Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/01
Paper 1
April 2024
1 hour
You must answer on the question paper.
You will need:
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
• Write your name, centre number and candidate number in the boxes at the top of the page.
• Write your answer to each question in the space provided.
• Do not use an erasable pen or correction fluid.
• Do not write on any bar codes.
• You should show all your working in the booklet.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
This document has 12 pages.
04_0862_01/8RP
© UCLES 2024
[Turn over
2
1
Youssef thinks of a number, n.
He adds 3
His answer is greater than or equal to –5 and less than 17
Write the correct inequality signs to complete the inequality.
–5
n+3
17
[1]
2
200−3 =
1
200w
Write the value of w.
[1]
w=
3
Solve the simultaneous equations.
x – 2y = 2
5x + 2y = 58
x=
y=
[2]
4
Find the exterior angle of a regular 10-sided polygon.
° [1]
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0862/01/A/M/24
3
5
Here is a sequence of calculations.
1 × 7 ‒ 2 ×1 = 5
3 × 8 – 4 × 2 = 16
5 × 9 ‒ 6 × 3 = 27
7 × 10 ‒ 8 × 4 = 38
9 × 11 ‒ 10 × 5 = 49
Complete the next calculation in this sequence.
11 × 12
–
×
=
[1]
6
A regular polygon has k lines of symmetry.
Tick () the correct statement about the order of rotational symmetry of the polygon.
The order of rotational symmetry is 1
The order of rotational symmetry is clockwise
The order of rotational symmetry is k
The order of rotational symmetry is k + 1
[1]
© UCLES 2024
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4
7
(a) Mike and Pierre are each asked to write the equations of two lines that have a
positive y-intercept.
Tick () to show if each student is correct or not correct.
Both equations have a
positive y-intercept
Correct
Not correct
Mike
y = –x + 3
y=2–x
Pierre
y = x + 0.5
y = 7 – 5x
[1]
(b) The equation of a line is 7 = 3x + y
Find the gradient and the y-intercept of this line.
gradient =
y-intercept =
[2]
8
Tick () to show if each conversion is correct or not correct.
Correct
Not correct
60 nm = 6 mm
2000 GB = 2 MB
[1]
© UCLES 2024
0862/01/A/M/24
5
9
Represent –2 < x ≤ 4 on the number line.
–5 –4 –3 –2 –1
0
1
2
3
4
5
6
x
[1]
10 The diagram shows a shape made with three identical rhombuses.
NOT TO
SCALE
70°
70°
70°
x°
Find the value of x.
x=
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[4]
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6
11 Gabriella collects the heights of 11 indoor plants and 12 outdoor plants.
The table and the incomplete back-to-back stem-and-leaf diagram show information about
her results.
Outdoor plants
Modal height
39 cm
Minimum height
17 cm
Range
26 cm
Indoor plants
9
Outdoor plants
9
8
7
0
9
5
4
1
9
8
6
2
3
7
7
0
3
4
5
8
4
1
9
Key: 6 | 2 | 3 represents indoor plant height of 26 cm
and outdoor plant height of 23 cm
(a) Use the information in the table to complete the back-to-back stem-and-leaf diagram.
[3]
(b) Calculate the range of heights for the indoor plants.
cm
12 Work out the value of
n 4 + 29
n+7
[1]
when n = 3
[2]
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7
13 (a) Write 62 000 in standard form.
[1]
(b) Write 8.1 × 10–3 as an ordinary number.
[1]
14 The diagram shows a shape made from 6 congruent equilateral triangles and a regular
hexagon.
The regular hexagon has an area of 140 cm2.
Calculate the shaded area.
cm2
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[1]
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8
15 The table shows information about the mass of each of 23 boxes.
Mass (m, kg)
4≤m<8
8 ≤ m < 12
Frequency
8
7
12 ≤ m < 16 16 ≤ m < 20 20 ≤ m < 24
3
2
3
(a) On the grid, draw a frequency polygon to show this information.
10
9
8
7
6
Frequency 5
4
3
2
1
0
4
8
12
16
Mass (kg)
20
24
m
[3]
(b) Draw a ring around the interval that contains the median mass.
4≤m<8
8 ≤ m < 12
12 ≤ m < 16
16 ≤ m < 20
20 ≤ m < 24
[1]
© UCLES 2024
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9
16
•
1
= 0.1
9
7
to a decimal.
9
Give your answer correct to 3 decimal places.
Use this fact to convert
[2]
17 Jamila makes this sequence of patterns using white counters and black counters.
Pattern 1
Pattern 2
Pattern 3
Pattern 4
(a) Complete these sentences.
The first one has been done for you.
The number of white counters in pattern 4 is
15
The number of white counters in pattern 5 is
The number of white counters in pattern 100 is
[2]
(b) Write an expression, in terms of n, for the total number of counters in pattern n.
[2]
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10
18 Tick () to show if each of the calculations is equivalent to 37 × 10–3 or not.
Equivalent to
37 × 10–3
Calculation
Not equivalent to
37 × 10–3
3.7 × 0.01
3.7 × 10–2
3.7 × 10– 4
37 ÷ 103
[2]
19 Point A lies on the y-axis and point B lies on the x-axis.
y
A
NOT TO
SCALE
M
P = (60, 11)
0
B
x
M is the midpoint of AB.
P is the midpoint of MB.
Find the coordinates of point A and the coordinates of point B.
A=(
,
)
B=(
,
)
[2]
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11
20 x is an integer and 1 < 3 x < 2
Complete these sentences about x.
One possible value of x is
There is a total of
possible values of x.
[2]
21 Point P lies on the line y = 5 – 2x
The x-coordinate of P is a negative integer.
The y-coordinate of P is a prime number.
Find a possible pair of coordinates for point P.
P=(
© UCLES 2024
0862/01/A/M/24
,
)
[2]
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12
22 Work out.
8
1
4
+1 ÷ 4
9
3
5
Give your answer as a mixed number in its simplest form.
[4]
23 A square has a side length of x cm.
Mia enlarges this square by increasing each side length of the square by 200%.
(a) The side length of her enlarged square measures kx cm.
Draw a ring around the value of k.
2
3
4
200
300
[1]
(b) Find the percentage increase in the area of the square after enlargement.
% [2]
____________________________________________________________________________
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2024
0862/01/A/M/24
Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/02
Paper 2
April 2024
1 hour
You must answer on the question paper.
You will need:
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
• Write your name, centre number and candidate number in the boxes at the top of the page.
• Write your answer to each question in the space provided.
• Do not use an erasable pen or correction fluid.
• Do not write on any bar codes.
• You should show all your working in the booklet.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages. Any blank pages are indicated.
04_0862_02/8RP
© UCLES 2024
[Turn over
2
1
It will take 7 workers 6 days to pick some mangoes.
Calculate how many workers are needed to pick these mangoes in 3 days.
[1]
2
Calculate.
54 ÷ 6
[1]
3
The mass of a baby is 4 kg.
Each month the mass of the baby increases by 15% of its mass from the previous month.
Find the mass of the baby after 2 months.
4
kg
[2]
%
[1]
In a game Oliver can either lose or draw or win.
The probability Oliver loses the game is 50%.
The probability Oliver draws the game is 20%.
Work out the probability Oliver wins the game.
© UCLES 2024
0862/02/A/M/24
3
5
Anastasia has four fair spinners, A, B, C and D.
1
2
2
2
3
4
3
1
A
3
2
4
4
B
1
5
C
3
D
She spins one of the spinners 1200 times and gets an even number 486 times.
Write down the letter of the spinner she is most likely to have used.
[1]
6
Here is a mapping diagram for the function y = 4x2
Input (x)
Output (y)
10
................
................
100
................
Complete the mapping diagram with three different values.
© UCLES 2024
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[3]
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7
Here is a calculation.
1.5 × 1.5 × 28 =
a a
× × 28 = a × a × b
2 2
Find the value of a and the value of b.
a=
b=
[2]
8
Carlos sells previously owned clothes.
He will ask his customers one of these questions, A or B.
A On a scale of 1 to 10, what number would you choose to represent the condition
of the clothes?
1
2
Very poor
3
4
5
6
7
8
9
10
Excellent
B Which word(s) would you choose to represent the condition of the clothes?
Very poor
Average
Excellent
Carlos wants to work out a mean value to represent the condition of the clothes.
Tick () to show which question Carlos should ask his customers and the reason why.
Question A because it asks for quantitative data
Question A because it asks for qualitative data
Question B because it asks for quantitative data
Question B because it asks for qualitative data
[1]
© UCLES 2024
0862/02/A/M/24
5
9
Yuri enlarges square ABCD by a scale factor of 2
y
5
4
B
C
A
D
3
2
1
0
1
2
3
4
5 x
Point A does not move when the square is enlarged.
Draw a ring around the coordinates of the centre of enlargement.
(0, 0)
(2, 2)
(2, 4)
(4, 2)
(4, 4)
[1]
10 The diagram shows a solid metal cylinder with a radius of 4.1 cm and a height of 7 cm.
4.1 cm
NOT TO
SCALE
7 cm
The cylinder is melted and the metal is made into cubes.
The side length of each cube is 2 cm.
Calculate the number of whole cubes that are made.
[3]
© UCLES 2024
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6
11 The pie chart shows information about the different types of pizzas sold in a restaurant.
60°
40°
110°
150°
Meat
Vegetable
Tomato
Cheese
A total of 324 pizzas are sold.
Mia says, ‘20 more cheese pizzas are sold than meat pizzas.’
Tick () to show if Mia is correct or not correct.
You must show your working.
Correct
Not correct
[2]
© UCLES 2024
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7
12 The diagram shows a right-angled triangle.
NOT TO
SCALE
y cm
y cm
Find an expression, in terms of y, for the area of the triangle.
cm2
[1]
13 A polygon has 7 sides.
The sizes of the 6 largest interior angles of the polygon add up to 855º.
Calculate the size of the smallest interior angle.
° [2]
14 Solve.
56
= 8
y +1
y=
© UCLES 2024
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[2]
[Turn over
8
15 The graph shows the exchange rate between US dollars ($) and Japanese yen (¥).
(25, 3300)
Japanese
yen (¥)
0
US dollars ($)
Angelique changes $40 into Japanese yen.
Calculate how many Japanese yen Angelique receives.
¥
[2]
 2
1 
16 Triangle ABC is translated by the vector   to make triangle DEF.
 −3 
 to make triangle GHI.
7
Then triangle DEF is translated by the vector 
Describe fully the single transformation that maps triangle ABC onto triangle GHI.
[2]
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9
17 Rajiv bisects an angle.
Here is his construction.
There are arcs missing from his construction.
Construct the missing arcs accurately on the diagram.
[1]
18 The ratio of the sizes of the angles in a triangle is 5 : 8 : 3
Tick () to show if the triangle is right-angled or not right-angled.
You must show your working.
Right-angled
Not right-angled
[2]
© UCLES 2024
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10
19 Complete the table of values for 3y + 5x = 60
0
x
6
0
y
On the grid, draw the graph of 3y + 5x = 60
y
22
20
18
16
14
12
10
8
6
4
2
0
2
4
6
8
10
12
14
16 x
[3]
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11
20 The diagram shows a semicircle with a radius of 3 cm.
NOT TO
SCALE
3 cm
Tick () to show the area of the semicircle correct to the nearest cm2.
14 cm2
19 cm2
28 cm2
57 cm2
[1]
21 Here is a table of values for points that all lie on the same straight line.
x
5
6
7
11
y
27
32
37
57
14
Complete the table.
[1]
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12
22 Solve the inequality.
2x + 20 ≤ 16
[2]
23 Expand and simplify.
x (x + 4) + (x – 3) (x + 5)
[3]
© UCLES 2024
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13
24 Temperature is measured in °C and in °F.
The formula f =
9c
+ 32 is used to convert c °C to f °F.
5
The approximate formula f = 2c + 30 is also used to convert c °C to f °F.
Mike says,
‘There is a value of c where these two formulae give an equal value of f . ’
Find the value of c to show that Mike is correct.
c=
© UCLES 2024
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[3]
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14
25 Safia has two bags of sweets.
Each bag contains red sweets and green sweets only.
She takes one sweet at random from each bag.
The probability that she takes a red sweet from the first bag is 0.3
The probability that she takes a red sweet from both bags is 0.12
First bag
Second bag
red
P(red from both bags) = 0.12
............
red
0.3
............
green
red
............
............
green
............
green
Complete the five missing probabilities on the tree diagram.
[3]
© UCLES 2024
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15
26 The diagram shows a garden in the shape of a hexagon.
16 m
NOT TO
SCALE
20 m
9m
8m
16 m
Eva builds a fence along all 6 sides of the garden.
The fence costs $23 per metre.
Calculate the total cost of the fence.
$
© UCLES 2024
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[4]
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16
BLANK PAGE
____________________________________________________________________________
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2024
0862/02/A/M/24
Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/01
Paper 1
October 2023
1 hour
You must answer on the question paper.
You will need:
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
• Write your name, centre number and candidate number in the boxes at the top of the page.
• Write your answer to each question in the space provided.
• Do not use an erasable pen or correction fluid.
• Do not write on any bar codes.
• You should show all your working in the booklet.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
This document has 16 pages.
IB23 10_0862_01/7RP
© UCLES 2023
[Turn over
2
1
The area of the cross-section of a prism is 10 cm2.
The length of the prism is 4 cm.
NOT TO
SCALE
Area = 10 cm2
4 cm
Calculate the volume of the prism.
cm3 [1]
2
Draw a ring around the scatter graph that shows positive correlation.
y
y
x
x
y
y
x
x
[1]
© UCLES 2023
0862/01/O/N/23
3
3
Write each of these expressions in the correct column in the table.
( −2 )
43
3
3
−8
( −5 )
2
One has been done for you.
Equivalent to a natural number
Not equivalent to a natural number
43
[1]
4
Complete each statement using one of these symbols.
< or >
One has been done for you.
20 ÷ 1
1
2
20 ×
3
4
20
20 × 2
1
5
20
20 ÷
1
5
20
<
20
[1]
5
Solve.
36
=4
t
t=
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0862/01/O/N/23
[1]
[Turn over
4
6
Calculate.
9 1
1− − 
8 2
[2]
7
Draw a ring around the statement that is true.
3< 7 < 4
4 < 18 < 5
5 < 36 < 6
6 < 50 < 7
[1]
8
Jamila works out an estimate of 104.37 × 0.615
Her estimate is 100 × 1 = 100
Complete the statement to show how to work out a better estimate of 104.37 × 0.615
104.37 × 0.615 is approximately
×
=
[1]
9
A team can either win, lose or draw a game of softball.
The table shows the probability the team will win or lose a game.
Outcome of game
Win
Lose
Probability
0.5
0.4
Complete the table.
© UCLES 2023
Draw
[1]
0862/01/O/N/23
5
10 Each diagram shows a pair of angles on parallel lines.
Diagram A
Diagram B
Diagram C
Diagram D
Complete the table to show if each diagram shows a pair of corresponding angles or not.
One has been done for you.
Corresponding angles
Not corresponding angles
A
[1]
11 (a) Write 7 000 000 in standard form.
[1]
(b) Write these numbers in order of size, starting with the smallest.
5.5 × 104
6.4 × 10–1
5.5 × 10–1
............................
smallest
............................
............................
largest
[1]
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6
12 Five quadrilaterals are shown on the grid.
y
6
5
P
4
3
2
1
–4
–3
–2
–1 0
–1
1
2
3
4
5
6
x
–2
–3
–4
Quadrilateral P is transformed by a reflection followed by a translation.
Draw a ring around the unshaded quadrilateral that is not a possible image of
quadrilateral P.
[1]
© UCLES 2023
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7
13 (a) Tick () to show each fraction that is equivalent to a recurring decimal.
1
6
6
8
4
12
[1]
(b) n is an integer where 0 < n < 15
n
is equivalent to a terminating decimal.
15
Draw a ring around the number of possible values of n.
0
1
2
4
[1]
© UCLES 2023
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8
14 The table shows some powers of 7 and their final digit.
Power of 7
Value
Final digit
71
7
7
7
2
49
9
7
3
343
3
7
4
2401
1
7
5
16 807
7
7
6
117 649
9
77
823 543
3
(a) The final digit of 7n is 1
Write down a possible value of n if n > 7
[1]
(b) Use patterns in the table to find the final digit of 722
[1]
15 Calculate.
6 × −1.8
−0.2
[2]
© UCLES 2023
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9
16 Construct an angle of 30°.
The construction has been started for you.
[2]
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10
17 A function is defined by this function machine.
×2
Input
cube
Output
(a) Complete the table.
Input
Output
5
3
2
[2]
(b) Calculate the input when the output is −64
[2]
18 Pierre spins this fair spinner twice.
1
2
3
He adds together his two numbers to get a total.
Pierre makes two statements.
Tick () to show if each statement is true or false.
True
False
The possible totals are 2, 3, 4, 5 and 6
P(total is 3) =
1
5
[1]
© UCLES 2023
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11
19 Solve.
2 x − y = 17
x + 3 y = −2
x=
y=
[3]
© UCLES 2023
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12
20 Draw the graph of y = x2 + 2 for values of x between –3 and 3
You may use the table to help you.
–3
x
–2
–1
0
1
2
3
y
y
12
11
10
9
8
7
6
5
4
3
2
1
–3
–2
–1
0
1
2
3
x
[3]
21 A quadrilateral has an area of 5 cm2.
The quadrilateral is enlarged by scale factor 4
Calculate the area of the enlarged quadrilateral.
cm2 [2]
© UCLES 2023
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13
22 There are 20 children in Class A and 20 children in Class B.
Each child completes a test.
The back-to-back stem-and-leaf diagram shows some of the marks scored by the children.
The highest mark for Class B is not included.
Class A
8
Class B
0
8
9
7
6
4
1
0
3
6
7
9
7
3
3
1
2
2
4
4
9
6
2
0
0
0
3
1
3
5
7
7
7
5
2
4
2
7
6
1
5
8
9
8
Key: 4 | 1 | 0 represents a mark of 14 in Class A and 10 in Class B
(a) The range of marks for Class A is the same as the range of marks for Class B.
Complete the diagram for Class B by writing in the highest mark.
[2]
(b) Tick () to show if each conclusion is true or false.
True
False
A total of 5 students in the two classes scored less than 15 marks.
The modal mark for Class A is greater than the modal mark for
Class B.
[1]
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14
23 The diagram shows some information about two rectangles.
Rectangle A
width
Perimeter = 56 cm
NOT TO
SCALE
Rectangle B
width
Perimeter = 56 cm
length : width = 5 : 2
length
length
The length of rectangle B is 2.5 cm less than the length of rectangle A.
Calculate the ratio length : width for rectangle B.
Give your answer in its simplest form.
:
© UCLES 2023
0862/01/O/N/23
[3]
15
24 The term-to-term rule of a sequence is multiply by 2
The first term of the sequence is a.
The sum of the first term and the third term is 35
Work out the sum of the first two terms.
[3]
25 0.45 × 10 p = 4500 and 5070 × 10 q = 0.0507
Find the value of 0.038 ÷ 10 p + 2q
[2]
© UCLES 2023
0862/01/O/N/23
[Turn over
16
26 A polygon has 7 sides.
The mean of the sizes of the 6 smallest angles in the polygon is 115°.
Calculate the size of the largest angle.
°
[3]
27 The solution, x, to the equation 4x = 12 – px is an integer.
p is a positive integer.
Find a possible value of p.
[1]
_________________________________________________________________________________________________________________________________________
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download
at www.cambridgeinternational.org after the live examination series.
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2023
0862/01/O/N/23
Mathematics
Stage 9
Paper 1
2023
1 hour
Additional materials: Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
3143_01_3RP
© UCLES 2023
2
1
Tick () to show which of these expressions is the number 87 000 000 written in standard
form.
870 × 105
87 × 106
8.7 × 107
0.87 × 108
[1]
2
Complete the table of values for y = x2 + 4
–2
x
–1
0
5
4
y
1
2
8
[1]
3
Here are two triangles, ABC and XYZ.
y
6
Z
5
C
4
3
A
–3
B
1
X
–4
2
–2
–1
Y
0
1
2
3
4
5
6
x
Describe fully the enlargement that maps triangle ABC onto triangle XYZ.
[2]
© UCLES 2023
3143_01
3
4
Here are two inequality symbols.
<
>
Write the correct inequality symbol in each box to complete these statements.
12.62 × 0.91
12.62
12.62 ÷ 0.91
12.62
0.91 ÷ 12.62
12.62
[1]
5
In a game a player either wins, draws or loses.
Gabriella plays the game.
The probability that Gabriella wins is 0.55 and the probability that she draws is 0.15
Find the probability that Gabriella draws or loses her next game.
[2]
© UCLES 2023
3143_01
[Turn over
4
6
Here is an algebraic fraction.
12 x + 4
4
Tick () to show which expression is equivalent to this fraction.
12x
3x
12x + 1
3x + 1
3x + 4
[1]
7
Here are the first four terms in a sequence.
1,
8,
27,
64
(a) Find the next term in this sequence.
[1]
(b) Find the nth term of this sequence.
[1]
© UCLES 2023
3143_01
5
8
Given that 8.95 × 5.62 = 50.299 complete these calculations.
895 × 0.562 =
502.99 ÷ 56.2 =
[2]
9
(a) Find the exterior angle of a regular pentagon.
° [1]
(b) Find the interior angle of a regular pentagon.
° [1]
(c) Tick () to show which of these regular polygons will tessellate and which
will not tessellate.
One has been done for you.
Regular polygons
Will tessellate
Will not tessellate
Equilateral triangles
Squares

Regular pentagons
Regular hexagons
[1]
© UCLES 2023
3143_01
[Turn over
6
10 Eleven students each take a physics test and a chemistry test.
Mike starts to draw this back-to-back stem-and-leaf diagram showing the marks from the
chemistry test.
Physics test
Chemistry test
4
9
5
2
8
6
1
1
7
7
0
6
9
8
2
8
Key: 2 ǀ 4 ǀ 9 represents 42 marks in
physics and 49 marks in chemistry.
Here are the marks from the physics test.
64
73
60
55
46
69
88
55
71
57
42
(a) Complete the back-to-back stem-and-leaf diagram.
[2]
(b) Complete the table.
Physics
Chemistry
Mean
61.8
65.7
Median
60
Mode
55
61
Range
46
33
[1]
© UCLES 2023
3143_01
7
(c) Tick () to show which subject has marks that have a greater spread.
Physics
Chemistry
Explain how you know using appropriate values from the table in part (b).
[1]
11 Here is the distance–time graph for a journey.
120
100
80
Distance
from home 60
(km)
40
20
0
6 am
7 am
Time
8 am
Calculate the speed for this journey.
Give your answer in km/h.
km/h [1]
© UCLES 2023
3143_01
[Turn over
8
12 Here are some inputs and outputs of the same function machine.
Input
Output
5
2
20
8
–10
–4
–1
n
Complete the missing input and the missing output.
[2]
13 A speed camera records the speeds of 50 cars in one hour.
Speed, s (km/h)
Number of cars
20 ≤ s < 30
9
30 ≤ s < 40
17
40 ≤ s < 50
18
50 ≤ s < 60
4
60 ≤ s < 70
2
(a) Write down the class interval that contains the median speed.
≤s<
[1]
(b) Draw a ring around the value that could be the range of the 50 speeds.
10
16
18
48
70
[1]
© UCLES 2023
3143_01
9
14 When n = –1 three of these expressions have the same value.
2 – n2
n2
1 – 2n
n 1
+
2 2
4n + 5
Draw a ring around each of the three expressions.
[2]
15 The diagram shows three straight lines crossing each other.
Some of the angles are marked.
y
y
x
NOT TO
SCALE
60°
Explain why angle 𝑥 is 60°.
Give geometrical reasons in your answer.
[2]
© UCLES 2023
3143_01
[Turn over
10
16 The equation of a line is 5x + 2y = 6
Find the gradient and the y-intercept of this line.
gradient =
y-intercept =
[3]
17 Work out.
5
2 3
1 +2 ×
6
3 16
Give your answer as a mixed number in its simplest form.
[4]
© UCLES 2023
3143_01
11
18 (a) Naomi thinks of a number n.
She changes her number using this rule
• multiply by 3
• then square
• then add 4
Tick () to show the expression for her number after using this rule.
9n + 4
3n2 + 4
9n2 + 4
3(n + 4)2
[1]
(b) Mia thinks of a number m.
She changes her number using the rule 4(m – 5)2
Complete the rule for Mia’s number.
Her rule is
●
● then
● then
[1]
© UCLES 2023
3143_01
[Turn over
12
19 Here is a circle with centre C.
C
Use a straight edge and compasses only to construct an inscribed square.
Do not rub out your construction arcs and lines.
[2]
20 A straight line joins the points A(2, 1) and B(8, 10).
The point C(6, 𝑦) lies on the line AB.
Find the 𝑦-coordinate of C.
y=
© UCLES 2023
3143_01
[1]
13
21 (a) In this question x is a whole number.
Find the largest possible value of x for which the inequality is correct.
27
x
>
x 27
x=
[1]
(b) In this question y is a whole number.
Find the largest possible value of y for which the inequality is correct.
2 y
>
y 8
y=
© UCLES 2023
3143_01
[1]
[Turn over
14
22 Yuri and Chen are playing a game.
They each have four cards numbered 1 to 4
Yuri
1
2
3
Chen
4
1
2
3
4
They place their cards face down.
Each child turns over one of his cards at random.
The winner is the child who turns over the largest number.
If they turn over the same number, then neither of them wins.
Show that the probability that Yuri wins the game is
3
8
[2]
© UCLES 2023
3143_01
15
23 Here are some equations involving indices.
(23)2 ÷ 2–2 = 2w
4–2 × 4 × 4x = 412
6 y × 6 y = 6–16
Find the values of w, x and y.
w=
x=
y=
[3]
© UCLES 2023
3143_01
[Turn over
16
24 Here is a rectangle.
NOT TO
SCALE
119 cm2
(5x + 2) cm
The area of the rectangle is 119 cm2.
The length of the shorter side of the rectangle is (5x + 2) cm.
(a) Write down an expression in terms of x for the length of the longer side of the
rectangle.
cm [1]
(b) The longer side of the rectangle is 7 cm.
Find the value of x.
x=
[2]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced annually and is available to download at
https://lowersecondary.cambridgeinternational.org/
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2023
3143/01
Mathematics
Stage 9
Paper 1
2024
1 hour
Additional materials: Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
3143_01_5RP
© UCLES 2024
2
1
The diagram shows a quadrilateral with the exterior angles marked.
100°
NOT TO
SCALE
100°
100°
x°
Calculate the value of x.
x=
2
[1]
Here are some calculations.
–9 × 7
(–3)2
–8 ÷ (– 4)
12 ÷ (–3)
Write each calculation in the correct column in the table.
One has been done for you.
Answer is positive
Answer is negative
–9 × 7
[1]
© UCLES 2024
M/S9/01
3
3
The term-to-term rule of a sequence is square and then add 2
The 1st term of the sequence is 3
Find the 2nd term of the sequence.
[1]
4
Draw a ring around the number that is rational.
2
4
6
8
[1]
5
Show that the area of the trapezium is smaller than the area of the square.
4 cm
NOT TO
SCALE
9 cm
18 cm
10 cm
[2]
6
The value of x is an integer.
9 < x + 4 < 12
Write down the two possible values of x.
or
© UCLES 2024
M/S9/01
[1]
[Turn over
4
7
Here are the equations of some straight-line graphs.
y = 2x + 3
y = –2x
y = 2x
y = –2x + 5
Write each equation in the correct place in the table.
One has been done for you.
Gradient is positive
Gradient is negative
Passes through (0, 0)
y = 2x + 3
Does not pass through (0, 0)
[1]
8
Find the 5th term for each of the sequences in the table.
n th term rule
5th term
n
4
n 2 – 11
n3
[2]
© UCLES 2024
M/S9/01
5
9
The diagram shows the positions of points A, B, C and D.
North
A
D
C
B
Draw a line to join each bearing to the correct description.
Bearing of B from A
Less than 180°
Bearing of C from B
180°
Bearing of D from B
More than 180°
[1]
10 Write a number in each box to complete the calculation.
3.5 ÷
7
=
8
×
2
=
7
[1]
© UCLES 2024
M/S9/01
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6
11 The data shows the marks scored by students in a test.
45
46
47
49
50
50
52
53
54
55
56
57
57
58
59
59
61
62
64
65
66
72
73
74
Jamila records the test marks in this table.
Test mark
Frequency
20 – 39
0
40 – 59
16
60 – 79
8
80 – 99
0
(a) Explain why the class intervals chosen by Jamila are not the most appropriate.
[1]
(b) Complete the frequency table to record the data using more appropriate class intervals.
You should choose class intervals with equal widths.
You may not need all the rows in the table.
Test mark
Frequency
[2]
© UCLES 2024
M/S9/01
7
12 Simplify.
(a )
3 4
4n + 6
2
[2]
13 (a) Write 50 000 in standard form.
[1]
(b) Write 4.07 × 10–3 as an ordinary number.
[1]
14 The counters in a bag are either red or blue or green or yellow.
A counter is picked at random from the bag.
The table shows the probability of some of the outcomes.
Colour of counter
Red
Blue
Green
Probability
0.15
0.05
0.35
Yellow
Find the probability that the counter is red or yellow.
[2]
© UCLES 2024
M/S9/01
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8
15 The diagram shows a circle with a horizontal diameter and a vertical diameter drawn.
Use the diagram to construct an inscribed regular octagon.
Do not rub out your construction arcs.
© UCLES 2024
M/S9/01
[2]
9
16 Naomi measures the mass of each of 50 bananas.
Mass, m (grams)
Frequency
100 ≤ m < 110
12
110 ≤ m < 120
15
120 ≤ m < 130
17
130 ≤ m < 140
4
140 ≤ m < 150
2
(a) Draw a frequency polygon to show this information.
0
100
110
120
130
Mass, m (grams)
140
150
[3]
(b) Draw a ring around the class interval that contains the median mass.
100 ≤ m < 110
110 ≤ m < 120
120 ≤ m < 130
130 ≤ m < 140
[1]
© UCLES 2024
M/S9/01
[Turn over
10
17 Find the value of
103 × 29 × 10–3
[1]
18 The values of a, b and c are a = 10 b = 7 c = 4
Tick () to show if the value of each of these expressions is equal to 64 or not equal to 64
Equal to 64
Not equal to 64
6(a + c)
a 2 + 28
2
(6 – 2b)2
b2 + c2 – 1
[2]
© UCLES 2024
M/S9/01
11
19 Calculate.
3
1  1 1
– 1 + 1 
4  2 3
[3]
20 Write the correct power in each box.
65 × 6–1 = 6
84 ÷ 8–2 = 8
1
=9
81
[2]
© UCLES 2024
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12
21 BCD and EFG are parallel lines.
ACFH is a straight line.
A
NOT TO
SCALE
y°
110°
B
E
(x – 40)°
C
D
G
x° F
H
Calculate the value of y.
y=
© UCLES 2024
M/S9/01
[2]
13
22 Triangle J is shown on the grid.
y
8
7
6
5
4
3
2
J
1
–6
–5
–4
–3
–2
0
–1
1
2
3
4
5
6 x
–1
–2
–3
–4
Triangle J is reflected in the line y = 3 to give triangle K.
Triangle K is then rotated by 90° anticlockwise, centre (0, 2), to give triangle L.
Draw and label triangle L on the grid.
[2]
23 Tick () to show if each statement is true or false.
True
2+3×
3
False
36 = 30
8×3+3 = 9
[1]
© UCLES 2024
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14
24 The diagram shows the graph of the line 2x + 3y = k.
y
5
4
3
2
1
–1
0
1
2
3
4
5
6
7 x
–1
–2
Draw a ring around the value of k.
4
6
12
24
[1]
25 Calculate.
0.82 − 0.01
−0.09
[3]
© UCLES 2024
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15
26 The values of x and y satisfy these simultaneous equations.
y = 4x – 2
3y = 7x + 14
Find the value of 2x – y.
[4]
© UCLES 2024
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16
27 Chen and Hassan each play a game.
They can each either win or lose or draw the game.
Hassan
Probability Hassan wins is 0.5
Probability Hassan draws is 0.2
Chen
Probability Chen wins is 0.3
Probability Chen draws is 0.1
The outcome of Chen’s game is independent of the outcome of Hassan’s game.
Find the probability that Chen and Hassan both lose their games.
[2]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced annually and is available to download at
https://lowersecondary.cambridgeinternational.org/
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2024
M/S9/01
Mathematics
Stage 9
Paper 2
2024
1 hour
Additional materials: Calculator
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You may use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
3143_02_6RP
© UCLES 2024
2
1
Draw a ring around the sum of the interior angles in a hexagon.
180°
360°
720°
1080°
[1]
2
The diagram shows two straight lines, ABC and DBE.
ABC and DBE are not perpendicular.
A
E
NOT TO
SCALE
B
C
D
Tick () to show if each of these statements is true or false.
True
False
ABE and DBC are corresponding angles.
Angle ABE = angle DBC.
Angle ABE + angle DBC = 180°.
[1]
© UCLES 2024
M/S9/02
3
3
The back-to-back stem-and-leaf diagram shows the ages of some of the people in two
choirs.
Choir A
7
4
9
Choir B
2
3
5
5
3
3
1
3
4
4
9
1
6
0
2
4
5
2
3
5
4
6
8
7
7
3
6
0
7
1
7
5
Key: 2 | 5 | 3 represents a person aged 52 years in Choir A and
a person aged 53 years in Choir B
The ages of four people have not been included in the diagram.
Choir A
Choir B
Pierre is 28 years old
Mike is 29 years old
Anastasia is 68 years old
Samira is 72 years old
Complete the diagram by entering the ages of these four people.
[2]
4
Here are two properties about a number x.
x is greater than 344
x rounds to 340 correct to 2 significant figures.
Write down a possible value of x.
[1]
© UCLES 2024
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[Turn over
4
5
Solve.
18
=3
y
y=
6
[1]
A is the point (1, 4) and B is the point (1, 10).
Find the coordinates of the point one third of the way along AB from A.
(
7
,
) [1]
Angelique’s journey is represented in the distance–time graph.
240
200
160
Distance
travelled 120
(km)
80
40
0
0
1
2
3
Time (hours)
4
Calculate Angelique’s speed on her journey.
km/h [1]
© UCLES 2024
M/S9/02
5
8
Here are some symbols.
<
>
=
Complete each statement by writing one of the symbols.
1 light year
1000 km
1 tonne
1000 kg
1 microgram
1000 grams
1 terabyte
1000 bytes
[2]
9
The diagram shows the cross-section of a prism.
8 cm
NOT TO
SCALE
6 cm
10 cm
13 cm
The prism has a length of 7 cm.
Calculate the volume of the prism.
cm3 [2]
© UCLES 2024
M/S9/02
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6
10 An old coin has a value of $5000
The value of the coin increases by 2% every year.
Calculate the value of the coin after 3 years.
$
[2]
11 Write a number in each box to complete each expansion.
( x − 3)( x + 11) = x 2 +
( x + 7)2 = x 2 +
x − 33
x + 49
[2]
12 Ahmed wants to find out how much time students in his school spend on their homework.
He decides to choose 12 students from his class as his sample.
Safia says, ‘Ahmed could improve his sample by making some changes.’
Tick () each of the changes that should give Ahmed a better sample.
Choose more students.
Choose students from different classes.
Choose students from different schools.
[1]
© UCLES 2024
M/S9/02
7
13 Draw the graph of y = x 2 between x = 0 and x = 4
Use the table to help you.
x
0
y
0
1
2
3
4
16
y
20
18
16
14
12
10
8
6
4
2
0
1
2
3
4
x
[3]
© UCLES 2024
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8
14 Sequence A is the linear sequence that begins 3, 6, 9, 12, …
The nth term for sequence B is 4n + 2
Tick () to show if each statement is true or false.
True
False
All terms in sequence B are even numbers.
22 is a term in both sequences.
The numbers that are common to both sequences are multiples of 6
[1]
15 Two quadrilaterals, P and Q, are shown on the grid.
y
10
9
8
7
6
Q
5
4
P
3
2
1
–3 –2 –1 0
–1
1
2
3
4
5
6
7
8
9 10 x
–2
–3
Describe fully the single transformation that maps quadrilateral P to quadrilateral Q.
[3]
© UCLES 2024
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9
16 Oliver draws this diagram to show some information about people he has surveyed.
The diagram shows
the number of people in each age interval,
the proportion of people in each age interval that own a car.
Do you own a car?
Age of people surveyed
378
330
Number
of people
Under
40 years
40 years
and older
Age group
Under 40 years
40 years and older
Do not
own
a car
Own a
car
Do not
own
a car
160°
300°
Own a car
Calculate the total number of people surveyed who own a car.
[2]
© UCLES 2024
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[Turn over
10
17 Hassan and Lily share some pens in the ratio 1 : 3
Tick () to show if each statement must be true, could be true or must be false.
Must be true
Could be true
Must be false
Lily gets more pens than Hassan.
Hassan gets
1
of the pens.
3
The total number of pens is 20
[2]
18 The circumference of a circle is 36.5 cm.
Find the area of the circle.
cm2 [3]
© UCLES 2024
M/S9/02
11
19 Here is a function.
Input
Output
x
y = 2 x3
Input, x
Output, y
Complete the table.
2.5
54
[2]
20 Point P has coordinates (– 4, 3).
Point P is translated to the point (x, 0), where x > 0
Write down a possible vector for this translation.
[1]
21 Rearrange the formula
3h 2
p=
5
to make h the subject.
h=
© UCLES 2024
M/S9/02
[2]
[Turn over
12
22 A rectangle has a length of (8x + 10) cm and a width of (3x + 10) cm.
The length of the rectangle is twice the width.
By first writing and solving an equation, show that the area of the rectangle is 1250 cm2.
[3]
© UCLES 2024
M/S9/02
13
23 Gabriella has two fair spinners.
One spinner is blue and the other is red.
She spins both spinners and adds the two results to give a total score.
She says,
‘Each section of my two spinners is numbered 1 or 2 or 3
1’
The probability that my total score equals 3 is
9
The diagram shows the numbers on the blue spinner.
3
1
3
..........
1
2
..........
..........
2
..........
..........
Blue spinner
..........
Red spinner
Write six possible numbers on the red spinner to make both of Gabriella's statements true.
You may use the table to help you.
Red spinner
+
1
1
Blue
spinner
2
2
3
3
[2]
© UCLES 2024
M/S9/02
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14
24 Here are two ratios.
a : b = 2 : 1 and b : c = 4 : 1
Draw a ring around the ratio that is equivalent to a + b : c.
12 : 1
8:1
6:1
3:1
[1]
25 Eva can pick 7200 apples in 6 hours.
Yuri picks the same number of apples in 8 hours as Eva picks in 7.5 hours.
Calculate how many apples Yuri can pick in 9 hours.
[2]
© UCLES 2024
M/S9/02
15
26 The diagram shows a solid triangular prism.
NOT TO
SCALE
8 cm
The base of the prism is a square with an area of 225 cm2.
The height of the prism is 8 cm.
Calculate the total surface area of the prism.
cm2 [4]
© UCLES 2024
M/S9/02
[Turn over
16
27 The cube and the cuboid have equal volumes.
NOT TO
SCALE
x cm
(x + 5) cm
x cm
Find an expression for the side length of the cube.
cm [2]
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge
Assessment International Education Copyright Acknowledgements Booklet. This is produced annually and is available to download at
https://lowersecondary.cambridgeinternational.org/
Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge
Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.
© UCLES 2024
M/S9/02
Cambridge Lower Secondary Sample Test
For use with curriculum published in
September 2020
Mathematics Paper 1
Stage 9
1 hour
Name
Additional materials: Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
Maths_S9_01/7RP
© UCLES 2020
2
1
Write one of the signs
<
=
>
to complete each statement.
0.3 × 102
9
20 × 10‒1
2
[1]
2
Here are some ratios.
A
B
C
D
9 mm : 1.5 cm
60 cm : 1 m
800 g : 1.2 kg
150 m : 0.25 km
Write each ratio in the correct position in the table.
One has been done for you.
Ratios equivalent to 2 : 3
Ratios equivalent to 3 : 5
A
[1]
© UCLES 2020
M/S9/01
3
3
(a) Simplify.
5mn
2n
[1]
(b) Simplify.
4n +12
6
[1]
(c) Expand and simplify.
(x + 2) (x – 2)
[1]
4
Solve.
4x – 1 < 2x + 19
[2]
© UCLES 2020
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4
5
Work out.
(a) (8 × 0.75)2 × 0.5
[1]
(b)
2
2
×127 − × 7
5
5
[2]
6
A has coordinates (6, –2).
B has coordinates (18, 8).
Pierre says that the midpoint of AB has coordinates (12, 5).
Show that Pierre is wrong.
Show your working.
[1]
© UCLES 2020
M/S9/01
5
7
Some boys take a mathematics test.
The scatter graph shows the time taken by each boy to complete the test and the mark
they each got.
40
30
Mark 20
10
0
10
20
30
Time (minutes)
40
(a) Draw a ring around the type of correlation shown on the scatter graph.
strong negative
weak negative no correlation
weak positive
strong positive
[1]
(b) Seven girls take the same mathematics test.
The scatter graph for the girls shows strong positive correlation.
Complete the scatter graph to show a possible set of results for the girls.
40
30
Mark 20
10
0
10
20
30
Time (minutes)
40
[1]
© UCLES 2020
M/S9/01
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6
8
Look at the numbers in the box.
π
3
8
2
5
1.289
8
1.5
Draw a ring around all the irrational numbers.
9
[1]
The point P has coordinates (1, 2).
y
6
5
4
3
P
2
1
−6
−5
−4
−3
−2
−1 0
1
2
3
4
5
6
x
−1
−2
−3
−4
−5
−6
 −5 
 to give the point Q.
 1 
The point P is translated by the vector 
The point Q is then reflected in the line y = –1 to give the point R.
Find the coordinates of the point R.
(
© UCLES 2020
M/S9/01
,
) [2]
7
10 Here are the nth term rules of three sequences.
Sequence A
Sequence B
Sequence C
7n
5n – 1
20 – 3n
Match each of these numbers to the sequence it is a term in.
24
Sequence A
11
Sequence B
35
Sequence C
[1]
11  is an integer greater than 1
 is a decimal smaller than 1
 ÷  = 60
Write down possible values for  and 
=
=
[1]
© UCLES 2020
M/S9/01
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8
12 In this question use a ruler and compasses only.
Show your construction lines.
(a) Complete this construction of an angle of 60°.
[1]
(b) In the diagram angle BAC = 90°.
Use the diagram to construct an angle of 45°.
B
A
C
[2]
© UCLES 2020
M/S9/01
9
13 Look at this sequence of calculations.
1 × 5 – 2 × 3 = ‒1
2×6–3×4=0
3×7–4×5=1
4×8–5×6=2
(a) Write down the next calculation in this sequence.
×
×
–
=
[1]
(b) Use the sequence to work out.
37 × 41 – 38 × 39
[1]
14 (a) The population of Italy is about 60 000 000
Write this population in standard form.
[1]
(b) The mass of a beetle is 0.0032 kg.
Write this mass in standard form.
kg
© UCLES 2020
M/S9/01
[1]
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10
15 A film is shown at a cinema at 2 pm and at 7 pm every day.
The diagram shows the number of people watching the film at 7 pm on 10 days.
2 pm
7 pm
2
0
5
7
8
1
1
3
5
2
0
5
9
9
3
4
Key : 2 | 2 | 0 represents 22 people watching at 2 pm and 20 people watching at 7 pm.
The number of people watching the film at 2 pm on these days is
32
25
18
37
22
43
27
31
34
28
(a) Complete the back-to-back stem-and-leaf diagram above to show the information
for 2 pm.
One has been done for you.
[2]
(b) Make one comparison between the number of people that watch the film at 7 pm and
the number that watch at 2 pm.
[1]
© UCLES 2020
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11
16 The diagram shows a trapezium.
All dimensions are in centimetres.
NOT TO
SCALE
6n
2n
10n
Find an expression for the area of the trapezium.
Simplify your answer as much as possible.
cm2 [2]
17 Solve.
9
=6
x−5
x=
© UCLES 2020
M/S9/01
[2]
[Turn over
12
18 The diagram shows the positions of two aeroplanes, A and B.
NOT TO
SCALE
North
B
25°
A
Naomi says,
‘The bearing of B from A is 25°.’
Write down two criticisms of Naomi’s statement.
Criticism 1
Criticism 2
[2]
19 Work out.
2
2
1
÷1
3
5
Give your answer as a mixed number in its simplest form.
[3]
© UCLES 2020
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13
20 Yuri and Mia each make a journey.
The travel graph shows Yuri’s journey.
400
300
Yuri
Distance travelled
(km)
200
100
0
0
1
2
3
Time (hours)
4
5
Mia starts her journey at the same time as Yuri.
Mia’s journey lasts 2 hours less than Yuri’s journey.
Mia’s average speed is twice Yuri’s average speed.
Draw a straight line on the travel graph to show Mia’s journey.
[2]
© UCLES 2020
M/S9/01
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14
21 Chen has two fair spinners.
Spinner A
Blue
Spinner B
Red
Yellow
Yellow
Red
Red
Yellow
Red
Yellow
Chen spins both spinners.
(a) Complete the tree diagram.
Outcome from Spinner A
Outcome from Spinner B
1
5
3
4
............
Red
Red
............
............
Yellow
Red
Blue
............
Yellow
[2]
(b) Calculate the probability that both spinners land on a red section.
[1]
© UCLES 2020
M/S9/01
15
22 A linear function maps input numbers to output numbers.
Complete the input-output table for this function.
Input
Output
1
4
2
10
5
28
10
n
[2]
23 Use algebra to solve the simultaneous equations.
x − 2 y = 13
2 x + y = 11
x=
© UCLES 2020
y=
M/S9/01
[3]
[Turn over
16
24 The diagram shows a triangular prism.
5 cm
3 cm
NOT TO
SCALE
6 cm
4 cm
The triangular faces are painted red.
The rectangular faces are painted blue.
Find the fraction of the surface area that is painted red.
[3]
Copyright © UCLES, 2020
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
© UCLES 2020
M/S9/01
Cambridge Lower Secondary Sample Test
For use with curriculum published in
September 2020
Mathematics Paper 2
Stage 9
1 hour
Name
Additional materials: Calculator
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You may use a calculator.
INFORMATION
The total mark for this paper is 50.
The number of marks for each question or part question is shown in brackets [ ].
•
•
Maths_S9_02/7RP
© UCLES 2020
2
1
Simplify.
x4 × x5
[1]
2
Here is an expression 3( x − 2)
2
5
A value of x is substituted into the expression.
Tick () the operation that is performed first when the value of this expression is
calculated.
×3
–2
Square
÷5
[1]
3
The length of a book is 25 cm to the nearest centimetre.
Complete these statements about the length of the book.
The lower limit for the length of the book is
cm.
The upper limit for the length of the book is
cm.
[2]
© UCLES 2020
M/S9/02
3
4
The diagram shows two straight lines crossing a pair of parallel lines.
NOT TO
SCALE
a
e
b
c
d
Here are some statements about angle a.
Tick () the two correct statements.
Angle a is corresponding to angle b.
Angle a is alternate to angle c.
Angle a is equal to angle d.
Angle a is vertically opposite to angle e.
[1]
© UCLES 2020
M/S9/02
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4
5
(a) Find the size of each interior angle in a regular pentagon.
°
[2]
(b) The cross-section of a prism is a regular pentagon.
Draw a ring around the number of planes of symmetry of the prism.
1
2
5
6
[1]
© UCLES 2020
M/S9/02
5
6
A cylinder has a radius of 7 cm and a height of 15 cm.
NOT TO
SCALE
7 cm
15 cm
Calculate the volume of the cylinder.
cm3
© UCLES 2020
M/S9/02
[2]
[Turn over
6
7
(a) Complete the table of values for y = x2 – 4
x
–3
–2
–1
0
y
0
1
2
–4
–3
0
3
[1]
(b) Draw the graph of y = x2 – 4 for values of x between –3 and 3
y
6
5
4
3
2
1
–3
–2
–1
0
1
2
3
x
–1
–2
–3
–4
[2]
© UCLES 2020
M/S9/02
7
8
The table shows information about the temperatures in 20 cities one day.
Temperature, t (°C)
Frequency
6≤t<8
3
8 ≤ t < 10
2
10 ≤ t < 12
4
12 ≤ t < 14
3
14 ≤ t < 16
8
(a) Complete the frequency polygon to show this information.
8
6
Frequency
4
2
0
6
8
10
12
14
16
Temperature, t (°C)
[1]
(b) Put a ring around the interval that contains the median temperature.
6≤t<8
8 ≤ t < 10
10 ≤ t < 12
12 ≤ t < 14
14 ≤ t < 16
[1]
(c) Find the greatest possible value of the range of the temperatures.
°C
© UCLES 2020
M/S9/02
[1]
[Turn over
8
9
(a) Here are the equations of some straight line graphs.
y=x+2
y = 2x – 3
2y = x – 3
x=2
Draw a ring around the graph with gradient 2
[1]
(b) Yuri’s teacher asks him to write down three properties that the graphs of y = 2x + 1
and y = 6x + 1 both have in common.
Yuri has written down two properties.
1
They are both straight lines.
2
They both have a positive gradient.
3
Complete Yuri’s list by writing down another property the two graphs both have in
common.
[1]
© UCLES 2020
M/S9/02
9
10 The diagram shows two shapes on a grid.
y
10
9
8
7
Q
6
5
4
3
2
P
1
0
1
2
3
4
5
6
7
8
9
10 x
Shape Q is an enlargement of shape P.
(a) Write down the scale factor of this enlargement.
[1]
(b) Find the centre of the enlargement.
(
© UCLES 2020
M/S9/02
,
) [1]
[Turn over
10
11 The diagram shows a semi-circle with a radius of 12.3 cm.
NOT TO
SCALE
Calculate the perimeter of the semi-circle.
cm
[3]
12 It takes 5 workers 300 minutes to decorate some cakes.
Find how many minutes it would take 12 workers to decorate the same number of cakes.
minutes
© UCLES 2020
M/S9/02
[2]
11
13 The table shows the prices of two laptops.
Laptop A
$650
Laptop B
$760
The price of Laptop A increases by 12%.
The price of Laptop B decreases by 5%.
Tick () to show which laptop is more expensive after these changes.
Laptop A
Laptop B
Show how you worked out your answer.
[3]
© UCLES 2020
M/S9/02
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12
14 The nth term of a sequence is n2 + a.
The 6th term of the sequence is 29
Find the sum of the first 4 terms.
[3]
15 Make t the subject of the formula w =
2t
−1
5
t=
[2]
16 Show that 4y(5 – 9y) + 6y(6y – 1) simplifies to 14y.
[2]
© UCLES 2020
M/S9/02
13
17 ABCD is a kite.
E is a point on CD.
A
NOT TO
SCALE
78°
B
x°
D
E
38°
C
Calculate the value of x.
[3]
© UCLES 2020
M/S9/02
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14
18 Rajiv sells balloons that are coloured either red, green, blue or yellow.
A customer is given a balloon at random.
25% of the balloons are red.
The probability that a customer is given a green balloon is 0.05
A customer is twice as likely to be given a blue balloon as a green balloon.
Calculate the probability that the balloon is yellow.
You may use the table to help you.
Colour
Red
Green
Blue
Yellow
Probability
[2]
19 Bag A contains 56 counters.
The counters in Bag A are shared between Angelique and Hassan in the ratio 3 : 5
Bag B also contains some counters.
The counters in Bag B are shared between Angelique and Hassan in the ratio 4 : 3
In total Angelique receives 45 counters.
Find the number of counters in total in Bag B.
[3]
© UCLES 2020
M/S9/02
15
20 The table gives some information about the distances jumped by a group of boys and by
a group of girls.
Boys
Girls
Mean
3.36 metres
3.18 metres
Range
1.52 metres
1.05 metres
Mia writes these comparisons of the distances jumped by the boys and the girls.
1
2
The boys have a larger mean than the girls.
The boys have a larger range than the girls.
Mia’s teacher tells her that her comparisons would be better if she wrote them in context.
Write improved comparisons of the distances jumped by the boys and the girls.
1
2
[2]
21 Gabriella is a music teacher.
She wants to know if children in her school like music.
She asks a sample of children from the school orchestra if they like music.
Explain why the data Gabriella collects is likely to be biased.
[1]
© UCLES 2020
M/S9/02
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16
22 The diagram shows a rectangle ABCD.
E
A
F
B
NOT TO
SCALE
12.5 cm
18 cm
D
24 cm
C
E is the midpoint of AB.
EF = 12.5 cm.
Calculate the shaded area.
cm2
[4]
Copyright © UCLES, 2020
Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of the University of
Cambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
publisher will be pleased to make amends at the earliest possible opportunity.
© UCLES 2020
M/S9/02