Free Printable MIRACLE IGCSE MATHS REVISION

1.

Find the HCF of 12 and 16...

a)

2

b)

4

c)

6

d)

8

2.

Find the LCM of 12 and 16...

a)

48

b)

36

c)

64

d)

96

3.

List the first 5 multiples of 3

a)

3, 6 10, 15, 20

b)

1, 3

c)

3, 6, 9, 12, 15

d)

6, 9, 12, 15, 18

4.

A prime number is...

a)

a number that has only one factor.

b)

a number that has at least two factors.

c)

a number that has more than two factors.

d)

a number that has only two factors.
(1 and itself)

5.

write 140 as the product of its prime factors

a)

2x2x5x7

b)

2x2x2x2

c)

3x2x3x5

d)

7x9x5x2

6.

Which is a factor of 15?

a)

2

b)

3

c)

4

d)

6

7.

Which of the following numbers is not composite?

a)

24

b)

40

c)

66

d)

61

8.

Find the HCF of 32 and 80.

a)

8

b)

16

c)

24

d)

32

9.

A number is expressed as

2³x 3³x 5.

What is the number?

a)

11

b)

72

c)

270

d)

1080

10.

What is a rational number ?

a)

A rational number is a number that cannot be written as a fraction.

b)

A rational number is a number that can be written as a fraction.

c)

A rational number cannot be a repeating decimal.

11.

Which number is rational below?

a)

√20

b)

√64

c)

6π

d)

√7

12.

List the following numbers from least to greatest:
-64 , 3.5 , √27 , 6.666...

a)

-64 , 3.5 , √27 , 6.666...

b)

3.5 , √27 , 6.666..., -64

c)

3.5, -64, √27, 6.666...

d)

6.666, √27, -64, 3.5

13.

Which of the following is irrational?

a)

0.444444444

b)

-4/5

c)

π

d)

0.2

14.

Order 75%, 9/10 and 0.09 from Greatest to Least.

a)

75%, 9/10, 0.09

b)

0.09, 75%, 9/10

c)

9/10, 75%, 0.09

15.

What is 98.907 rounded to 1 significant figure?

a)

98.9

b)

90

c)

100

d)

98.91

16.

Find the nth term of...
1,3,5,7...

a)

2n+1

b)

2n-1

c)

2n+2

d)

2n-2

17.

What is the next number in the following sequence?

8, 14, 20, 26, ...

a)

30

b)

32

c)

34

d)

36

18.

Which number is the largest?

33%, 1/3, 0.3 or 0.03

a)

33%

b)

1/3

c)

0.3

d)

0.03

19.

The following number has been rounded to 1 significant figure.

800

Find the lower bound...

a)

850

b)

750

c)

849

d)

749

20.

The following number has been rounded to the nearest metre.

370m

Find the upper bound...

a)

375m

b)

370.5m

c)

370.05m

d)

375.5m

21.

The height (h, meters ) of a tree correct to the nearest meter is 17m.
Which of the following statements is true?

a)

16.5≤h≤17.5

b)

15.5≤h<17.5

c)

16.5≤h<17.5

d)

16.5<h<17.5

22.

Convert 3.41 to a percentage

a)

34.1%

b)

0.341%

c)

0.0341%

d)

341%

23.

What is 30% as a decimal?

a)

0.333...

b)

0.3

c)

3/10

d)

3

24.

Convert 40% to a fraction

Simplify as much as possible

a)

⁴⁰/₁₀₀

b)

⁴/₁₀

c)

²/₅

d)

¹/₄

25.

What is the value of 30 - (5 × 2³ - 15)?

a)

-25

b)

5

c)

15

d)

-15

26.

What is the value of 5 × 3 - 12 ÷ 4 + 8 ?

a)

3

b)

4

c)

14

d)

20

27.

What would you do first in the following equation?

10 - 4 x (1 + 5) =

a)

subtraction

b)

brackets

c)

multiplication

d)

division

28.

Simplify:
b⁴ x b⁻³ ÷ b⁻²

a)

b³

b)

b⁻³

c)

b⁵

d)

b⁻¹

29.

What is 98.907 rounded to 1 significant figure?

a)

98.9

b)

90

c)

100

d)

98.91

30.

2x + 3(5x - 7) = 47

a)

1

b)

2

c)

3

d)

4

31.

a)

1/7

b)

47/36

c)

7

d)

23

32.

Factorsie x² +4x -32

a)

(x - 8)(x + 4)

b)

(x + 8)(x - 4)

c)

(x + 8)( x + 4)

d)

(x - 8)(x - 4)

33.

What is the LCM of 32 and 40?

a)

180

b)

160

c)

140

d)

200

34.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

35.

Find the nth term of...
1,3,5,7...

a)

2n+1

b)

2n-1

c)

2n+2

d)

2n-2

36.

How many times does this object STOP moving?

a)

None

b)

Once

c)

Twice

d)

Three times

37.

Write the equation of the line.

a)

y=-3x-4

b)

y=-4x-3

c)

y=(-3/4)x-3

d)

y=(-4/3)x-3

38.

Solve 4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

39.

A wildlife reserve has a population of 70 elephants. A group of researchers trapped 30 elephants and recorded their vital statistics. Of the trapped elephants, 24 were female. If that rate holds true for the entire population of 70 elephants, how many female elephants are on the wildlife reserve?

a)

56

b)

204

c)

100

d)

216

40.

.

a)

Yes they're similar

b)

No they're not similar

c)

Cannot be determined

41.

f : x → 0.5(4 + 5x) + 10. What is the inverse of the function?

a)

x → ½(-5x - 4).

b)

x → ⅕(5x - 10).

c)

x → ⅕(2x - 24).

d)

x → -½(-4 - 5x) - 10

42.

Find the size of angle y.

a)

45^o

b)

57^o

c)

78^o

d)

90^o

43.

a)

21.78cm³

b)

24.78cm³

c)

25.23cm³

d)

26.97cm³

44.

Joanna drives for 400km at an average speed of 80km/h. How long was her journey?

a)

Joanna's journey was 5hrs long

b)

Joanna's journey was 10hrs long

c)

Joanna's journey was 20hrs long

d)

Joanna's journey was 15hrs long

45.

a)

6/5x

b)

(x-4)/(x-2)

c)

(x+3)/(x+2)

d)

(x+3)/(x-4)

46.

After 4 minutes a submarine has submerged 600 feet below sea level. After 10 minutes it has reached a depth of 1,500 feet and after 25 minutes it is 3,750 feet below sea level. What is the constant of proportionality at which the submarine dives?

a)

300

b)

150

c)

3750

d)

600

47.

Find the angle sum of the interior angles of the polygon.

a)

180°

b)

540°

c)

720°

d)

1080°

48.

What is the measure of ONE interior angle in a regular pentagon (5-sides)?

a)

90°

b)

108°

c)

120°

d)

180°

49.

What is
the Bearing
of A
from B?

a)

45

b)

130

c)

045

d)

135

50.

Find side a?

a)

10

b)

8.08

c)

14

d)

12.12

51.

The figure below show a triangular shaped garden located inside a rectanualr shaped, grassy yard. What is the area of the grassy yard?

a)

480 m^2

b)

384 m^2

c)

360 m^2

d)

336 m^2

52.

What is the volume of the prism?

a)

60 cubic cm

b)

90 cubic cm

c)

120 cubic cm

d)

150 cubic cm

53.

Two tangents CD and CB intersect circle A. Find the length of the tangent segment BC.

a)

2

b)

3

c)

9

d)

14

54.

what are the values of c and d?

a)

c = 218, d = 71

b)

d = 109, c = 71

c)

c = 142, d = 218

d)

c = 142, d = 109

55.

Write the following as one fraction...

a)

3y / 11

b)

3y / 30

c)

17y / 30

d)

2y / 30

56.

Share £80 in the ratio 3:2:5

a)

£24 : £16 : £40

b)

£16 : £24 : £40

c)

£40 : £24 : £16

d)

£40 : £16 £24

57.

Person A and person B are sharing money in the ratio 4:2. Person A has $60 more than person B. How much does person B have?

a)

$10

b)

$50

c)

$30

d)

$15

58.

The angles of a triangle are in the ratio 3:1:2. What type of triangle is this?

a)

Isosceles

b)

Acute

c)

90

d)

Right Angle

59.

Make x the subject:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

60.

Fully factorise the following expression...

12x - 8

a)

3(4x - 3)

b)

3(4x - 2)

c)

4(3x - 2)

d)

4(3x - 1)

61.

Expand and simplify

(x - 7)(x + 7)

a)

x² + 7x - 49

b)

x² - 7x + 49

c)

x² - 49

d)

x² + 49

62.

(3x²y³)²

a)

9x⁴y⁶

b)

3x⁴y⁵

c)

6x⁴y⁶

d)

9xy

63.

a)

x⁴

b)

4x³

c)

3x³

d)

4x²

64.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

65.

If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?

a)

{3, 5, 7}

b)

{2, 3, 5, 7}

c)

{2, 3, 5, 7, 9}

d)

{1, 2, 3, 5, 7, 9}

66.

Identify the shaded area...

a)

A

b)

B

c)

A'

d)

B'

67.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

68.

Identify the shaded area...

a)

A∩B

b)

A∪B

c)

A'∩B'

d)

A'∪B'

69.

Solve the following quadratic...

x² + 11x + 24 = 0

a)

x = -3, -8

b)

x = 2, 12

c)

x = -4, -6

d)

x = -2, -12

70.

Convert this decimal to a percentage 0.175

a)

17.5%

b)

1750%

c)

175%

d)

1.75%

71.

I have just paid £88 for my water bill. This is an increase of 10% from last year. How much did I pay last year?

a)

£80

b)

£70

c)

£90

d)

£78

72.

Find the measure of angle 1.

a)

28^o

b)

136^o

c)

44^o

d)

6^o

73.

Solve for y.

a)

y = 20

b)

y = 120

c)

y = 60

d)

y = 10

74.

Write 135 as the product of it's prime factors...

Write your answer in index form...

a)

3² x 5²

b)

3³ x 5

c)

3 x 3 x 3 x 5

d)

3 x 3 x 5 x 5

75.

What is the speed of a jet plane that flies 7200 km in 9 hours ( in km/hr)

a)

800 km/hr

b)

80 km/hr

c)

800 hrs

d)

64,800 km/hr

76.

What is the equation to calculate time?

a)

time = speed/distance

b)

time = distance/speed

c)

time = speed x distance

d)

time = distance x speed

77.

What two types of measurements make up DENSITY?

a)

Mass and Volume

b)

Temperature and Mass

c)

Grams and Centimeters

d)

Volume and Weight

78.

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

79.

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

a)

$x=-4,\ y=3$

b)

$x=3,\ y=-4$

c)

$x=3,\ y=-8$

d)

$x=4,\ y=8$

80.

Compare the numbers
0.632 0.609

a)

>

b)

<

c)

=

d)

?

81.

17.34 - 1.001

a)

89

b)

16.339

c)

16

d)

163.39

82.

What is 3/4 written as a decimal?

a)

0.75

b)

0.750

c)

0.7500

d)

All of the above

83.

#8. Tom has 7/ 8 cup of olive oil. He uses 1/2 cup to make salad dressing and 1/4 cup to make tomato sauce. How much olive oil does Tom have left?

a)

5/4

b)

5/8

c)

3/8

d)

1/8

84.

#10. Derek made a rope swing with a length of 5 3/4 feet. Nick’s rope swing is 6 1/8 feet long. How much longer is Nick’s swing than Derek’s swing?

a)

1 2/4 feet

b)

1 5/8 feet

c)

3/8 feet

d)

2/8 feet

85.

A florist is told that 40% of the 350 flowers ordered must be red roses. How many red roses must be in the order?

a)

390 roses

b)

100 roses

c)

140 roses

d)

240 roses

86.

A new television costs £328 plus 20% VAT. What is the total cost of the TV?

a)

£393.60

b)

£360.80

c)

£348.00

d)

£382.60

87.

The store is having a 75% off all items for 2 day only.
If a bed cost £1325 normally.
How much will the bed cost during the sale?

a)

£993.75

b)

£939.75

c)

£331.25

d)

£331.50

88.

There are 6 girls in a class of 25. Express the number of girls as a percentage of the whole class.

a)

12%

b)

24%

c)

60%

d)

75%

89.

Emilio borrows $1200 from a bank with 8% simple interest per year. How much will he have to pay back total in 2 years?

a)

$150

b)

$192

c)

$1350

d)

$1392

90.

Davy Crockett earned $10,000 from his raccoon skin hat company. He deposited it into an account that earned 3% interest compounded annually. How much interest did he earn after 4 years?

a)

$11,255.09

b)

$1255.09

c)

$1200

d)

$11,200

91.

Which of the following numbers will NOT round to 400 when rounding to the nearest hundred?

a)

409

b)

445

c)

345

d)

398

92.

What is 98.907 rounded to 1 significant figure?

a)

98.9

b)

90

c)

100

d)

98.91

93.

what is 0.27845 rounded to 3 decimal places?

a)

0.28

b)

0.27

c)

0.278

d)

0.3

94.

2x + 3(5x - 7) = 47

a)

1

b)

2

c)

3

d)

4

95.

a)

1/7

b)

47/36

c)

7

d)

23

96.

a)

30

b)

43

c)

46

d)

54

97.

What is 25^½

a)

12.5

b)

5

c)

625

d)

10

98.

16^-½

a)

¼

b)

½

c)

8

d)

-8

99.

Expand 2xy(x + y)

a)

2x²y + 2xy²

b)

2xy + 2yx

c)

2x² + 2y²

d)

2x²y²

100.

Factorise 16x² - 24x

a)

8x(2x - 3)

b)

4x(4x - 6)

c)

2x(8x - 12)

d)

8x(x - 3)

101.

Factorise fully: 6x² - 3x

a)

3x(2-x)

b)

3(2x²-x)

c)

3x(2x-1)

d)

6x(x-3)

102.

Factorsie x² +4x -32

a)

(x - 8)(x + 4)

b)

(x + 8)(x - 4)

c)

(x + 8)( x + 4)

d)

(x - 8)(x - 4)

103.

What is the LCM of 32 and 40?

a)

180

b)

160

c)

140

d)

200

104.

(2⁸)²

a)

2¹⁶

b)

2¹⁰

c)

2⁶

d)

2⁴

105.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

106.

a)

(3,-1)

b)

(-3,-1)

c)

(1,2)

d)

(-1,2)

107.

a)

(10,-2)

b)

(2,-2)

c)

(1,4)

d)

(-1,4)

108.

When x = 3, y = 6 and z = 7, find 2x - z

a)

-1

b)

-2

c)

-3

d)

-4

109.

Find the nth term of...
1,3,5,7...

a)

2n+1

b)

2n-1

c)

2n+2

d)

2n-2

110.

What is the n-th term of
1,4,9,16,25

a)

2n

b)

n+2

c)

n²

d)

n⁴

111.

0,3,8,15,24

a)

n²-2

b)

n²-1

c)

2n²-2

d)

n²-n

112.

1,6,11,16,21

a)

1n-5

b)

5n-4

c)

-4n+5

d)

n+n

113.

Solve the equation. Check your solution.

a)

⁴/₅

b)

-⁴/₅

c)

4

d)

28

114.

The sum of two consecutive integers is 123. What is the smallest of the two integers?

a)

60

b)

61

c)

62

d)

63

115.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

116.

Solve 3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

117.

How many times does this object STOP moving?

a)

None

b)

Once

c)

Twice

d)

Three times

118.

What happened during A to B point?

a)

not moving

b)

increasing speed at a constant rate

c)

moving at a constant speed

d)

moving at 10 m/s²acceleration

119.

Which graph represents y = -3?

a)

A

b)

B

c)

C

d)

D

120.

Write the equation of the line.

a)

y=-3x-4

b)

y=-4x-3

c)

y=(-3/4)x-3

d)

y=(-4/3)x-3

121.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

122.

Jane and Miguel are siblings. They go to different schools. Jane walks 6 blocks east from home. Miguel walks 8 blocks north. How many blocks apart would the two schools be if you could walk straight from one school to the other?

a)

14

b)

10

c)

5.3

d)

2

123.

What is the distance between the two points?

a)

6.3

b)

6.5

c)

6.7

d)

16

124.

4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

125.

6 - 2h > 30

a)

h < 24

b)

18 > h

c)

h > 12

d)

h < -12

126.

a)

x is less than or equal to -2

b)

x < -2

c)

-2 < x

d)

x is greater than -2

127.

Calculate 2a³ x 5a⁴

a)

10a⁷

b)

10a¹²

c)

7a⁷

d)

7a¹²

128.

Calculate (3a¹¹)³

a)

27a³³

b)

27a¹⁴

c)

9a³³

d)

9a¹⁴

129.

Ms. Ginsberg's second period Journalism class has 30 students. 18 of these students are earning an A or a B. This rate holds true in all of Ms. Ginsberg's classes. If Ms. Ginsberg has 80 students total, how many of these Journalism students are earning an A or a B?

a)

48

b)

55

c)

114

d)

168

130.

A wildlife reserve has a population of 70 elephants. A group of researchers trapped 30 elephants and recorded their vital statistics. Of the trapped elephants, 24 were female. If that rate holds true for the entire population of 70 elephants, how many female elephants are on the wildlife reserve?

a)

56

b)

204

c)

100

d)

216

131.

Which of the following constructions is illustrated?

a)

An angle is congruent to a given angle

b)

The bisector of a given angle

c)

The bisector of a given segment

d)

The perpendicular bisector of a given segment.

132.

Which one is the correct construction for a perpendicular bisector?

a)

1

b)

2

c)

3

d)

4

133.

What is the value of x?

a)

60

b)

26

c)

14

d)

10

134.

What is the value of x?

a)

8

b)

22.5

c)

11.25

d)

60

135.

Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1). Graph the figure and its rotated image after a counterclockwise rotation of 180° about the origin. What are the coordinates of Tʹ?

a)

(-3, -1)

b)

(-3,-2)

c)

(5,2)

d)

(5,4)

136.

Which of the following scale factors will NOT produce an enlargement?

a)

1

b)

1.2

c)

34.5

d)

5/4

137.

What is the difference between the mean and the mode of the scores 20, 40, 50, 20, 60?

a)

A) 2

b)

B) 12

c)

C) 18

d)

D) 20

138.

Wilson and his father enjoy playing chess together. Over three months, Wilson records the results of their chess matches.

Matches Wilson Wins: 20
Matches Wilson’s Father Wins: 34
Matches that are Draws: 6
What is the best estimate for the number of games Wilson’s father will win in the next 30 chess matches?

a)

34

b)

20

c)

17

d)

10

139.

A box contains 7 yellow pencils and 3 black pencils. Michael randomly chooses a pencil and does not replace it. Then he chooses a second pencil. What is the probability that both pencils are black?

a)

.67%

b)

6.7%

c)

67.0%

d)

10%%

140.

What is the probability that the person picked will be a boy given they speak german?

a)

.7273

b)

.4

c)

.16

d)

.22

141.

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. How tall is the tree?

a)

144 feet

b)

72 feet

c)

36 feet

142.

.

a)

Yes they're similar

b)

No they're not similar

c)

Cannot be determined

MIRACLE IGCSE MATHS REVISION

Total questions: 142

Worksheet time: 7hrs 46mins

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