10cc

b)

10c²

c)

52c

d)

10c

32.

Simplify

3x^2y\times4xy^4

a)

$12x^3y^5$

b)

$7x^3y^5$

c)

$12x^2y^4$

d)

$34x^3y^5$

33.

Simplify

\frac{4xy}{2y}

a)

$\frac{2xy}{y}$

b)

$2xy^2$

c)

$8x$

d)

$2x$

34.

Solve the equation by factoring.

a)

x = {3,8}

b)

x = {-3,8}

c)

x = {3,-8}

d)

x = {-3,-8}

35.

How many solutions can a quadratic have?

a)

1 solution

b)

3 solutions

c)

0 solutions

d)

2 solutions

36.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

37.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

38.

Solve for r:

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

-3

39.

Solve the following quadratic equation: $4x^2-9=0$

a)

$x=\frac{3}{2}$ & $x=-\frac{3}{2}$

b)

$x=\frac{2}{3}$ & $x=\frac{-2}{3}$

c)

$x=\frac{9}{4}$

d)

$x=\frac{4}{9}$

40.

If discriminant of a quadratic equation is negative, then roots of the equation are __________.

a)

Distinct Roots

b)

Equal roots

c)

Unequal roots

d)

none

41.

Find the nature of roots in the quadratic equation 3x² - 9x+5=0

a)

Real and Equal

b)

Real and distinct

c)

Unreal and distinct

d)

None

42.

What is the quadratic formula?

a)

b)

c)

d)

43.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

44.

Which of the following is NOT a quadratic function

a)

f(x) = -3x²

b)

f(x) = -5x - x²

c)

y = 3x³- 4x + 5

d)

A = pi.r²

45.

How many solutions can a quadratic have?

a)

1 solution

b)

3 solutions

c)

0 solutions

d)

2 solutions

46.

What are the values of a, b, and c in the quadratic equation 3x² - 10 = -4x

a)

a = 3x² b = -10 c = -4x

b)

a = 3 b = -10 c = -4

c)

a = 3 b = -4 c = -10

d)

a = 3 b = 4 c = -10

47.

The graph of a quadratic function is called

a)

a line

b)

a hyperbola

c)

a parabola

d)

a cubic

48.

What are the green dots called?

a)

axis of symmetry

b)

vertex

c)

parabola

d)

roots or x-intercepts

49.

Can both the roots of quadratic equation be zero?

a)

Yes. Possible

b)

NO. Not possible

50.

Say 'TRUE' or 'FALSE'
A quadratic equation ax² + bx + c = 0 has equal roots, then b² - 4ac = 0

a)

TRUE

b)

FALSE

51.

The area of a certain rhombus is given by the equation L²- 5L = 6 where l represents the length of the rhombus in centimeters. What is the length of the rhombus?

a)

6 cm

b)

-6 cm

c)

1 cm

d)

-1 cm

52.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

53.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

54.

The length of a rectangle is 3 cm more than its width. If the area of the rectangle is 40 sq. cm., what is the width of the rectangle?

a)

3

b)

2

c)

5

d)

8

55.

Solve by finding square roots and simplify completely:
$2x^2=20$

a)

$x=\pm10$

b)

$x=\sqrt{10}$

c)

$x=\pm\sqrt{10}$

d)

No real solutions

56.

Solve using the Quadratic Formula:
$5x^2+3x-1=0$

a)

$x=\frac{3\pm\sqrt{29}}{5}$

b)

$x=\frac{8}{5}\ or\ x=-\frac{2}{5}$

c)

$x=\frac{-3\pm\sqrt{29}}{10}$

d)

No real solutions

57.

if you used the quadratic formula to solve

x^{2\ }-7x\ =-12

what would be the total for

b^2+\ \left(-4\right)\left(a\right)\left(c\right)

a)

x=3 and x= 4

b)

87

c)

1

d)

x= -3 and x= -4

58.

Willis drove 239.82 miles in 4.2 hours at a constant speed. How long would it take him to drive 445.38 miles at the same speed?

a)

4.2 hours

b)

7.8 hours

c)

7.2 hours

d)

57 hours

59.

What is a Ratio?

a)

It's a comparison of two things

b)

Multiplying two fractions

c)

A number over another number

d)

Two decimals that can be multiplied

60.

Express the ratio as a fraction in simplest form:
18 ounces to 3 cups

a)

6 to 1

b)

1/6

c)

18/3

d)

3/18

61.

A class has 30 students. 18 are boys. What is the ratio of boys to girls?

a)

12:18

b)

3:2

c)

30:18

d)

18:7

62.

Solve for x

a)

x=6.5

b)

x=8

c)

x=4

d)

x=5.5

63.

The ratio of cars to trucks in the parking lot is 3:5. If there are 360 vehicles in the parking lot, how may are trucks?

a)

x = 270 cars

b)

x = 225 cars

c)

x = 225 trucks

d)

x = 270 trucks

64.

Hamburger sells for 3 pounds for $6. If Alicia buys 10 pounds of hamburger, how much will she pay?

a)

$30

b)

$20

c)

$60

d)

$10

65.

A barrel contained 60 gallons of water. Water leaked out of the barrel at a rate of 5 gallons every 3 days.

At this rate, how many days did it take for all 60 gallons of water to leak out of the barrel?

a)

20 days

b)

12 days

c)

100 days

d)

36 days

66.

10 students want hotdogs for lunch and 26 want hamburgers. What is the ratio of the number of students who want hot dogs to the number of students who want hamburgers?

a)

26:10

b)

10:26

c)

10:36

d)

25:36

67.

Solve: $\frac{4}{\left(x-8\right)}=\frac{9}{\left(x-6\right)}$

a)

2.8

b)

-5

c)

-6.6

d)

9.6

68.

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

69.

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

70.

sf = 0.8

a)

Reduction

b)

Enlargement

71.

sf = 6/5

a)

Reduction

b)

Enlargement

72.

What is the formula for scale factor?

a)

$\frac{new}{old}$

b)

$\frac{old}{new}$

73.

What is the scale factor from the smaller quadrilateral to the larger?

a)

scale factor = 4

b)

scale factor = 10

c)

scale factor = 3

d)

scale factor = 2

74.

What is Dilation?

a)

Dilation means to enlarge or reduce

b)

Dilation means to reflect on something

c)

Dilation means to like something

d)

Dilation means to make something different by making it smaller

75.

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)

a)

A'(9,9) B'(18,18) C'(27,9)

b)

A'(6,6) B'(9,9) C'(12,6)

c)

A'(0,0) B'(3,3) C'(6,0)

d)

A'(1,1) B'(2,2) C'(3,1)

76.

Which choice correctly describes the dilation shown here?

a)

Enlargement by scale factor $\frac{2}{5}$

b)

Reduction by scale factor 2.5

c)

Enlargement by scale factor 2.5

d)

Reduction by scale factor $\frac{2}{5}$

77.

You are using a magnifying glass that shows the image of an object that is six times the object’s actual size. Determine the length of the image of the spider with length 2.5 mm through the magnifying glass.

a)

2.4 mm

b)

11.9 mm

c)

15 mm

d)

37.5 mm

78.

A rectangular field has a length of 9 m and a width of 11 m.

Length are measured to the nearest metre.

What is the greatest possible area of the field?

(a)

79.

A metal rod has a length of 2 cm to the nearest cm.

What is the greatest possible length of the rod?

(a)

80.

A rectangular field has a length of 10 m and a width of 11 m. Length are measured to the nearest metre.

What is the greatest possible area of the field?

(a)

81.

A cuboid measures 5 x 4 x 19 m measured to the nearest metre.

What is the least possible volume of the cuboid?

(a)

82.

A cuboid measures 11 x 13 x 7 m measured to the nearest metre. What is the greatest possible volume of the cuboid?

(a)

83.

The volume of oil in a tank is 1000 litres, correct to the nearest 10 litres.

The oil is poured into tins of volume 2.5 litres, correct to one decimal place.

Calculate the upper bound of the number of tins which will be required.

(a)

84.

In a race, Paula runs 25 laps of a track.

Each lap of the track is 400 m, correct to the nearest metre.

Paula’s average speed is 5.0 m/s, correct to one decimal place. Calculate the upper bound for the time that Paula takes to run the race. Give your answer in minutes and seconds, correct to the nearest second

(a)

85.

A metal cube has sides of length 4.5cm, correct to the nearest 0.5cm. The cube is melted down and the metal is used to make small spheres. Each sphere has a radius of 3mm, correct to the nearest millimetre. Work out the greatest number of spheres that could be made from the metal.

(a)

86.

40% of the 25 students in a class have black hair. How many students is this?

a)

10

b)

15

c)

20

d)

5

87.

16 out of the 28 biscuits in a packet have cream centres. What percentage of the packet are cream-centred biscuits?

a)

57%

b)

58%

c)

100%

d)

30%

88.

50% of $36

(a)

89.

CHANGE THE FOLLOWING INTO PERCENT.

5/20

a)

50%

b)

20%

c)

25%

d)

76%

90.

CHANGE THE FOLLOWING INTO PERCENT:

6.07

a)

6.07%

b)

607%

c)

670%

d)

60.7%

91.

Calculate 10% of $40

a)

40

b)

4

c)

10

92.

A T-shirt costs $50. You get 10% off in the sales. How much do you pay for the T-shirt ?

a)

$55

b)

$10

c)

$5

d)

$45

93.

The bottom of a fraction is called the?

a)

numerator

b)

denominator

c)

Bottom

94.

Convert to a decimal

a)

0.67

b)

6.7

c)

0.067

d)

6.07

95.

Convert 19% to a fraction

a)

¹⁹/₁₀₀

b)

⁹/₂₀

c)

¹/₉

d)

⁹/₅₀

96.

Convert 30% to a fraction

Simplify as much as possible

a)

³⁰/₁₀₀

b)

¹⁵/₅₀

c)

³/₁₀

d)

¹/₃

97.

Convert 25% to a fraction in its simplest form

a)

²/₅

b)

²⁵/₁₀₀

c)

⁵/₂₀

d)

¹/₄

98.

Convert to a percentage

a)

12%

b)

25%

c)

20%

d)

50%

99.

What is 1/4 as a decimal?

a)

0.2

b)

0.25

c)

0.4

d)

0.15

100.

Which describes the shaded portion of the figure?

a)

1/2 = 50%

b)

1/6 = 0.166....

c)

1/5 = 25%

d)

1/5 = 20%

101.

Express 0.2 as a percentage

a)

20%

b)

2%

c)

0.2%

d)

200%

102.

How do you change .45 to a percent?

a)

Move the decimal point 3 places to the right

b)

Move the decimal point 2 places to the left

c)

Move the decimal point 2 places to the right

d)

Move the decimal point 3 places to the left

103.

5/7 + 1/28 =

a)

6/35

b)

12/196

c)

21/28

d)

1

104.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

105.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

106.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

107.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

108.

.

a)

A

b)

B

c)

C

d)

D

109.

Simplify the expression: $x^{\frac{1}{2}} \cdot x^{\frac{1}{3}}$

a)

$x^{\frac{5}{6}}$

b)

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

c)

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

d)

$x^{\frac{4}{5}}$

110.

Convert the expression to radical form: $y^{\frac{3}{4}}$

a)

$\sqrt[4]{y^3}$

b)

$\sqrt[3]{y^4}$

c)

$\sqrt[4]{y}^3$

d)

$\sqrt{y^3}$

111.

Simplify the expression: $(27x^9)^{\frac{1}{3}}$

a)

$3x^3$

b)

$9x^3$

c)

$3x^2$

d)

$9x^2$

112.

Convert the expression to exponential form: $\sqrt[5]{a^3}$

a)

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

b)

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

c)

$a^{\frac{1}{15}}$

d)

$a^{15}$

113.

Simplify the expression: $4^{\frac{1}{2}} \cdot 4^{\frac{1}{4}}$

a)

$4^{\frac{3}{4}}$

b)

$4^{\frac{1}{8}}$

c)

$4^{\frac{3}{2}}$

d)

$2^{\frac{3}{4}}$

114.

Convert the expression to radical form: $m^{\frac{2}{3}}$

a)

$\sqrt[3]{m^2}$

b)

$\sqrt[2]{m^3}$

c)

$\sqrt{m^2}^3$

d)

$\sqrt[3]{m}^2$

115.

Simplify the expression: $(8y^6)^{\frac{1}{3}}$

a)

$2y^2$

b)

$4y^2$

c)

$2y^3$

d)

$4y^3$

116.

Convert the expression to exponential form: $\sqrt[3]{x^2}$

a)

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

b)

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

c)

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

d)

$x^{6}$

117.

Simplify the expression: $9^{\frac{1}{2}} \cdot 9^{\frac{1}{4}}$

a)

$9^{\frac{3}{4}}$

b)

$3^{\frac{3}{4}}$

c)

$9^{\frac{1}{8}}$

d)

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

IGCSE Math Ch3 Algebra

Total questions: 117

Worksheet time: 3hrs 5mins

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