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
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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]
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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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[1]
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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]
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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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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]
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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]
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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]
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9
16 Construct an angle of 30°.
The construction has been started for you.
[2]
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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]
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11
19 Solve.
2 x − y = 17
x + 3 y = −2
x=
y=
[3]
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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]
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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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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.
:
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[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]
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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
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Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/02
Paper 2
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 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.
IB23 10_0862_02/6RP
© UCLES 2023
[Turn over
17/67
2
1
Draw a ring around the sum of the exterior angles of an equilateral triangle.
120°
180°
360°
900°
[1]
2
Draw a ring around the unit that would be most suitable for measuring the mass of a ship.
light year
megabyte
microgram
tonne
[1]
3
Mia says,‘y is 3 more than x squared’.
Write down a formula for y in terms of x.
y=
4
[1]
Here are the first five terms of a sequence.
11,
14,
19,
26,
35
Find the next two terms in the sequence.
and
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[2]
3
5
Here is the net of a triangular prism.
It is formed from three rectangles and two right-angled triangles.
NOT TO
SCALE
12 cm
13 cm
5 cm
6 cm
Tick () to show if each of these facts about the faces of the triangular prism is true
or false.
True
False
Three faces have the same area.
The area of the largest face is 72 cm2.
[1]
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4
6
Point A has coordinates (1, 2).
y
6
5
4
3
A
2
1
–4
–3
–2
–1 0
–1
1
2
3
4
5
6
x
–2
–3
–4
 3
Point A is first translated by vector   to give point B.
1 
0
Point B is then translated by vector   to give point C.
 −5 
Find the coordinates of point C.
(
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,
) [2]
5
7
Pencils can be bought in small packets or large packets.
small packet has 3 pencils
large packet has 5 pencils
Mike buys m small packets and n large packets.
Altogether he buys 86 pencils.
Draw a ring around the equation that represents this situation.
3m + 5n = 86
8 ( m + n ) = 86
m + n = 86
5m + 3n = 86
[1]
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8
The graphs show the costs, in $, of different masses of strawberries and raspberries.
Strawberries
Raspberries
16
200
12
150
8
Cost ($)
100
4
50
Cost ($)
0
1
2
0
3
5
Mass (kg)
10
15
Mass (kg)
Find how much more 1 kg of raspberries costs than 1 kg of strawberries.
$
9
[2]
It will take 5 workers 12 days to harvest some apples.
Calculate how many workers are needed to harvest these apples in 4 days.
[1]
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7
10 Complete each statement to make it true.
8
=
4x
x
y11 ×
(
= y12
2
( = w10
[3]
11 A train company says the probability that a train arrives at a station on time is 0.85
Ahmed selects a random sample of 80 trains arriving at this station.
Calculate the expected number of these trains that will arrive at this station on time.
[1]
12 (a) Draw lines to match the equivalent inequalities.
x −1 > 2
x >1
2x > 2
x>2
x
>1
2
x>3
[1]
(b) Solve the inequality.
11 – 2x ≤ 20
[2]
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13 Here are the coordinates of four points.
A(4, –6)
B(–4, 5)
C(–3, –2)
D(–3, 2)
Tick () to show if the midpoint of each line segment is above, on or below the x-axis.
Line segment
Above x-axis
On x-axis
Below x-axis
AB
CD
[1]
14 When 80 is increased by a % the result is between 105 and 110
a is a multiple of 4
Find a possible value of a.
a=
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[1]
9
15 The grid shows the positions of triangle P and triangle Q.
y
12
11
Q
10
9
P
8
7
6
5
4
3
2
1
0
x
1
2
3
4
5
6
7
8
9
10
11
12
(a) Describe fully the single transformation that maps triangle P onto triangle Q.
[3]
(b) Triangle R is congruent to triangle P.
Triangle R maps onto itself when it is reflected in the line y = x.
Draw a possible position for triangle R on the grid.
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[1]
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10
16 The diagram shows two circles, each with centre O.
NOT TO
SCALE
11 cm
7 cm
O
Show that the circumference of the larger circle is approximately 44 cm more than the
circumference of the smaller circle.
[2]
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11
17 The table shows information about the ages of 100 runners.
Age (A, years)
Frequency
20 ≤ A < 30
34
30 ≤ A < 40
18
40 ≤ A < 50
28
50 ≤ A < 60
20
Calculate an estimate of the mean age of these runners.
years [3]
18 A teacher asks three students to state the equations of two lines with a positive gradient.
Tick () to show if each student’s answer is correct.
Answer is correct
Chen
y = x + 8 y = 2x – 3
Eva
y=4–x
y = 7 – 2x
Lily
y = 3x
y=
1
x
2
[1]
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19 A shape is formed from
a right-angled triangle ABC
and
a semicircle with diameter CB.
A
NOT TO
SCALE
6 cm
C
B
AC = CB = 6 cm.
(a) Find the area of the whole shape.
cm2 [3]
(b) Calculate the length of AB.
cm [2]
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13
20 Anastasia asks the audience of a film if they liked it or did not like it.
The compound bar chart shows her results.
Key:
100
did not like
90
80
liked
70
60
Frequency
50
40
30
20
10
0
Adults
Children
Show that 30% of people in the audience did not like the film.
[2]
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14
21 (a) The distance between two cities is 17 000 km correct to the nearest 1000 km.
Complete the inequality to show the limits of the distance.
km
16 500 km ≤ distance <
[1]
(b) The mass of a bag is 1.00 kg correct to 2 decimal places.
Find the lower limit of the mass.
kg
[1]
cm2
[3]
22 A solid cylinder has a height of 18 cm.
NOT TO
SCALE
18 cm
The curved surface area of the cylinder is 845 cm2.
Find the area of the top of the cylinder.
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23 Find the values of the integers a and b when
(x – 5)(x + 5) + ax = (x – 3)(x + 12) + b
a=
b=
[3]
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16
24 Rajiv has a bag containing only red counters and blue counters.
Safia has a different bag containing only red counters and blue counters.
They each take one counter at random from their bag.
The probability that Rajiv picks a red counter from his bag is 0.6
The probability that they both pick a red counter is 0.18
Rajiv
Safia
red
P(red and red) = 0.18
red
0.6
blue
red
blue
blue
Find the probability that they both pick a blue counter.
You may use the tree diagram to help you.
[4]
_________________________________________________________________________________________________________________________________________
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
0862/02/O/N23
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Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/01
Paper 1
April 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 04_0862_01/7RP
© UCLES 2023
[Turn over
33/67
2
1
A regular polygon has exactly 8 lines of symmetry.
Tick () to show if these facts about the polygon are true, false or if you cannot tell.
True
False
Cannot tell
The polygon has 16 sides.
The polygon has rotational symmetry of order 8
[1]
2
Carlos rolls a fair six-sided dice 60 times.
Calculate how many times Carlos should expect to roll a 3
[1]
3
Write the letter for each calculation in the correct column of the table.
One has been done for you.
A
B
C
D
7×6
75 × 7
76 ÷ 70
72 × 73
Equal to 76
Not equal to 76
A
[1]
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3
4
Expand and simplify.
(c + 4)(c + 10)
[2]
5
Draw a line to match each calculation to its answer.
One has been done for you.
5 × 10–1
0.005
0.05 × 104
0.5
5 ÷ 10–3
500
0.5 ÷ 102
5000
[1]
6
Work out the value of
(10 − 2 x )
4
when x = 4
[2]
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4
7
A pyramid has
• a square base with a side length of 10 cm
• four congruent triangular faces each with a height of 12 cm.
NOT TO
SCALE
12 cm
10 cm
Calculate the surface area of the pyramid.
cm2 [2]
8
The arrow points to a number.
4
5
6
Draw a ring around the number the arrow points to.
11
22
30
35
[1]
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5
9
Ahmed draws this graph to show how the number of visitors to his town has increased.
Big increase in the number of visitors to the town
Number of
visitors
Give one reason why the graph could be misleading.
[1]
10
1
is equivalent to a recurring decimal.
n
n is a whole number.
Safia says, ‘n must be greater than 5’
Write a number to complete this sentence.
Safia is not correct because the value of n could be
[1]
11 (a) Write 70 000 in standard form.
[1]
(b) Write 7.5 × 10–3 as an ordinary number.
[1]
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6
12 Here is Eva’s method for drawing the perpendicular bisector of line AB.
5 cm
6 cm
A
B
She draws an arc radius 5 cm centre A.
She draws an arc radius 6 cm centre B.
She draws a line to connect the points where her arcs intersect.
Explain why Eva’s method is not correct.
[1]
13 Here is a formula.
y = w−2
Draw a ring around the correct rearrangement of the formula.
w=
y+2
w=
w = ( y + 2)
y +2
2
w = y2 + 2
[1]
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7
14 (a) Write down the value of
7
3
×5×
3
7
[1]
9
2
÷2
5
10
Give your answer as a fraction in its simplest form.
(b) Calculate
[3]
15 The internal storages of three games consoles are
500 000 MB
32 GB
1 TB
Write these values in order of size, starting with the smallest.
smallest
largest
[1]
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8
16 The diagram shows a triangle T drawn on a grid.
y
6
5
4
3
T
2
1
–6
–5
–4
–3
–2
–1 0
–1
1
2
3
4
5
6
x
–2
–3
–4
–5
–6
(a) Triangle T is rotated by 180° about centre (0, 0).
The new triangle is then rotated by 180° about centre (0, –3) to give triangle U.
Draw the position of triangle U on the grid.
[2]
(b) Draw a ring around the type of transformation that maps triangle T onto triangle U.
translation
reflection
rotation
enlargement
[1]
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9
17 The table shows information about the masses of 70 boxes.
Mass, x (kg)
Frequency
14 ≤ x < 16
10
16 ≤ x < 18
7
18 ≤ x < 20
13
20 ≤ x < 22
20
22 ≤ x < 24
20
(a) Draw a ring around the interval that contains the median.
14 ≤ x < 16
16 ≤ x < 18
18 ≤ x < 20
20 ≤ x < 22
22 ≤ x < 24
[1]
(b) Draw a frequency polygon to show the information in the table.
24
22
20
18
16
14
Frequency
12
10
8
6
4
2
0
13
14
15
16
17
18
19
20
Mass, x (kg)
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21
22
23
24
25
[2]
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10
18 (a) The nth term of a sequence is n2 + 5
Find the 7th term of the sequence.
[1]
(b) Here are the first five terms of a different sequence.
0,
3,
8,
15,
24
Find an expression for the nth term of this sequence.
[1]
19 Find the coordinates of two points on the line y = 5 − 3x which have
a negative x-coordinate
and
a y-coordinate which is a multiple of 4
(
,
)
(
,
)
[2]
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11
20 Chen records the length, in millimetres, of 10 shells.
34
46
37
55
38
52
68
40
31
47
He draws this stem-and-leaf diagram to show the data.
6
8
4
0
6
7
3
1
4
7
5
2
5
8
Chen’s stem-and-leaf diagram contains some errors.
Draw a correct stem-and-leaf diagram to show Chen’s data.
[2]
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12
21 The diagram shows a rectangle ABCD.
A
G
B
NOT TO
SCALE
46°
E
F
x
20°
D
C
H
EF is parallel to AB.
EG is parallel to HF.
Calculate the size of the angle marked x.
x=
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° [2]
13
22 Lily heats the water in her swimming pool.
The graph shows the temperature, in °C, of the water for the first 50 minutes after 9 am.
17
16.9
16.8
16.7
16.6
16.5
Temperature (°C)
16.4
16.3
16.2
16.1
16
15.9
0
5
10
15
20
25
30
35
40
45
50
Minutes after 9 am
The temperature of the water continues to increase at this constant rate.
Find the temperature of the water at 11 am.
°C [2]
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14
23 Oliver and Angelique each have a jar that contains only green counters and red counters.
Oliver’s jar
Angelique’s jar
Total number of counters = 42
Total number of counters = ?
green : red = 3 : 4
green : red = 5 : 2
Angelique has the same number of red counters as Oliver.
Find the total number of counters in Angelique’s jar.
[3]
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15
24 The area of a trapezium is 24.5 cm2.
a cm
NOT TO
SCALE
h cm
b cm
a, b and h are integers greater than 1
a < b.
Find a set of possible values for a, b and h.
a=
b=
h=
[2]
25 Solve.
12
= −3
5 − 2x
x=
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[3]
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16
26 A bag contains a large number of coloured balls.
Each ball is red or green or blue or yellow.
A ball is picked at random from the bag.
The table shows some of the probabilities.
Colour of ball
Red
Green
Blue
Yellow
Probability
0.3
0.1
x
1.5x
Calculate the probability that the ball picked is blue or green.
[4]
____________________________________________________________________________
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.
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Cambridge Lower Secondary Checkpoint

MATHEMATICS
0862/02
Paper 2
April 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 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 20 pages. Any blank pages are indicated.
IB23 04_0862_02/6RP
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2
1
A square has a side length of x cm.
x cm
x cm
Find an expression for the area of the square.
Give your answer in its simplest form.
cm2 [1]
2
A circle has a radius of 8.7 cm.
NOT TO
SCALE
8.7 cm
Find the area of the circle.
cm2 [2]
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3
3
Naomi and Samira share some apples.
Naomi receives less than half of the apples.
Draw a ring around the possible value of the ratio of Naomi’s share to Samira’s share.
1:5
3:2
1:1
7:5
[1]
4
Use the numbers in the box to complete the sentences.
19
19
6
82
and
are rational numbers.
and
are irrational numbers.
[1]
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4
5
The diagram shows a square drawn on a coordinate grid.
y
12
11
10
9
8
7
6
5
4
3
2
1
–4 –3 –2 –1 0
–1
1
2
3
4
5
6
7
8
9
10
x
–2
Draw the image of the square after an enlargement, scale factor 3, centre (2, 3).
[2]
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5
6
The bar chart shows the number of small, medium and large potatoes in a sack.
11
10
9
8
7
Frequency
6
5
4
3
2
1
0
Small
Medium
Size of potato
Large
Complete the pie chart to show this information.
Small
[3]
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6
7
The diagram shows two parallel lines and two transversals.
NOT TO
SCALE
d
c
b
e
70°
a
Draw a ring around all the angles that must be equal to 70°.
a
b
c
d
e
[1]
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7
8
Here are three scatter diagrams.
y
Diagram A
y
Diagram B
x
x
y
Diagram C
x
Draw a line to match each scatter diagram to the best description of its correlation.
Strong positive
Diagram A
Weak positive
Diagram B
No correlation
Weak negative
Diagram C
Strong negative
[1]
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8
9
Ahmed has two bags each containing four balls.
The balls in bag A are numbered 1, 3, 5 and 6
The balls in bag B are numbered 2, 3, 4 and 6
Ahmed picks a ball at random from each bag.
He adds together the numbers on the two balls to get a total score.
Show that P(total score is even) = P(total score is more than 8).
You may use the table to help you.
Bag A
+
1
2
3
3
5
6
8
3
Bag B
10
4
6
[3]
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9
10 (a) Here are the definitions of some angles.
A=
interior angle of an
equilateral triangle
B =
interior angle of a
regular pentagon
C =
exterior angle of a
regular pentagon
D =
exterior angle of a
regular hexagon
Draw a ring around the two angles that add up to 180°.
A
B
C
D
[1]
(b) Find the sum of the interior angles of a 7-sided polygon.
° [1]
11 (a) A number, x, rounded to the nearest 100 is 1500
Complete the inequality to show the possible values of x.
≤x<
[1]
(b) The time taken to run a race is 9.87 seconds correct to 3 significant figures.
Write down the upper limit for the time.
s [1]
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10
12 (a) Yuri wants to investigate how exercise changes his heart rate.
He considers two methods for measuring his heart rate.
Method A
Method B
68
B PM
Find his heart rate by placing
two fingers on his wrist and
counting the beats.
Find his heart rate using a
digital heart rate monitor.
Yuri decides to use method A.
Give one reason why this may not be the better method.
[1]
(b) Yuri also wants to compare his results with those for other people his age.
He decides to repeat his experiment on 40 members of a gym.
Explain why his sampling method may not give him reliable data about the heart rates
of other people his age.
[1]
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11
13 Hassan thinks of a number, n.
He multiplies it by 4
His answer is greater than –8 and less than or equal to 20
(a) Write the correct inequality signs to complete the inequality.
–8
4n
20
[1]
(b) Solve the inequality to find the possible values of n.
Give your answer as an inequality in terms of n.
[2]
14 In September a coat costs $62.50
In October the cost of the coat increases by 4% of the cost in September.
In November the cost of the coat increases by a further 14.6% of the cost in October.
Find the cost of the coat after both increases.
$
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[2]
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12
15 Find the equation of the graph.
Give your answer in the form y = mx + c.
y
7
6
5
4
3
2
1
–2
–1
0
1
2
3
4
5
x
–1
–2
y=
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[2]
13
16 The first term of a sequence is – 0.7
The term-to-term rule of the sequence is ‘multiply by –1 and then add 0.5’
(a) Show that the sum of the first four terms of the sequence is 1
[2]
(b) Complete the following statements.
The sum of the first 12 terms of this sequence is
The sum of the first 400 terms of this sequence is
[1]
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14
17 The map shows the position of a shop, S, and a library, L, on an island.
The scale of the map is 1 cm to 50 m.
North
Scale: 1 cm to 50 m
North
Land
S
L
Sea
A restaurant, R, is built on the island
on a bearing of 130° from the shop
and
220 metres from the library.
Mark the position of the restaurant on the map.
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[2]
15
18 The graph of 2y = 11 − 8x is shown on the grid.
y
8
7
6
5
4
3
2
1
–1
0
1
2
3
4
5
6
x
–1
–2
–3
–4
2y = 11 – 8x
(a) Draw the graph of 2x − 5y = 10 on the grid.
Use the table of values to help you.
x
0
0
y
[2]
(b) Use your graph to solve the simultaneous equations.
2y = 11 – 8x
2x − 5y = 10
x=
y=
[2]
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16
19 The cross-section of a prism is a regular polygon.
The prism has exactly 6 planes of symmetry.
Draw a ring around the shape of the cross-section.
square
pentagon
hexagon
octagon
[1]
20 A jug is a cylinder with a diameter of 14 cm.
The height of the water in the jug is 31 cm.
NOT TO
SCALE
31 cm
14 cm
The capacity of a glass is 315 cm3.
Find how many of these glasses can be completely filled using the water in the jug.
[3]
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17
21 Here are some of the inputs and outputs of a function.
input
output
x
→
5x2
a
→
180
a is an integer.
Find the two possible values of the output when the input is a + 1
and-
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[3]
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18
22 ABCD is a rectangle measuring 4 cm by 10.5 cm.
NOT TO
SCALE
A
E
B
6.5 cm
1.6 cm
F
4 cm
D
10.5 cm
C
EF = 6.5 cm
BF = 1.6 cm
Calculate DE.
cm [4]
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19
23 a and b are positive integers.
a
= 0.37 correct to 2 significant figures.
b
b is a cube number less than 200
Find a possible pair of values for a and b.
a=
b=
[2]
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