CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
Name
Date
Stage 9 End-of-year test
1 a Circle the irrational numbers in this list.
−2.7
27
3
−27
2
7
[1]
π
b Write down two irrational numbers with a rational product.
[1]
2 a
3 3
(12 )
= 12 n
Work out the value of n.
n=
[1]
b Write 8−1 as a power of 2.
[1]
3 a The distance from Earth to the Sun is approximately 150 000 000 km.
Write this distance in standard form.
km
[1]
b The wavelength of a laser is 0.7 μm.
Write this length in metres in standard form.
m
[2]
4 Here is an expression: ( x − 3)( x − 4).
2
3
a Find the value of the expression when x = 5 . Give your answer as a mixed number.
[2]
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
b Expand the expression. Write it without brackets as simply as possible.
[2]
5 3 x + 12 < 5 x − 18
Work out the range of possible values of x. Write your answer as an inequality.
[2]
6 Here are two rectangles:
a The perimeter of rectangle A is 60. Write an equation to show this.
[1]
b The perimeter of rectangle B is 114. Use this fact and the answer to part a to work out
the values of x and y.
__________________________________________________ x = ________ y = ________
[3]
7 The attendance at a football match, to the nearest thousand, is 47 000.
Write down an inequality to show the possible value of the attendance.
[1]
8 The mass of a baby is 4.0 kg.
In one month the mass of the baby increases by 15%. In the next month the mass
of the baby increases by 25%.
Calculate the mass of the baby after two months.
kg
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[2]
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
9 A car travels 18 km in 20 minutes.
a The car travels at the same speed. How far does the car travel in one hour?
km
[1]
km
[1]
______________________________________________________ $ ________ or $ ________
[2]
b The car travels twice as fast. How far does the car travel in 20 minutes?
10 Two people share some money in the ratio 3 : 5.
One person gets $75. Find two possible values for the amount of money the other
person gets.
11 Here is a formula: e =
12
.
d +3
Rearrange the formula to make d the subject.
[2]
12
Work out the area of this shape.
cm2
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[2]
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
13 Here is a semicircle:
a Calculate the area of the semicircle.
cm2
[2]
b Show that the perimeter of the semicircle, in centimetres, is 8(π + 2)
[2]
14 Here is a right-angled triangle:
Calculate the value of x.
______________________________________________________________ x = ________cm [2]
15 The sides of a cuboid are 5 cm, 5 cm and 10 cm.
a Sketch the cuboid, showing the lengths of the sides.
[1]
b How many planes of symmetry does the cuboid have?
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
[1]
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
16 Here is a triangular prism:
The cross-section of the prism is a right-angled triangle.
a Calculate the volume of the prism.
cm3
[2]
cm2
[3]
b Calculate the surface area of the prism.
17 Here is an equation: 3 x + 2 y = 18.
a Complete this table of values.
x
0
2
4
6
8
y
[2]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
b Draw a graph of 3 x + 2 y = 18.
[2]
c Find the gradient of the line.
[1]
d The equation of another line is 2 x + 5 y = 100.
Find the gradient of this line.
[1]
18 Here are two fair spinners. Each sector is equally likely on each spinner.
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
Work out the probability of spinning
a red on both spinners
[1]
b red on at least one spinner.
[2]
19 Find the nth term for each of these sequences.
a 1, 4, 9, 16, 25, …
[1]
b 4, 7, 12, 19, …
[1]
c
1 1 1 2 5
, , , , , ...
6 3 2 3 6
[1]
20
a Reflect triangle A in the line x = 5 . Label the new shape B.
[2]
b Reflect B in the line y = 5 . Label the new shape C.
[2]
c Describe completely the transformation that takes C to A.
[1]
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
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CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: END-OF-YEAR TEST
21 a The exterior angle of a regular polygon is 30 °. How many sides does the polygon have?
[1]
b The sum of the interior angles of a regular polygon is 900 °. How many sides does
the polygon have?
[1]
[Total: 60 marks]
END OF TEST
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
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