Mathematics
Stage 9
Paper 1
2022
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_6RP
© UCLES 2022
2
1
A prism is made from four identical cubes.
Tick () to show the number of planes of symmetry the prism has.
1
2
3
4
[1]
2
A bag contains pencils of four different colours.
Here are some of the probabilities of picking a pencil of each colour.
Probability
Red
Yellow
Blue
0.35
0.25
0.1
Green
(a) Find the probability of picking a pencil that is red or yellow.
[1]
(b) Complete the table.
[1]
3
Solve.
12
=3
x
x=
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[1]
3
4
Use a straight edge and compasses only to construct an equilateral triangle ABC.
The side AB has been drawn for you.
Do not rub out your construction arcs.
A
B
[1]
5
Here are some pairs of events.
Tick () to show if each pair of events is independent or not independent.
Independent
Pick a disk from a
box at random and
replace it.
Pick another disk
from the same box
at random.
Pick a disk from a
box at random and
do not replace it.
Pick another disk
from the same box
at random.
Pick a disk from a
box at random and
do not replace it.
Roll a dice.
Not independent
[1]
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[Turn over
4
6
The diagram shows triangle ABC drawn on a grid.
y
7
6
5
4
C
3
2
1
–5 – 4 –3 –2 –1 0
A –1
–2
–3
1
2
3 4
B
5
6
x
The triangle ABC is enlarged by a scale factor of 2 from centre of enlargement (0, 0).
Find the coordinates of the new position of vertex C.
(
7
,
) [1]
A circle has a radius of 3 cm.
Tick () to show the area of the circle correct to the nearest cm2.
6
9
18
28
81
[1]
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5
8
Find the value of
4 − 3x
+ 8 when x = 2
x
[1]
9
A rectangle has an area of 8 cm2.
The sides of the rectangle are enlarged by a scale factor of 3
Find the area of the enlarged rectangle.
cm2 [1]
10 Work out.
3  5

1 −  ÷ 1 − 
5  9

Give your answer as a fraction in its simplest form.
[2]
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6
11 The distance–time graph represents Jamila’s journey from home.
100
75
Distance
from home 50
(km)
25
0
12 noon
1 pm
2 pm
3 pm
4 pm
5 pm
Time
Stage 1. She travels at a constant speed of 50 km/h for 1 hour.
Stage 2. She stops for 1 hour.
(a) Describe fully the next two stages of Jamila’s journey.
Stage 3
Stage 4
[2]
(b) At 3 pm Jamila travels home at a constant speed of 50 km/h without stopping.
Complete the graph to show Jamila’s journey home.
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[1]
7
12 Here are some shapes on a grid.
A
X
B
C
D
E
F
Write the letter A to F for each of the shapes in the correct part of the Carroll diagram.
Shape A has been done for you.
Congruent to shape X
Similar to shape X
Not congruent to shape X
A
Not similar to shape X
[2]
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8
13 Write a number in the box to make the statement correct.
71 =
.426…
[1]
14 (a) A scientist writes the number 760 000 000 in standard form.
Draw a ring around the correct answer.
7.6 × 107
76 × 107
7.6 × 108
7.6 × 109
[1]
(b) The scientist measures the width of a human hair as 0.000 046 m.
Write this number in standard form.
m [1]
15 Mike runs 4.5 laps of a field.
He runs a total distance of 3.78 km.
Find the distance of each lap.
km [1]
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9
16 Carlos says,
All fractions with an odd denominator
are equivalent to recurring decimals,
for example, 13 0.3
Find an example to show that Carlos is wrong.
[1]
17 The function y = ( x − 3)2 can be represented by this function machine.
Input (x) →
–3
→
Square → Output (y)
(a) Find the output if the input is −1
[1]
(b) Find the two inputs that give an output of 9
[2]
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10
18 (a) Solve.
2x − 9 < 6x + 3
[2]
(b) Show your solution on the number line.
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
x
[1]
19 Work out.
4
2
2 1
−2 +
5
3 3
Give your answer as a mixed number in its simplest form.
[3]
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11
20 The table shows information about the wingspans of 50 butterflies.
Wingspan (𝒙 cm)
Frequency
4.0 ≤ x < 4.4
5
4.4 ≤ x < 4.8
12
4.8 ≤ x < 5.2
23
5.2 ≤ x < 5.6
8
5.6 ≤ x < 6.0
2
Draw a frequency polygon to show this information.
25
20
15
Frequency
10
5
0
4.0
4.4
4.8
5.2
Wingspan (cm)
5.6
6.0
[3]
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12
21 Shape A and shape B are drawn on the grid.
y
7
6
5
4
3
A
2
1
– 4 –3 –2 –1 0
–1
1
2
3
4
5
6
7
8
x
–2
B
–3
–4
–5
Shape A is mapped onto shape B by a combination of two transformations.
The first transformation is a reflection in the line y = x
Describe fully the second transformation.
[2]
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13
22 The diagram shows a triangle ABC.
DE is parallel to AC.
B
x
NOT TO
SCALE
E
D
115°
60°
A
C
Calculate the size of the angle marked 𝑥 .
° [2]
23 The line segment joining (a, b) to (c, d) has a midpoint of (3.5, –2).
Suggest possible coordinates for (a, b) and (c, d).
(a, b) = (
,
)
(c, d) = (
,
)
[2]
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14
24 Simplify.
4 p − 12 pq
4p
[1]
25 The nth term of sequence S is 2n + 5
The nth term of sequence T is 3n – 6
(a) Show that 91 is a term in sequence S.
[1]
(b) Show that 91 is not a term in sequence T.
[1]
(c) Find the value of the term that is in both sequences and is in the same position in each
sequence.
[2]
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15
26 Mia asks the boys and girls in her class how many siblings (brothers and sisters) they
each have.
She draws this chart of her results.
Number of
children
boys
girls
0
0
1
2
3
Number of siblings
4 or more
Tick () to show if the boys or the girls generally have more siblings.
Boys
Girls
Explain how you know.
Tick () to show if the range of the number of siblings is bigger for the boys or the girls.
Boys
Girls
Explain how you know.
[2]
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16
27 Solve the simultaneous equations.
4 x + 5 y = 17
2 x + 4 y = 13
x=
y=
[3]
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 2022
M/S9/01
Mathematics
Stage 9
Paper 1
Cambridge Lower Secondary Progression Test
Mark Scheme
3143_01_MS_6RP
© UCLES 2022
2022
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
2022
General guidance on marking
Difference in printing
It is suggested that schools check their printed copies for differences in printing that may affect the
answers to the questions, for example in measurement questions.
Brackets in mark scheme
When brackets appear in the mark scheme this indicates extra information that is not required but
may be given.
For example:
Question
Answer
Mark
5
19.7 or 19.6(58…)
1
Part marks
Guidance
This means that 19.6 is an acceptable truncated answer even though it is not the correct rounded
answer.
The … means you can ignore any numbers that follow this; you do not need to check them.
Accept
• any correct rounding of the numbers in the brackets, e.g. 19.66
• truncations beyond the brackets, e.g. 19.65
Do not accept
• 19.68 (since the numbers in brackets do not have to be present but if they are they should be
correct).
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
2022
These tables give general guidelines on marking learner responses that are not specifically
mentioned in the mark scheme. Any guidance specifically given in the mark scheme supersedes this
guidance.
Number and place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept trailing zeros, unless the question has asked for a specific number of decimal places or
significant figures, e.g.
0.7000
Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. Units are provided on the answer line unless finding the units is part of what is
being assessed.
The table shows acceptable and unacceptable versions of the answer 1.85 m.
Accept
Do not accept
If the unit is given on the
answer line, e.g.
............................ m
Correct conversions, provided
the unit is stated
unambiguously,
e.g. ......185 cm...... m (this is
unambiguous since the unit cm
comes straight after the
answer, voiding the m which is
now not next to the answer)
......185...... m
......1850...... m etc.
If the question states the unit
that the answer should be
given in, e.g. ‘Give your answer
in metres’
1.85
1 m 85 cm
185; 1850
Any conversions to other units,
e.g. 185 cm
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
2022
Money
In addition to the rules for units, the table below gives guidance for answers involving money.
The table shows acceptable and unacceptable versions of the answer $0.30
If the amount is in dollars and
cents, the answer should be
given to two decimal places
If units are not given on the
answer line
If $ is shown on the answer line
If cents is shown on the answer
line
Accept
Do not accept
$0.30
$0.3
For an integer number of
dollars it is acceptable not to
give any decimal places, e.g.
$9 or $9.00
$09 or $09.00
Any unambiguous indication of
the correct amount, e.g.
30 cents; 30 c
$0.30; $0–30; $0=30; $00:30
30 or 0.30 without a unit
All unambiguous indications,
e.g. $......0.30......;
$......0-30......;
$......0=30......;
$......00:30......
$......30......
......30......cents
......0.30......cents
$30; 0.30 cents
Ambiguous answers, e.g.
$30 cents; $0.30 c; $0.30 cents
(as you do not know which unit
applies because there are units
either side of the number)
Ambiguous answers, e.g.
$......30 cents......;
$......0.30 cents......
unless units on the answer line
have been deleted, e.g.
$......30 cents......
Ambiguous answers, e.g.
......$30 ......cents;
......$0.30 ......cents
unless units on the answer line
have been deleted, e.g.
......$0.30......cents
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
2022
Duration
In addition to the rules for units, the table below gives guidance for answers involving time durations.
The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes.
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr, hrs),
minutes (m, min, mins) and
seconds (s, sec, secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
Incorrect or ambiguous formats, e.g.
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h (this is because this indicates 0.3 of
an hour (i.e.18 minutes) rather than 30 minutes)
Any correct conversion with appropriate units,
e.g.
2.5 hours; 150 mins
unless the question specifically asks for time
given in hours and minutes
02:30 (as this is a 24-hour clock time, not a time
interval)
2.5; 150
Time
The table below gives guidance for answers involving time.
The table shows acceptable and unacceptable versions of the answer 07:30
Accept
Do not accept
If the answer is required in
24-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
07:30 with any separator in
place of the colon, e.g.
07 30; 07,30; 07-30; 0730
7:30
7:30 am
7 h 30 m
7:3
730
7.30 pm
073
07.3
If the answer is required in
12-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
7:30 am with any separator in
place of the colon, e.g.
7 30 am; 7.30 am; 7-30 am
Absence of am or pm
1930 am
7 h 30 m
7:3
730
7.30 pm
7.30 in the morning
Half past seven (o’clock) in the
morning
Accept am or a.m.
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Mathematics Stage 9 Paper 1 Mark Scheme
2022
Algebra
The table shows acceptable and unacceptable versions of the answer 3x – 2
Accept
Do not accept
x3 – 2; 3 × x – 2
3x + –2 if it is supposed to be in simplest form
Case change in letters
Changes in letters as long as there is
no ambiguity
Accept extra brackets when factorising, e.g. 5(x + (3 + y))
Teachers must mark the final answer given. If a correct answer is seen in working but final answer is
given incorrectly then the final answer must be marked. If no answer is given on the answer line then
the final line of the working can be taken to be the final answer.
Inequalities
The table shows acceptable and unacceptable versions of various answers.
For the following
Accept
Do not accept
For 6 ≤ x < 8
[6, 8)
<x<
For x ≤ –2
(–∞,–2]
x < –2
For x > 3
(3, ∞)
3<x
Just ‘3’ written on the answer line, even if x > 3
appears in the working
Plotting points
The table shows acceptable and unacceptable ways to plot points.
Accept
Crosses or dots plotted within ±
Do not accept
1
square of the
2
correct answer
A horizontal line and vertical line from the axes
meeting at the required point
The graph line passing through a point implies
the point even though there is no cross
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
Answer
1
1
2

3
Marks
4
Part Marks
2022
Guidance
1
Accept any clear indication.
2(a)
0.6
1
Accept equivalent fractions or
6
or 60%
percentage, e.g.
10
2(b)
0.3
1
Accept if not inserted in table, but
clearly the final answer.
Accept equivalent fractions or
3
percentage, e.g
or 30%
10
3
( x =) 4
1
4
Correct equilateral triangle with correct
construction arcs left visible.
1
Label C not required.
Tolerance ± 2 mm
1
Accept any clear indication.
5
Independent
Not independent
All three answers correct for the
mark.



6
(4, 6)
7
6
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1
9
18
28 
81
1
Page 7 of 12
Accept any clear indication.
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
Answer
Marks
Part Marks
8
7
1
9
72 (cm2)
1
10
2
9
2022
10
Award 1 mark for
2
5
×
9
4
Guidance
or
18
45
÷
20
45
1 mark implied by any equivalent
9
18
e.g.
fraction to
10
20
11(a)
(Stage 3) She travels at (a constant speed
1
of) 50 km/h for
an hour.
2
(Stage 4) She travels at (a constant speed
1
an hour.
of) 25 km/h for
2
2 Award 1 mark for one stage correctly
described or for two correct speeds
with times missing/wrong.
Accept equivalent times,
e.g. 30 minutes.
11(b)
A straight line from (3 pm, 87.5) to
(4.45 pm, 0).
1
Accept values closer to 4.45 pm than
4.30 pm or 5 pm.
12
Five letters (B to F) correctly placed in the
Carroll diagram.
2 Award 1 mark for three or four letters
(B to F) correctly placed in the Carroll
diagram.
Similar to
shape X
Not similar
to shape X
13
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8
Congruent
to shape X
Not congruent
to shape X
(A) D
B F
C E
1
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
Answer
Marks
Part Marks
14(a)
7.6 × 107
14(b)
4.6 × 10− 5 (m)
1
15
0.84 (km)
1
16
Any correct example of a fraction with an
odd denominator showing it is not a
1
recurring decimal, e.g. = 0.2
5
1
17(a)
16
1
17(b)
0 and 6
2 Award 1 mark for one correct value.
18(a)
x > −3
2 Award 1 mark for gathering the terms
in x on one side and constant terms
on the other side,
e.g. 2 x − 6 x < 3 − − 9
(ignore inequality for this mark, may
replace with =)
76 × 107
7.6 × 108
7.6 × 109
Must show fraction and correct
decimal equivalent for the mark.
Award 1 mark for x > −3 in the working
with just −3 on the answer line
or for x = −3 on the answer line.
© UCLES 2022
– 6 –5 – 4 –3 –2 –1 0 1 2 3 4 5 6 x
Guidance
Accept any clear indication.
1
or
18(b)
2022
1 Follow through their inequality from
part (a).
Page 9 of 12
Accept 0 and 6 in either order for
2 marks.
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
19
Answer
2
1
15
Marks
Part Marks
3
correct answer only
2022
Award 2 marks for
31
15
Guidance
or equivalent
fraction.
or
Award 1 mark for
22
or
8
5
3
2
1
or 2 + −
or 4 − 2
5 3
5
3
6
10
5
or 4
−2
+
15
15 15
2
20
Straight lines joining (4.2, 5) and (4.6, 12)
and (5.0, 23) and (5.4, 8) and (5.8, 2).
25
3 Award 1 mark for four or five plots
correct horizontally
(x = 4.2, 4.6, 5.0, 5.4, 5.8).
and
20
Award 1 mark for four or five plots
correct vertically
(frequency = 5, 12, 23, 8, 2).
15
Frequency
10
5
0
4.0
© UCLES 2022
1
4.4 4.8 5.2 5.6
Wingspan (cm)
6.0
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Mark intention.
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
21
Answer
 − 4

 −9 
Translation of 
Marks
2022
Part Marks
2 Award 1 mark for the word translation
 − 4
or for  
 −9 
Guidance
 − 4
 expressed in
 −9 
Do not accept 
words.
or for a correct reflection of A in y = x
drawn on the grid.
22
55 (°)
2 Award 1 mark for
60 (°) correctly marked at BED or
65 (°) correctly marked at BDE or
65 (°) correctly marked at BAC.
23
Any pair of coordinates (a, b), (c, d) where
a+c
b+d
= 3.5 and
= −2
2
2
but not (3.5, –2) and (3.5, –2) as this is not
a line segment.
2 Award 1 mark for any pair of
coordinates (a, b), (c, d) where
a+c
b+d
= 3.5 or
= −2
2
2
24
1 − 3q correct answer only
1
25(a)
2n + 5 = 91
2n = 86
n = 43 or 86 is even/a multiple of 2
1
3n – 6 = 91
3n = 97
n = 32.3 … or equivalent or 97 is not a
multiple of 3
1
27
2 Award 1 mark for 2n + 5 = 3n − 6
implied by n = 11
25(b)
25(c)
© UCLES 2022
Accept a and c as 3.5 or b and d as
–2, but not both, for 1 or 2 marks, as
appropriate.
0 marks for (3.5, –2) and (3.5, –2).
Full working required for the mark.
Accept sequence extended up to 91
Full working required for the mark.
Accept sequence extended up to 93
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S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
Question
26
Answer
Boys ticked and more boys have (2 or 3 or)
4 or more siblings or equivalent
and
Boys ticked and the range for boys is 4 or
more and/or the range for girls is 3
27
( x =) 0.5 and ( y =) 3
Marks
Part Marks
2 Award 1 mark for
Boys ticked and more boys have (2 or
3 or) 4 or more siblings or equivalent
or
Boys ticked and the range for boys is 4
or more and/or the range for girls is 3
3 Award 2 marks for
x = 0.5 or y = 3
or
Award 1 mark for a correct method for
eliminating either x or y,
e.g.
• Re-arranging one of the equations
to make one variable the subject
and then substitute their
arrangement into the other
equation.
• Making the coefficients of x or y
equal with no more than one
arithmetic error or sign error,
followed by an appropriate,
consistent subtraction or addition
across all three terms.
• Correct substitution and evaluation
from incorrect first value, i.e. two
values satisfying one of the original
equations.
© UCLES 2022
2022
Page 12 of 12
Guidance
Or equivalent for first explanation, e.g.
• Fewer girls have (2 or 3 or) 4 or
more siblings.
• No girls have 4 or more siblings.
• More girls have 0 or 1 sibling.
• Fewer boys have 0 or 1 sibling.
For first explanation, accept reference
to taller bars, e.g. the bar for boys is
taller than for girls for (2 or 3 or) 4 or
more siblings.
Accept x =
1
2
Mathematics
Stage 9
Paper 2
2022
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_5RP
© UCLES 2022
2
1
A plant is 6.2 cm tall.
The height of the plant increases by 11% each week.
Find how tall the plant will be after two weeks.
cm [2]
2
Pierre says,
I think of a number n
I multiply by 4
Then I square.
Then I add 6
Write down an algebraic expression for Pierre’s rule.
[1]
3
Draw a ring around each of the rational numbers.
8100
22
7
7
7
3
8
[1]
© UCLES 2022
M/S9/02
3
4
A line is drawn on the grid.
y
8
6
4
2
0
2
4
6
8 x
Find the equation of the line.
[2]
5
Oliver and Mia attempt this question.
Round 0.027 648 correct to three significant figures.
Oliver says, ‘The answer is 0.028’
Mia says, ‘The answer is 0.0276’
Tick () to show who is correct.
Oliver
Mia
Explain why the other answer is not correct.
[1]
© UCLES 2022
M/S9/02
[Turn over
4
6
Draw a line to match each scatter graph to the best description.
Strong positive
correlation
Weak positive
correlation
Weak negative
correlation
Strong negative
correlation
[1]
7
Calculate.
0.6 + (1.78 − 0.28) 2
5
[1]
© UCLES 2022
M/S9/02
5
8
Safia drives for 4 hours from A to B.
Angelique drives at half the speed of Safia.
Find how many hours Angelique takes to drive from A to B.
hours [1]
9
The table gives information about the masses of 20 watermelons.
Mass, m (kg)
Frequency, f
Midpoint, x
f ×x
2≤m<4
2
3
6
4≤m<6
4
5
20
6≤m<8
9
7
63
8 ≤ m < 10
5
Total = 20
Total =
(a) Complete the table.
[1]
(b) Calculate an estimate of the mean mass of these watermelons.
kg [1]
(c) Explain why your answer to part (b) is an estimate.
[1]
© UCLES 2022
M/S9/02
[Turn over
6
10 Lily counts the number of people on the 12 buses that arrive at Pugu bus station in one day.
23
29
20
27
44
27
41
28
19
16
17
8
She draws a stem-and-leaf diagram of her results.
0
8
1
6
7
9
2
0
3
7
4
1
8
9
3
4
Key:
1 6 represents 16 buses
Lily makes some mistakes on her stem-and-leaf diagram.
Redraw the stem-and-leaf diagram correctly below.
Key:
..................................................
..................................................
[3]
© UCLES 2022
M/S9/02
7
11 The exterior angle of a regular polygon is 40°.
Draw a ring around the number of sides this polygon has.
7
8
9
10
[1]
12 Some equations of straight lines have been placed in the Venn diagram.
y
A
y
3x 3
y
y
y
x3
3x 2
y
B
9x 2
3x 4
y
y
x2
2x 2
4x 2
y
2x 4
(a) Write down a description of the straight lines in set A.
[1]
(b) Write down a description of the straight lines in set B.
[1]
(c) Write the equation y = − 2 x + 3 in the correct part of the Venn diagram.
© UCLES 2022
M/S9/02
[1]
[Turn over
8
13 The map shows the positions of two lighthouses, A and B.
The map is drawn to a scale of 1 : 50 000
North
A
B
Scale 1 : 50 000
The bearing of ship S from lighthouse A is 080°.
The distance of ship S from lighthouse B is 1.8 km.
Show the two possible positions for ship S on the map.
[3]
14 Expand and simplify.
( x + 4)( x − 7)
[2]
© UCLES 2022
M/S9/02
9
15 Yuri has a box containing white, milk and plain chocolates in the ratio
white : milk : plain
12 : 7 : 2
There are more than 50 chocolates in the box.
Find the smallest possible number of milk chocolates in the box.
[1]
16 Rearrange the formula to make x the subject.
y=
9
x+4
5
x=
© UCLES 2022
M/S9/02
[2]
[Turn over
10
17 (a) Complete the table of values for 3x + 2 y = 4
x
–1
0
3
y
[2]
(b) Draw the graph of 3x + 2 y = 4 for values of x between –1 and 3
y
4
3
2
1
–1
0
1
2
3 x
–1
–2
–3
[1]
© UCLES 2022
M/S9/02
11
18 A cylinder has a radius of 6 cm and a height of 20 cm.
20 cm
NOT TO
SCALE
6 cm
Find the total surface area of this cylinder.
cm2 [3]
© UCLES 2022
M/S9/02
[Turn over
12
19 Chen prepares food and drink for his friends.
He prepares either samosas or chapattis for the food.
The probability that he prepares samosas is 0.4
He prepares either tea or coffee for the drink.
He is equally likely to prepare tea or coffee.
Food
Drink
Tea
..............
Samosas
0.4
..............
Coffee
Tea
..............
..............
Chapattis
..............
(a) Complete the tree diagram.
Coffee
[2]
(b) Find the probability that he prepares chapattis and tea.
[2]
© UCLES 2022
M/S9/02
13
20 A cuboid is formed by joining together four identical cubes.
NOT TO
SCALE
The total surface area of this cuboid is 54 cm2.
These four cubes are rearranged to form a cuboid with a different total surface area.
Find the total surface area of the new cuboid.
cm2 [2]
21 Eva thinks of a number.
When she rounds the number correct to two significant figures the answer is 43 000
When she rounds the number correct to three significant figures the answer is 43 500
Complete the inequality to show the limits for Eva’s number.
≤ Eva’s number <
© UCLES 2022
M/S9/02
[2]
[Turn over
14
22 A shape is made from part of a circle, centre C, with a radius of 4.2 cm and a square with
sides of 4.2 cm.
4.2 cm
C
NOT TO
SCALE
4.2 cm
Find the area of the shape.
Give your answer correct to one decimal place.
cm2 [4]
© UCLES 2022
M/S9/02
15
23 Here is a triangular prism ABCDEF.
E
B
F
D
12.1 cm
A
13.3 cm
NOT TO
SCALE
2.3 cm
C
ABC is a right-angled triangle.
BC = 12.1 cm, AC = 13.3 cm and CF = 2.3 cm.
Calculate the volume of this triangular prism.
cm3 [4]
© UCLES 2022
M/S9/02
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 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 2022
M/S9/02
Mathematics
Stage 9
Paper 2
Cambridge Lower Secondary Progression Test
Mark Scheme
3143_02_MS_6RP
© UCLES 2022
2022
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
2022
General guidance on marking
Difference in printing
It is suggested that schools check their printed copies for differences in printing that may affect the
answers to the questions, for example in measurement questions.
Brackets in mark scheme
When brackets appear in the mark scheme this indicates extra information that is not required but
may be given.
For example:
Question
Answer
Mark
5
19.7 or 19.6(58…)
1
Part marks
Guidance
This means that 19.6 is an acceptable truncated answer even though it is not the correct rounded
answer.
The … means you can ignore any numbers that follow this; you do not need to check them.
Accept
• any correct rounding of the numbers in the brackets, e.g. 19.66
• truncations beyond the brackets, e.g. 19.65
Do not accept
• 19.68 (since the numbers in brackets do not have to be present but if they are they should be
correct).
© UCLES 2022
Page 2 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
2022
These tables give general guidelines on marking learner responses that are not specifically
mentioned in the mark scheme. Any guidance specifically given in the mark scheme supersedes this
guidance.
Number and place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept trailing zeros, unless the question has asked for a specific number of decimal places or
significant figures, e.g.
0.7000
Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. Units are provided on the answer line unless finding the units is part of what is
being assessed.
The table shows acceptable and unacceptable versions of the answer 1.85 m.
Accept
Do not accept
If the unit is given on the
answer line, e.g.
............................ m
Correct conversions, provided
the unit is stated
unambiguously,
e.g. ......185 cm...... m (this is
unambiguous since the unit cm
comes straight after the
answer, voiding the m which is
now not next to the answer)
......185...... m
......1850...... m etc.
If the question states the unit
that the answer should be
given in, e.g. ‘Give your answer
in metres’
1.85
1 m 85 cm
185; 1850
Any conversions to other units,
e.g. 185 cm
© UCLES 2022
Page 3 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
2022
Money
In addition to the rules for units, the table below gives guidance for answers involving money.
The table shows acceptable and unacceptable versions of the answer $0.30
If the amount is in dollars and
cents, the answer should be
given to two decimal places
If units are not given on the
answer line
If $ is shown on the answer line
If cents is shown on the answer
line
Accept
Do not accept
$0.30
$0.3
For an integer number of
dollars it is acceptable not to
give any decimal places, e.g.
$9 or $9.00
$09 or $09.00
Any unambiguous indication of
the correct amount, e.g.
30 cents; 30 c
$0.30; $0–30; $0=30; $00:30
30 or 0.30 without a unit
All unambiguous indications,
e.g. $......0.30......;
$......0-30......;
$......0=30......;
$......00:30......
$......30......
......30......cents
......0.30......cents
$30; 0.30 cents
Ambiguous answers, e.g.
$30 cents; $0.30 c; $0.30 cents
(as you do not know which unit
applies because there are units
either side of the number)
Ambiguous answers, e.g.
$......30 cents......;
$......0.30 cents......
unless units on the answer line
have been deleted, e.g.
$......30 cents......
Ambiguous answers, e.g.
......$30 ......cents;
......$0.30 ......cents
unless units on the answer line
have been deleted, e.g.
......$0.30......cents
© UCLES 2022
Page 4 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
2022
Duration
In addition to the rules for units, the table below gives guidance for answers involving time durations.
The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes.
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr, hrs),
minutes (m, min, mins) and
seconds (s, sec, secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
Incorrect or ambiguous formats, e.g.
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h (this is because this indicates 0.3 of
an hour (i.e.18 minutes) rather than 30 minutes)
Any correct conversion with appropriate units,
e.g.
2.5 hours; 150 mins
unless the question specifically asks for time
given in hours and minutes
02:30 (as this is a 24-hour clock time, not a time
interval)
2.5; 150
Time
The table below gives guidance for answers involving time.
The table shows acceptable and unacceptable versions of the answer 07:30
Accept
Do not accept
If the answer is required in
24-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
07:30 with any separator in
place of the colon, e.g.
07 30; 07,30; 07-30; 0730
7:30
7:30 am
7 h 30 m
7:3
730
7.30 pm
073
07.3
If the answer is required in
12-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
7:30 am with any separator in
place of the colon, e.g.
7 30 am; 7.30 am; 7-30 am
Absence of am or pm
1930 am
7 h 30 m
7:3
730
7.30 pm
7.30 in the morning
Half past seven (o’clock) in the
morning
Accept am or a.m.
© UCLES 2022
Page 5 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
2022
Algebra
The table shows acceptable and unacceptable versions of the answer 3x – 2
Accept
Do not accept
x3 – 2; 3 × x – 2
3x + –2 if it is supposed to be in simplest form
Case change in letters
Changes in letters as long as there is
no ambiguity
Accept extra brackets when factorising, e.g. 5(x + (3 + y))
Teachers must mark the final answer given. If a correct answer is seen in working but final answer is
given incorrectly then the final answer must be marked. If no answer is given on the answer line then
the final line of the working can be taken to be the final answer.
Inequalities
The table shows acceptable and unacceptable versions of various answers.
For the following
Accept
Do not accept
For 6 ≤ x < 8
[6, 8)
<x<
For x ≤ –2
(–∞,–2]
x < –2
For x > 3
(3, ∞)
3<x
Just ‘3’ written on the answer line, even if x > 3
appears in the working
Plotting points
The table shows acceptable and unacceptable ways to plot points.
Accept
Crosses or dots plotted within ±
Do not accept
1
square of the
2
correct answer
A horizontal line and vertical line from the axes
meeting at the required point
The graph line passing through a point implies
the point even though there is no cross
© UCLES 2022
Page 6 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
Answer
Marks
Part Marks
1
7.6(3…) (cm)
2 Award 1 mark for 6.88(2) (cm) or
6.9 (cm) after 1 week
or for any fully correct working,
e.g. 6.2 × 1.11 × 1.11 (may be seen in
stages).
2
(4n)2 + 6 or 16n2 + 6
1
3
4
5
© UCLES 2022
8100
22
7
y = 0.5 x + 3 or y =
7
1
2
7
3
8
x + 3 or equivalent
Mia ticked
and
Gives correct explanation,
e.g. (The other answer) is to 2 significant
figures.
or
(The other answer) is to 3 decimal places.
or
6 is the 3rd significant figure.
or
7 is the 2nd significant figure.
or
2 is the 1st significant figure.
or
The 0 after the decimal point is not a
significant figure.
1
2022
Guidance
Accept better for 2 marks, e.g. 7.64
Accept any clear indication.
All four answers correct for the mark.
2 Award 1 mark for
y = mx + 3, m ≠ 0.5 or equivalent
or y = 0.5 x + c, c ≠ 3 or equivalent
or 0.5 x + 3 or equivalent.
1
Page 7 of 14
Both Mia ticked and any correct
explanation needed for the mark.
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
Answer
6
Marks
Strong positive
correlation
Part Marks
1
Weak positive
correlation
Weak negative
correlation
Strong negative
correlation
7
0.57
1
8
8 (hours)
1
© UCLES 2022
Page 8 of 14
2022
Guidance
All four lines correct for the mark.
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
Answer
Marks
Part Marks
2022
Guidance
9(a)
(Midpoint, x) 9 and ( f × x) 45 and (Total) 134
1
All three answers correct for the
mark.
9(b)
6.7 (kg)
1
Follow through their total f × x
correctly divided by 20
9(c)
Exact values are not known.
or
The data is grouped.
or
Midpoints have been used.
1
Accept any correct explanation.
10
Correct stem-and-leaf diagram drawn.
3 Award 3 marks for correct
stem-and-leaf diagram.
One error, e.g.
Incorrectly ordered leaves in one row.
or
Not including all five stems.
or
Not including all 12 leaves.
or
Incorrect key.
0
8
1
6
7
9
2
0
3
7
1
4
or
Award 2 marks for one error.
7
8
9
or
3
4
Award 1 mark for two errors.
Key:
1 6 represents 16 people
11
© UCLES 2022
7
8
9
10
1
Page 9 of 14
Accept any clear indication.
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
Answer
Marks
Part Marks
12(a)
(They all have) gradient of 3
1
12(b)
(They all have) intercept on y-axis of – 2
1
12(c)
y = − 2 x + 3 placed in ε outside of A or B
1
13
Two correct positions for ship S marked on
the map (bearing from A of 080° and
distance from B of 3.6 cm).
3 Award 2 marks for one correct position
for ship S marked on the map.
2022
Guidance
Accept any correct description of
intercept on y-axis.
Tolerance ± 2 mm and 2°.
or
North
Award 1 mark for a ship S marked on
a bearing of 080°
or for a ship S marked at a distance of
3.6 cm from B
or for a correct calculation of 3.6 cm.
A
B
14
x2 − 3 x − 28
2 Award 1 mark for three correct terms
2
from x − 7 x + 4 x − 28
15
21
1
© UCLES 2022
Page 10 of 14
Note – 3x counts as two terms.
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
16
Answer
( x =)
5
9
( y − 4)
Marks
2022
Part Marks
2
Award 1 mark for y − 4 =
Guidance
9
5
x
or
5 y = 9 x + 20
or
y 1
4
= x+
9 5
9
17(a)
3.5 and 2 and – 2.5
2 Award 1 mark for one or two correct
values.
17(b)
Straight line joining (–1, 3.5) to (3, – 2.5).
1
18
980 (cm2)
3
Accept equivalent answers for
2 marks,
5 y − 20
e.g. ( x =)
9
Accept values in range of 979 to 981
for 3 marks.
Accept values for π in the range of
22
3.14 to
7
Award 1 mark for π × 12 × 20 or
better.
Or better, e.g.753.9...
and
Award 1 mark for area of circle π × 62
or better.
© UCLES 2022
Page 11 of 14
Or better, e.g. 113.0...
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
Answer
Marks
Part Marks
2022
Guidance
19(a)
0.6 for chapattis and 0.5 for all drink
branches
2 Award 1 mark for 0.6 for chapattis
or 0.5 for all drink branches.
Accept equivalent fractions and
percentages.
19(b)
0.3
2
Accept equivalent fractions and
percentages.
Award 1 mark for their P(chapattis)
× their P(tea).
20
48 (cm2)
2 Award 1 mark for 54 ÷ 18, implied by 3
or 16 × their 3
21
43 450 ≤ Eva’s number < 43 500
2 Award 1 mark for one correct limit
or for
42 500 and 43 500 (limits for 43 000)
and
43 450 and 43 550 (limits for 43 500).
22
59.2 (cm2)
4 Award 3 marks for complete method,
3
i.e. × π × 4.22 + 4.22
4
or
Award 2 marks for
3
4
× π × 4.22
or
Award 1 mark for π × 4.22
and
If 3 marks not scored, award 1 mark
for 4.2 × 4.2 or for rounding their more
accurate area correctly to one decimal
place.
© UCLES 2022
Page 12 of 14
Their P(chapattis) and their P(tea)
must be between 0 and 1
3 marks implied by answers which
round to 59.2 (cm2).
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
Question
23
Answer
76.8 (cm3)
Marks
2022
Part Marks
Guidance
Accept 77 with correct working for
4 marks.
4
13.3 2 − 12.12
Award 2 marks for
2 marks implied by 5.52…
or
2
© UCLES 2022
2
2
Award 1 mark for x + 12.1 = 13.3
or better
Or better for 1 mark, e.g.
13.32 − 12.12 or 30.48
In addition, award 1 mark for their AB
from attempt at Pythagoras × 12.1 ×
0.5 × 2.3
An attempt at Pythagoras must
involve 13.3 2 and 12.12 , but these
may be added rather than subtracted.
Page 13 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
BLANK PAGE
© UCLES 2022
Page 14 of 14
2022
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
M/S9/01
[Turn over
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
20
30
10
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
[Turn over
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 
The point P is translated by the vector   to give the point Q.
 1 
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
[Turn over
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]
[Turn over
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.
7 pm
2 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
M/S9/01
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
M/S9/01
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
[Turn over
14
21 Chen has two fair spinners.
Spinner B
Spinner A
Blue
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 1
Mark Scheme
Stage 9
Maths_S9_01_MS/8RP
© UCLES 2020
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
from 2020
General guidance on marking
Difference in printing
It is suggested that schools check their printed copies for differences in printing that may affect the
answers to the questions, for example in measurement questions.
Brackets in mark scheme
When brackets appear in the mark scheme this indicates extra information that is not required but may
be given.
For example:
Question Answer
Mark
5
1
19.7 or 19.6(58)
Part marks
Guidance
This means that 19.6 is an acceptable truncated answer even though it is not the correct rounded
answer.
The … means you can ignore any numbers that follow this; you do not need to check them.
Accept
• any correct rounding of the numbers in the brackets, e.g. 19.66
• truncations beyond the brackets, e.g. 19.65
Do not accept
• 19.68 (since the numbers in brackets do not have to be present but if they are they should be
correct).
© UCLES 2020
Page 2 of 14
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
from 2020
These tables give general guidelines on marking learner responses that are not specifically
mentioned in the mark scheme. Any guidance specifically given in the mark scheme supersedes this
guidance.
Number and place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept tailing zeros, unless the question has asked for a specific number of decimal places or
significant figures, e.g.
0.7000
Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. Units are provided on the answer line unless finding the units is part of what is
being assessed.
The table shows acceptable and unacceptable versions of the answer 1.85 m.
Accept
Do not accept
If the unit is given
on the answer line,
e.g.
............................ m
Correct conversions,
provided the unit is stated
unambiguously,
e.g. ......185 cm...... m (this
is unambiguous since the
unit cm comes straight
after the
answer, voiding the m
which is now not next to
the answer)
......185...... m
......1850......m etc.
If the question states
the unit that the answer
should be
given in, e.g. ‘Give your
answer in metres’
1.85
1 m 85 cm
185; 1850
Any conversions to other
units, e.g. 185 cm
© UCLES 2020
Page 3 of 14
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
from 2020
Money
In addition to the rules for units, the table below gives guidance for answers involving money. The
table shows acceptable and unacceptable versions of the answer $0.30
Accept
Do not accept
If the amount is in dollars
and cents, the answer
should be given to two
decimal places
$0.30
$0.3
For an integer number of
dollars it is acceptable not to
give any decimal places, e.g.
$9 or $9.00
$09 or $09.00
If units are not given
on the answer line
Any unambiguous indication of
the correct amount, e.g.
30 cents; 30 c
$0.30; $0-30; $0=30; $00:30
30 or 0.30 without a
unit
$30;
cents
0.30
Ambiguous answers,
e.g.
$30 cents; $0.30 c; $0.30
cents (as you do not know
which unit applies because
there are units either side of
the number)
If $ is shown on the answer All unambiguous indications,
line
e.g. $......0.30......;
$......0-30......;
$......0=30......;
$......00:30......
$......30......
If cents is shown on the
answer line
......0.30......cents
......30......cents
Ambiguous answers, e.g.
$......30 cents......;
$......0.30 cents......
unless units on the answer
line have been deleted, e.g.
$......30 cents......
Ambiguous answers, e.g.
......$30 ......cents;
......$0.30 ......cents
unless units on the answer
line have been deleted, e.g.
......$0.30......cents
© UCLES 2020
Page 4 of 14
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
from 2020
Duration
In addition to the rules for units, the table below gives guidance for answers involving time durations.
The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes.
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr,
hrs), minutes (m, min, mins) and
seconds (s, sec, secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
Incorrect or ambiguous formats, e.g.
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h (this is because this indicates 0.3 of
an hour (i.e.18 minutes) rather than 30
minutes)
Any correct conversion with appropriate
units, e.g.
2.5 hours; 150 mins
unless the question specifically asks for
time given in hours and minutes
02:30 (as this is a 24-hour clock time, not a
time interval)
2.5; 150
Time
The table below gives guidance for answers involving time.
The table shows acceptable and unacceptable versions of the answer 07:30
Accept
Do not accept
If the answer is required in
24-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
07:30 with any separator in
place of the colon, e.g.
07 30; 07,30; 07-30; 0730
7:30
7:30 am
7 h 30 m
7:3
730
7.30 pm
073
07.3
If the answer is required in
12-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
7:30 am with any separator in
place of the colon, e.g.
7 30 am; 7.30 am; 7-30 am
Absence of am or pm
1930 am
7 h 30 m
7:3
730
7.30 pm
7.30 in the morning
Half past seven (o’clock) in the
morning
Accept am or a.m.
© UCLES 2020
Page 5 of 14
S9/01
Mathematics Stage 9 Paper 1 Mark Scheme
from 2020
Algebra
The table shows acceptable and unacceptable versions of the answer 3x – 2
Accept
Do not accept
x3 – 2; 3 × x – 2
3x + –2 if it is supposed to be in simplest form
Case change in letters
Changes in letters as long as there is
no ambiguity
Accept extra brackets when factorising, e.g. 5(x + (3 + y))
Teachers must mark the final answer given. If a correct answer is seen in working but final answer is
given incorrectly then the final answer must be marked. If no answer is given on the answer line then
the final line of the working can be taken to be the final answer.
Inequalities
The table shows acceptable and unacceptable versions of various answers.
For the following
Accept
Do not accept
For 6 ≤ x < 8
[6, 8)
<x<
For x ≤ –2
(–∞,–2]
x < –2
For x > 3
(3, ∞)
3<x
Just ‘3’ written on the answer line, even if x > 3
appears in the working
Plotting points
The table shows acceptable and unacceptable ways to plot points.
Do not accept
Accept
Crosses or dots plotted within ±
1
square of
2
A horizontal line and vertical line from the
axes meeting at the required point
the correct answer
The graph line passing through a point implies
the point even though there is no cross
© UCLES 2020
Page 6 of 14
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
1
Answer
Mark
>
=
2
Part Marks
Ratios equivalent
to 3 : 5
(A)
C
B
Guidance
Both symbols correct.
1
Ratios equivalent
to 2 : 3
from 2020
1
All entries correct.
D
3(a)
5m
5
or 2.5m or m
2
2
1
3(b)
2n + 6
2n
or
+2
3
3
1
3(c)
x2 – 4
1
4
x < 10 or 10 > x
2 Award 1 mark for 4x – 2x < 19 + 1 or
for 2x < 20 or equivalent.
5(a)
18
1
5(b)
48
2
© UCLES 2020
or equivalent simplified
2
× 120 or for sight
5
254
of either 50.8 or ( – )2.8 or
5
or
14
(–)
5
Award 1 mark for
Page 7 of 14
Accept use of = or > signs for 1 mark.
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
6
7(a)
Answer
Any correct demonstration that the
y-coordinate of the midpoint is not 5, e.g.
−2 + 8
•
=3
2
• 8 ‒ ‒2 = 10 and 8 – 5 = 3
• 5 is 7 away from –2 but only 3 away
from 8
strong negative weak negative no correlation
weak positive
7(b)
π
3
© UCLES 2020
(‒4, ‒5)
8
Part Marks
Guidance
1
Do not accept without working:
• The midpoint is at (12, 3)
• 5 is not halfway between –2 and 8
1
Accept any clear indication.
1
Accept six or eight points plotted.
1
Correct two answers ringed and no
other answers.
strong positive
seven points plotted demonstrating strong
positive correlation.
8
9
Mark
from 2020
2
5
1.289
8
1.5
Accept any clear indication.
2 Award 1 mark
either for (‒4, 3) seen or plotted on
grid
or for reflecting their point Q in the line
𝑦 = ‒1
Page 8 of 14
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
10
11
© UCLES 2020
Answer
24
Sequence A
11
Sequence B
35
Sequence C
Any possible values that satisfy all three
conditions:
 is an integer greater than 1
 is a decimal smaller than 1.
 ÷  = 60
Mark
Part Marks
from 2020
Guidance
1
1
Page 9 of 14
Possible values include
 = 30  = 0.5
 = 6  = 0.1
 = 15  = 0.25 etc.
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
Answer
Mark
12(a)
Part Marks
1
from 2020
Guidance
Arc drawn radius 5 cm (tolerance ± 2
mm) centred on 2nd dot and
intersecting first arc.
Line drawn to make the 60° angle.
12(b)
Correct bisection of angle BAC, e.g.
B
A
2 Award 1 mark for an arc drawn at A
that intersects both AB and AC.
C
13(a)
5×9–6×7=3
1
13(b)
35
1
14(a)
6 × 107
1
14(b)
3.2 × 10–3 (kg)
1
© UCLES 2020
Page 10 of 14
Arcs must be seen.
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
Answer
Mark
2 pm
15(a)
8
7
7
4
5
2
8
(2)
1
3
0
1
2
3
4
Part Marks
Any correct comparison, e.g.
• Fewer people watched at 7pm (on average)
• The number watching at 7pm is less
variable
1
16
16n2 (cm2)
2 Award 1 mark for a correct
unsimplified expression for the area,
6n + 10n
× 2n or 8n × 2n
such as
2
18
(x =) 6.5 or 6
1
2
Bearings should have 3 digits
and
Bearings should be measured (clockwise) from
the North line.
Guidance
2 Award 1 mark
either if the numbers in all rows are
correct but not ordered
or if rows are ordered but one number
is incorrectly entered or omitted.
15(b)
17
from 2020
The answer must involve a
comparison of the two sets of data.
2 Award 1 mark for 9 = 6(x – 5) or
9 = 6x – 30 or x – 5 = 1.5
Accept improper fraction.
2 Award 1 mark for one correct criticism.
For 1 mark accept
• The correct bearing is 65(°)
• She should have done 90 – 25
Accept the correct bearing is 065° for
2 marks.
© UCLES 2020
Page 11 of 14
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
19
Answer
2
2
9
Mark
3
from 2020
Part Marks
Award 2 marks for
Guidance
8 5
×
3 6
An answer of
40
20
or
implies 2
18
9
marks.
or
Award 2 marks for writing both
improper fractions with a common
40 18
denominator,
÷
15 15
Award 1 mark for sight of both
8
and
3
6
5
or
Award 1 mark for correct method of
dividing their improper fractions.
© UCLES 2020
Page 12 of 14
A correct method would be
either to invert the second fraction
8
5
and then multiply, their
× their ,
3
6
or to convert both improper fractions
to a common denominator.
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
20
Answer
Mark
Line between (0, 0) and (3, 300)
Part Marks
from 2020
Guidance
2 Award 1 mark
either for a line indicating a journey
lasting 3 hours.
400
or for a line with gradient 100
300
Distance
travelled
200
(km)
Yuri
100
0
21(a)
4
2
3
Time (hours)
1
Outcome from Spinner A
Outcome from Spinner B
1
5
3
4
1
4
Red
5
2 Award 1 mark for two or three
fractions correctly placed on diagram.
Red
4
5
1
5
Yellow
Red
Blue
4
5
Yellow
21(b)
3
or 0.15 or 15%
20
1
22
(10 →) 58
(n →) 6n – 2 or n × 6 – 2
2 Award 1 mark for any one correct.
© UCLES 2020
Accept equivalent fractions, decimals
or percentages.
Page 13 of 14
Accept equivalents.
Mathematics Stage 9 Paper 1 Mark Scheme
S9/01
Question
23
Answer
An algebraic method leading to x = 7, y = –3
Mark
Part Marks
3 Award 2 marks for sight of an
algebraic method leading to either
x = 7 or y = –3
Award 1 mark for correct substitution
and evaluation from incorrect first
value, i.e. two values satisfying one of
the original equations.
or
A correct method for eliminating either
x or y.
24
1
7
3 Award 2 marks for correct red area
(12) and correct blue area (72)
or
84
Award 1 mark for correct method to
1
1
find red area ( × 3 × 4 +
× 3 × 4) or
2
2
blue area (3 × 6 + 4 × 6 + 5 × 6)
© UCLES 2020
from 2020
Page 14 of 14
Guidance
Do not accept a trial and
improvement method.
Correct method could include:
•
re-arranging one of the equations
to make one variable the subject
and then substitute their
arrangement into the other
equation,
•
making the coefficients of x or y
equal with no more than one
arithmetic error or sign error,
followed by an appropriate,
consistent subtraction or addition
across all three terms.
Accept equivalent fractions to
1
7
Accept equivalent calculations.
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
2
Here is an expression 3( x − 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
[Turn over
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
P
2
1
0
1
2
3
4
5
6
7
8
10 x
9
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
[Turn over
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
[Turn over
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
[Turn over
16
22 The diagram shows a rectangle ABCD.
E
A
F
B
NOT TO
SCALE
12.5 cm
18 cm
D
C
24 cm
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
Cambridge Lower Secondary Sample Test
For use with curriculum published in
September 2020
Mathematics Paper 2
Mark Scheme
Stage 9
Maths_S9_02_MS/9RP
© UCLES 2020
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
from 2020
General guidance on marking
Difference in printing
It is suggested that schools check their printed copies for differences in printing that may affect
the answers to the questions, for example in measurement questions.
Brackets in mark scheme
When brackets appear in the mark scheme this indicates extra information that is not required
but may be given.
For example:
Question Answer
5
19.7 or 19.6(58)
Mark
Part marks
Guidance
1
This means that 19.6 is an acceptable truncated answer even though it is not the correct
rounded answer.
The … means you can ignore any numbers that follow this; you do not need to check them.
Accept
any correct rounding of the numbers in the brackets, e.g. 19.66,
•
•
truncations beyond the brackets, e.g. 19.65
Do not accept
•
19.68 (since the numbers in brackets do not have to be present but if they are they should
be correct).
© UCLES 2020
Page 2 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
from 2020
These tables give general guidelines on marking learner responses that are not specifically mentioned
in the mark scheme. Any guidance specifically given in the mark scheme supersedes this guidance.
Number and place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept tailing zeros, unless the question has asked for a specific number of decimal places
or
significant figures, e.g.
0.7000
Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. Units are provided on the answer line unless finding the units is part of what is
being assessed.
The table shows acceptable and unacceptable versions of the answer 1.85 m.
If the unit is given on the
answer line, e.g.
............................ m
Accept
Do not accept
Correct conversions,
provided the unit is stated
unambiguously,
e.g. ......185 cm...... m (this is
unambiguous since the unit
cm comes straight after the
answer, voiding the m which is
now not next to the answer)
......185...... m
......1850...... m etc.
1.85
If the question states the unit
that the answer should be
1 m 85 cm
given in, e.g. ‘Give your answer
in metres’
© UCLES 2020
Page 3 of 14
185; 1850
Any conversions to other units,
e.g. 185 cm
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
from 2020
Money
In addition to the rules for units, the table below gives guidance for answers involving money. The
table shows acceptable and unacceptable versions of the answer $0.30
If the amount is in dollars
and cents, the answer
should be given to two
decimal places
If units are not given on the
answer line
Accept
Do not accept
$0.30
$0.3
For an integer number of
dollars it is acceptable not to
give any decimal places,
e.g.
$9 or $9.00
$09 or $09.00
Any unambiguous indication
of the correct amount, e.g.
30 cents; 30 c
$0.30; $0-30; $0=30; $00:30
30 or 0.30 without a unit
$30; 0.30 cents
Ambiguous answers, e.g.
$30 cents; $0.30 c; $0.30
cents (as you do not know
which unit applies because
there are units either side of
the number)
If $ is shown on the answer
line
If cents is shown on the
answer line
All unambiguous indications,
e.g. $......0.30......;
$......0-30......;
$......0=30......;
$......00:30......
......30......cents
$......30......
Ambiguous answers, e.g.
$......30 cents......;
$......0.30 cents......
unless units on the answer
line have been deleted, e.g.
$......30 cents......
......0.30......cents
Ambiguous answers, e.g.
......$30 ......cents;
......$0.30 ......cents
unless units on the answer
line have been deleted, e.g.
......$0.30......cents
© UCLES 2020
Page 4 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
from 2020
Duration
In addition to the rules for units, the table below gives guidance for answers involving time durations.
The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes.
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr, hrs),
minutes (m, min, mins) and
seconds (s, sec, secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
Incorrect or ambiguous formats, e.g.
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h (this is because this indicates 0.3 of
an hour (i.e.18 minutes) rather than 30 minutes)
Any correct conversion with appropriate units,
e.g.
2.5 hours; 150 mins
unless the question specifically asks for time
given in hours and minutes
02:30 (as this is a 24-hour clock time, not a time
interval)
2.5; 150
Time
The table below gives guidance for answers involving time.
The table shows acceptable and unacceptable versions of the answer 07:30
Accept
Do not accept
If the answer is required in
24-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
07:30 with any separator in
place of the colon, e.g. 07 30;
07,30; 07-30; 0730
7:30
7:30 am
7 h 30 m
7:3
730
7.30 pm
073
07.3
If the answer is required in
12-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
7:30 am with any separator in
place of the colon, e.g.
7 30 am; 7.30 am; 7-30 am
Absence of am or pm
1930 am
7 h 30 m
7:3
730
7.30 pm
7.30 in the morning
Half past seven (o’clock) in the
morning
Accept am or a.m.
© UCLES 2020
Page 5 of 14
S9/02
Mathematics Stage 9 Paper 2 Mark Scheme
from 2020
Algebra
The table shows acceptable and unacceptable versions of the answer 3x – 2
Accept
Do not accept
x3 – 2; 3  x – 2
3x  –2 if it is supposed to be in simplest form
Case change in letters
Changes in letters as long as there is no
ambiguity
Accept extra brackets when factorising, e.g. 5(x  (3  y))
Teachers must mark the final answer given. If a correct answer is seen in working but final answer is
given incorrectly then the final answer must be marked. If no answer is given on the answer line then
the final line of the working can be taken to be the final answer.
Inequalities
The table shows acceptable and unacceptable versions of various answers.
For the following
Accept
Do not accept
For 6 ≤ x  8
[6, 8)
x
For x ≤ –2
(–∞,–2]
x  –2
For x > 3
(3, ∞)
3x
Just ‘3’ written on the answer line, even if x > 3
appears in the working
Plotting points
The table shows acceptable and unacceptable ways to plot points.
Accept
Crosses or dots plotted within ±
Do not accept
1
square of the
2
correct answer
A horizontal line and vertical line from the axes
meeting at the required point
The graph line passing through a point implies
the point even though there is no cross
© UCLES 2020
Page 6 of 14
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
Answer
1
x9
2
–2
3
Mark
from 2020
Part Marks
Guidance
1
1

24.5 or 24
2 Award 1 mark for one correct.
1
2
.
and
25.5 or 25
1
2

Accept 25.49
4
1
Both boxes ticked and no others.


5(a)
108()
2
5(b)
2
6
2309(.07…) (cm3)
5
6
360
or 72
5
or for (5 – 2)  180 or 540
Award 1 mark for
1
2 Award 1 mark for   72  15
Accept answers between 2307.9 and
2309.4
Accept 2310
© UCLES 2020
Page 7 of 14
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
7(a)
Answer
Mark
–3
–2
–1
0
1
2
3
5
0
–3
–4
–3
0
5
y
7(b)
Part Marks
1
2 Award 1 mark for plotting six or seven
of their points correctly.
6
5
4
3
2
1
–3
–2
–1
0
1
2
3
x
–1
–2
–3
–4
© UCLES 2020
Page 8 of 14
from 2020
Guidance
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
Answer
8(a)
Mark
from 2020
Part Marks
Guidance
1
8
6
Frequency
4
2
0
6
8
10
12
14
16
Temperature, t (°C)
8(b)
12 ≤ t < 14
1
8(c)
10 or 9.9(99…)(C)
1
9(a)
y=x2
9(b)
Both lines cross the y-axis at 1
or
Both have a y-intercept of 1
1
10(a)
3
1
10(b)
(0, 0)
1
11
63.2 or 63.2…(cm)
3
y = 2x – 3
2y = x – 3
x=2
1
Accept correct alternatives, e.g.
They have the same y-intercept.
They both have a positive y-intercept.
2    1 2 .3
2
( 12.3  2) or equivalent
Award 2 marks for
or
Award 1 mark for 2    12.3
© UCLES 2020
Page 9 of 14
Accept answer of 63 with correct
working for 3 marks
123
implied by
or 38.6…
10
implied by
123
or 77.2 to 77.3
5
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
12
Answer
125 (minutes)
Mark
2
Part Marks
Award 1 mark for 300 
from 2020
Guidance
5
12
or
for 300  5 (= 1500)
13
Ticks A and gives supporting figures 728 and
722
3 Award 2 marks for
650  1.12 or 650  650  0.12 or 728
and
760  0.95 or 760 – 760 × 0.05 or 722
Accept equivalent methods for finding
the percentage increase or decrease.
or
Award 1 mark for
650  1.12 or 650  650  0.12 or 728
or
760  0.95 or 760 – 760  0.05 or 722
14
2
3 Award 2 marks for (12 – 7) + (22 – 7) +
(32 – 7)  (42 – 7) or better
Award 1 mark for
either (a =) 29 – 36 or –7
or (12  their a) + (22  their a)  (32 
their a)  (42  their a)
© UCLES 2020
Page 10 of 14
their a can be any non-zero number.
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
15
Answer
t 
5 w  1
2
or equivalent
Mark
Part Marks
2 Award 1 mark for a correct first step of
2t
either w  1=
5
or 5w = 2t – 5
16
A complete demonstration showing correct
expansion of both brackets, e.g.
20y – 36y 2  36y 2 – 6y and 14y
2 Award 1 mark for 20y – 36y2 or for
36y 2 – 6y or for 20y – 6y
17
70(°)
3 Award 1 mark for
360  78  38
(ABC or ADC =)
2
or 122(°)
and
Award 1 mark for
(angle EBC =) 180 – 90 – 38 or 52(°)
or
360 – 90 – their ADC – 78
© UCLES 2020
from 2020
Page 11 of 14
Guidance
Accept (t = )
w 1
for 2 marks.
0 .4
Accept an unsimplified answer, e.g.
w 1
t=
scores 1 mark.
2
5
May be seen on diagram.
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
18
Answer
0.6 or 60% or
3
5
Mark
Part Marks
2 Award 1 mark for
0.25 + 0.05 + 0.1 (= 0.4)
or
from 2020
Guidance
Accept equivalent fractions.
For the award of 1 mark all
probabilities should be expressed in a
consistent form.
25(%) + 5(%) + 10(%) (= 40)
or
1 – their 0.4
19
42
3 Award 1 mark for correct method to
find number of counters Angelique
3
(= 21)
gets from Bag A, e.g. 56 
35
Award 1 mark
either for correct method to find the
number of counters Hassan gets from
3
Bag B, e.g. (45 – their 21) 
or 18
4
or for correct method to find the total
number of counters in Bag B, e.g.
34
(45 – their 21) 
4
© UCLES 2020
Page 12 of 14
Implied by the four numbers in their
table adding up to 1
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
20
Answer
A correct comparison of both the means and
ranges in context, e.g.
Mark
Part Marks
2 Award 1 mark for a correct comparison
of either the means or the ranges in
context.
from 2020
Guidance
Answers should refer to distances or
jumps.
Accept equivalent answers, e.g.
The girls (generally) jump shorter
distances.
The boys jumped further (on average than the
girls).
and
Do not allow answers which do not
give a contextual interpretation of
mean or range, e.g.
 The distances jumped by the boys
have a larger mean.
 The girls’ jumps have a smaller
range.
The distances jumped by the boys were more
varied/ less consistent / more spread out.
21
© UCLES 2020
An answer that implies that children in the
orchestra will not be representative of all
children, e.g.
 She should also ask children not in the
orchestra.
 Children in the orchestra are more likely to
like music.
1
Page 13 of 14
Mathematics Stage 9 Paper 2 Mark Scheme
S9/02
Question
22
Answer
2
411 (cm )
Mark
from 2020
Part Marks
4 Award 3 marks for AF = 3.5 cm and
correct method to find shaded area,
e.g. 24  18 – 0.5  3.5  12
Guidance
The shaded area could be divided into
a rectangle and a trapezium.
Award 2 marks for AF = 3.5 cm
or
Award 2 marks for a correct method to
find shaded area using a value for AF
found after attempting Pythagoras’
theorem
Award 1 mark for AF2  (24/2)2 = 12.52
or
Award 1 mark for correct method to
find shaded area using any value for
AF
© UCLES 2020
Page 14 of 14
AF =
12.5 2  (24  2)2
Cambridge Lower Secondary Progression Test
* 0 4 7 7 2 1 4 3 8 0 *
Mathematics paper 1
Stage 9
55 minutes
For Teacher’s Use
Page
Name ………………………………………………….……………………….
Additional materials: Geometrical instruments
Tracing paper (optional)
1
2
3
READ THESE INSTRUCTIONS FIRST
4
Answer all questions in the spaces provided on the question paper.
5
Calculators are not allowed.
6
You should show all your working on the question paper.
The number of marks is given in brackets [ ] at the end of each question
or part question.
The total number of marks for this paper is 45.
7
8
9
10
11
12
Total
MATHS_S9_01_8RP
© UCLES 2018
Mark
2
1
Complete these statements.
For
Teacher’s
Use
+ −3 = 6.3
× −3 = 6.3
÷ −3 = 6.3
[2]
2
Match each calculation to its answer.
The first one has been done for you.
0.6 × 0.6
0.36
0.64 × 0.4
1.6
0.64 ÷ 0.4
0.625
0.4 ÷ 0.64
0.256
[1]
3
(a) Draw a ring around the best estimate of
7.1
14
56
7.5
7.9
28
[1]
(b) Draw a ring around the best estimate of 3 25
2
3
5
8
[1]
© UCLES 2018
M/S9/01
3
4
These are the elevations and plan of a shape.
Front elevation
For
Teacher’s
Use
Side elevation
Plan
Write down the name of the shape.
.................................................. [1]
5
One of these statements is wrong.
Put a cross () next to the statement that is wrong.
26 × 25 = 26 × 100 ÷ 4
26 × 25 = (26 × 5) × (26 × 5)
26 × 25 = 25 × 26
26 × 25 = (30 × 25) – (4 × 25)
[1]
© UCLES 2018
M/S9/01
[Turn over
4
6
Oliver bakes 10 cakes.
The scatter graph shows the mass (in grams) of each cake and the cooking time (in
minutes).
90
80
70
60
Cooking
50
time
(minutes)
40
30
20
10
0
500
600
700
800 900 1000 1100 1200
Mass (grams)
(a) Write down the number of Oliver’s cakes that have a mass of more than 800 grams.
.................................................. [1]
(b) Describe the relationship between the mass of a cake and the cooking time.
..................................................................................................................................
............................................................................................................................. [1]
(c) Oliver sees a recipe for a cake with a mass of 800 grams.
The recipe says the cooking time is 80 minutes.
Use the graph to explain why this cooking time may be incorrect.
..................................................................................................................................
............................................................................................................................. [1]
© UCLES 2018
M/S9/01
For
Teacher’s
Use
5
7
Here is an arithmetic sequence.
24,
19,
For
Teacher’s
Use
14,
9,
4,
…
Find an expression for the nth term of the sequence.
.................................................. [2]
8
Calculate.
45.7 × 3.6
.................................................. [2]
9
(a) Write down the value of 20
.................................................. [1]
(b) Write 2−3 as a fraction.
.................................................. [1]
© UCLES 2018
M/S9/01
[Turn over
6
10 The scale drawing shows the position of two schools, A and B.
For
Teacher’s
Use
North
North
A
B
The scale is 1 : 200 000
(a) Work out the real-life distance between school A and school B.
Give your answer in kilometres.
............................................ km [1]
(b) School C is on a bearing of
085° from school A,
305° from school B.
Use your protractor to mark the position of school C on the scale drawing.
© UCLES 2018
M/S9/01
[2]
7
11 (a) Complete the table of values for the equation 2y − 2 = 4x
x
–1
y
–1
0
For
Teacher’s
Use
2
[1]
(b) Use your results to plot the graph of 2y − 2 = 4x on this grid.
y
6
5
4
3
2
1
–4
–3
–2
–1
0
1
2
3
4
5
x
–1
–2
–3
–4
[2]
© UCLES 2018
M/S9/01
[Turn over
8
12 Work out.
For
Teacher’s
Use
1
1
4 3
2
3
.................................................. [2]
13 Expand and simplify.
(x − 5)(x + 3)
.................................................. [2]
14 The cross-section of a prism is shown in the diagram.
NOT TO
SCALE
2 cm
3 cm
4 cm
The prism has a length of 15 cm.
Calculate the volume of the prism.
...........................................cm3 [2]
© UCLES 2018
M/S9/01
9
For
Teacher’s
Use
15 Tick () to show whether each of these statements is true or false.
True
False
10−1 = 0.1
400 × 104 = 400 000
0.3 ÷ 10−2 = 0.003
0.8 × 103 = 0.8 ÷ 10−3
[2]
16 The diagram shows two rectangles that both have a width of 6 cm.
NOT TO
SCALE
6 cm
6 cm
The difference between the perimeters of the two rectangles is 10 cm.
Calculate the difference between the areas of the two rectangles.
...........................................cm2 [2]
© UCLES 2018
M/S9/01
[Turn over
10
17 Mia has a box that contains a large number of coloured cubes.
She picks a cube at random.
The probabilities of her picking a red, a blue or a green cube are shown in the table.
Colour
Red
Blue
Green
Probability
0.35
0.25
0.3
(a) Explain how you know that the box must also contain some cubes of other colours.
..................................................................................................................................
............................................................................................................................. [1]
(b) Half of the other coloured cubes are yellow.
Work out the probability that Mia picks a yellow cube.
.................................................. [1]
18 Write this expression as a single fraction.
3a a

5
5
.................................................. [1]
173 = 4913
19
34 = 2 × 17
Use these facts to work out 343
.................................................. [2]
© UCLES 2018
M/S9/01
For
Teacher’s
Use
11
20 Use algebra to solve these simultaneous equations.
For
Teacher’s
Use
3x + y = 5
x _ 2y = 4
You must show how you worked out your answer.
x = ................................................
y = ................................................
[3]
© UCLES 2018
M/S9/01
[Turn over
12
21 The price of an electronic book is $2.40
The price of the electronic book is 75% less than the price of the paper book.
For
Teacher’s
Use
Calculate the price of the paper book.
$................................................ [2]
22 The diagram shows a quadrilateral containing two right angles.
NOT TO
SCALE
6 cm
7 cm
a cm
9 cm
Calculate the value of a.
a = ............................................ [3]
Copyright © UCLES, 2018
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 2018
M/S9/01
Cambridge Lower Secondary Progression Test
* 9 4 0 4 9 0 6 6 4 4 *
Mathematics paper 2
Stage 9
55 minutes
For Teacher’s Use
Name ………………………………………………….……………………….
Page
1
Additional materials: Calculator
Geometrical instruments
Tracing paper (optional)
READ THESE INSTRUCTIONS FIRST
Answer all questions in the spaces provided on the question paper.
2
3
4
5
6
Calculator allowed.
You should show all your working on the question paper.
The number of marks is given in brackets [ ] at the end of each question
or part question.
7
8
9
10
The total number of marks for this paper is 45.
11
12
13
14
Total
MATHS_S9_02_6RP
© UCLES 2018
Mark
2
1
20 litres of petrol costs $48.40
For
Teacher’s
Use
Work out the cost of 36 litres of the petrol.
$................................................ [2]
2
Factorise.
(a) 18a − 12
.................................................. [1]
(b) 2c 2 + 5c
.................................................. [1]
3
The diagram shows part of a regular polygon with 10 sides.
NOT TO
SCALE
(a) Calculate the exterior angle of the polygon.
................................................° [1]
(b) Calculate the interior angle of the polygon.
................................................° [1]
© UCLES 2018
M/S9/02
3
4
Yuri makes a data collection sheet to find the heights of students in his school.
He trials his data collection sheet with 15 students and gets these results.
Height to the nearest centimetre
Tally
For
Teacher’s
Use
Frequency
1–50
0
51–100
0
101–150
6
151–200
9
201–250
0
Yuri wants to improve his data collection sheet.
Complete the first column with more suitable intervals.
You may not need to use all the rows of the table.
Height to the nearest centimetre
[1]
5
Tick () to show if these statements are true or false when x = 3.5
x2 + 2 <14
True
False
10x - 2 H 33
True
False
[1]
© UCLES 2018
M/S9/02
[Turn over
4
6
Write as a power of n.
For
Teacher’s
Use
(a) n × n2
.................................................. [1]
(b) n3 ÷ n2
.................................................. [1]
7
This is a rectangle on a coordinate grid.
y
5
A
4
3
C
M
2
1
–2 –1 0
–1
1
2
3
4
5
6
7
x
–2
(a) The rectangle is enlarged with a scale factor of 2
The centre of the enlargement is C (0, 3).
Find the coordinates of the image of vertex A.
(.................. , ..................) [1]
(b) The rectangle is rotated 90° clockwise about the point M (4, 3).
Find the coordinates of the image of vertex A.
(.................. , ..................) [1]
© UCLES 2018
M/S9/02
5
8
A car travels 230 km.
It uses 18.5 litres of petrol.
For
Teacher’s
Use
Calculate the distance travelled per litre of petrol for this car.
Give your answer in km / l.
....................................... km / l [1]
9
Jamila has two sets of number cards.
1 3 5
2 4 6
She takes one card from each set.
She multiplies the numbers on her two cards.
Show the possible outcomes in the sample space diagram.
[2]
© UCLES 2018
M/S9/02
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6
10 A publisher is deciding how much to charge for a new book.
Carlos draws this graph to show how the expected sales of the book change with the
price.
14
12
10
Expected
sales of
8
book
(thousands) 6
4
2
0
0
2
4
6 8 10 12 14 16 18 20
Price of book ($)
(a) Describe how the expected sales vary with price.
..................................................................................................................................
............................................................................................................................. [1]
(b) Work out how many more books the publisher would sell by charging $6 for the
book instead of $12
...................................thousand [2]
© UCLES 2018
M/S9/02
For
Teacher’s
Use
7
11 One solution to x2 + 4x  25 is between 3 and 4
For
Teacher’s
Use
Use trial and improvement to find this solution.
Give your answer correct to 1 decimal place.
Show your working.
You may not need all the rows in the table.
x
x2 + 4x
Comment
3
3 2 + 4 # 3 = 21
Too small
4
4 2 + 4 # 4 = 32
Too big
x = ............................................ [3]
© UCLES 2018
M/S9/02
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8
12 The cost of a holiday last year is shown.
For
Teacher’s
Use
Hotel:
$1300
Flights:
$ 900
Total cost:
$2200
The cost of the hotel this year is 8% more expensive than last year.
The cost of flights this year is $961
Work out the percentage increase in the total cost of the holiday.
..............................................% [3]
13 Solve this equation.
5(c + 32) = 60
c = ........................................... [2]
© UCLES 2018
M/S9/02
9
14 Hassan produces apple juice using apples grown on his farm.
He has 180 apple trees.
Each tree produces 40 kilograms of apples per year.
For
Teacher’s
Use
To make 1 litre of apple juice, Hassan needs 2.5 kilograms of apples.
He sells his apple juice in 0.75 litre bottles.
Work out how many bottles of apple juice Hassan can expect to produce in one year.
..................................... bottles [3]
15 (a) Calculate.
59.5  37.4
59.5  37.4
Write down all the digits on your calculator display.
.................................................. [1]
(b) Round your answer to 2 significant figures.
.................................................. [1]
© UCLES 2018
M/S9/02
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10
16 A container for water is in the shape of a cuboid.
For
Teacher’s
Use
NOT TO
SCALE
25 cm
12 cm
12 cm
Calculate the capacity of the container, in litres.
........................................ litres [2]
17 The average speed for three of the journeys described below is the same.
Journey A:
180 km in 3 hours
Journey B:
140 km in 2.5 hours
Journey C:
30 km in 0.5 hours
Journey D:
10 km in 10 minutes
Draw a ring around the journey that has a different average speed from the others. [1]
© UCLES 2018
M/S9/02
11
18 The diagram shows a cube drawn on isometric paper.
For
Teacher’s
Use
Eight of these cubes are put together to make a larger cube.
Draw this larger cube on the isometric paper.
[1]
© UCLES 2018
M/S9/02
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12
19 Make t the subject of this formula.
For
Teacher’s
Use
r  7(t + 3)
t = ............................................ [2]
20 Nine students take a history exam and a geography exam.
Their marks out of 100 are:
History:
Geography:
46, 65, 45, 42, 71, 48, 50, 71, 51
43, 72, 50, 68, 77, 64, 74, 78, 50
(a) Complete the back to back stem-and-leaf diagram.
History
8
6
5
1
1
Geography
2
0
5
1
4
5
6
7
3
Key: 2 | 4 | 3 = 42 in history and 43 in geography
[2]
(b) Use the shapes of the distributions to compare the marks for history and geography.
..................................................................................................................................
............................................................................................................................. [1]
© UCLES 2018
M/S9/02
13
21 Manjit thinks of a factor of 24
Gabriella thinks of a multiple of 13
The square of Manjit’s number is 3 less than Gabriella’s number.
For
Teacher’s
Use
Work out the numbers that Manjit and Gabriella thought of.
Manjit’s number = ........................
Gabriella’s number = ........................
[2]
22 There are two different pairs of trainers in a sale, Alpha trainers and Bargain trainers.
Alpha trainers
Original price: $50
Sale price: $44
Bargain trainers
Original price: $30
Sale price: $24
Rajiv says, ‘The discount on the Bargain trainers is better.’
Explain why Rajiv is correct.
.........................................................................................................................................
.........................................................................................................................................
.................................................................................................................................... [1]
© UCLES 2018
M/S9/02
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14
23 The graph shows the number of students gaining the top grade in a mathematics exam
each year.
For
Teacher’s
Use
60
50
40
Number
of
30
students
20
10
0
2006 2007 2008 2009 2010 2011 2012
Year
Between 2011 and 2012 there was a 50% increase in the number of students gaining
the top grade.
Show this on the graph.
[2]
Copyright © UCLES, 2018
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 2018
M/S9/02
Cambridge Lower Secondary Progression Test
* 1 6 4 9 2 3 5 5 5 7 *
Mathematics paper 3 learner answer sheet
Stage 9
approx. 15 minutes
Name ………………………………………………….……………………….
No additional materials are allowed.
READ THESE INSTRUCTIONS FIRST
Answer all questions in the spaces provided.
Calculators are not allowed.
Each question is worth 1 mark.
The total number of marks is 20.
MATHS_S9_03_AS_6RP
© UCLES 2018
For Teacher’s Use
Total
2
Time: 5 seconds
Time: 10 seconds
1
6
Square
Triangle
Hexagon
Pentagon
3, 4, 6, 9, 13, …
2
A
7
B
3
x → ...................
x→x+3
Asia
8
122
Europe Africa
49
29
Total
200
4
9
5
10
11
© UCLES 2018
x = ......................
M/S9/03
1
p  t2
2
3
Time: 15 seconds
y
4
3
2
1
12
cement : sand
1:5
15 ...................... m3
–2 –1 0
–1
–2
1 2 3
x
NOT TO
SCALE
v
16
y = ........ x − 1
......................°
240 
13
17
...................... °
12 adults
48 children
2x 1 8
NOT TO
SCALE
14
0
5
10
10 cm
6 cm
18
360 cm3
1800 cm3
180 cm3
3600 cm3
46  45
48
19
20
© UCLES 2018
M/S9/03
...................... cm3
1.25 m3
4
BLANK PAGE
Copyright © UCLES, 2018
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 2018
M/S9/03
Cambridge Lower Secondary Progression Test
* 3 5 7 7 2 8 7 7 6 5 *
Mathematics paper 3 teacher instructions
Stage 9
approx. 15 minutes
READ THESE INSTRUCTIONS FIRST
1.
Learners should only have pens and answer sheet. They are not allowed to have any other
mathematical equipment or paper for working out.
2.
The teacher will need a watch or clock that tells the time accurately in seconds.
3.
The teacher should read each question twice slowly and then wait the correct number of seconds
(5 seconds for questions 1–5, 10 seconds for questions 6–14 and 15 seconds for questions 15–20)
before moving on to the next question.
4.
Learners are not allowed to ask questions during the test.
MATHS_S9_03_TI_5RP
© UCLES 2018
2
Read the text in italics to the learners:
Listen carefully to these instructions. You will not have the opportunity to ask questions during the test.
You will be asked 20 questions. On your sheet there is an answer box for each question. You should
work out your answers in your head. Do not try to write down your calculations because this will take
up too much time. For some of the questions, important information is already written down for you on
the sheet.
Each question will be read aloud twice. You will then have time to work out your answer. If you don’t
know the answer to the question, leave it and wait for the next question. If you want to change your
answer, put a cross through your first answer and write your new answer nearby.
For the first group of questions you will have 5 seconds to work out each answer. For the second group
of questions you will have 10 seconds to work out each answer. For the third group of questions you
will have 15 seconds to work out each answer. Each question is worth one mark.
Do you have any questions about the test?
(Answer any questions the learners may have.)
Write your name on the front of the answer sheet.
(Begin the test.)
Now we are ready to start the test.
For this first group of questions, you will have 5 seconds to work out each answer and write it down.
1
Find fifteen percent of sixty.
2
Look at your answer sheet.
Draw a ring around the name of the regular polygon that does not tessellate.
3
Write down the inverse of the function x maps to x plus three.
4
Look at the scatter graph on your answer sheet.
Write down the type of correlation shown.
5
Work out seven subtract negative fifteen.
© UCLES 2018
M/S9/03
3
For this group of questions, you will have 10 seconds to work out each answer and write it down.
6
Find the next term of the sequence on your answer sheet.
7
Look at your answer sheet.
Triangle A is enlarged to triangle B.
Draw a ring around the cross which is the correct centre of enlargement.
8
Look at the table on your answer sheet.
It shows the destinations of two hundred flights from an airport in one day.
Find the relative frequency of a flight to Asia.
9
Aiko drives x kilometres to work.
Blessy drives twice as far as Aiko.
In total they drive sixty kilometres to work.
Find the value of x.
10 Divide one half by one third.
11
Look at the formula on your answer sheet.
Find the value of p when t equals negative six.
12 Look at the graph on your answer sheet.
Complete the equation of this straight line.
13 Look at the calculation on your answer sheet.
Use this to find seventy-six point eight divided by twenty-four.
14 Look at the inequality on your answer sheet.
Represent the solution for x on the number line.
© UCLES 2018
M/S9/03
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4
For this group of questions, you will have 15 seconds to work out each answer and write it down.
15 A builder makes a concrete mix using cement and sand in the ratio one to five.
He needs to make two point four cubic metres of concrete mix.
How many cubic metres of cement are needed?
16 Look at the diagram on your answer sheet.
It shows a regular hexagon and a square.
Find angle v.
17 Mike draws a pie chart to show the proportion of adults and children at a party.
There are twelve adults and forty-eight children.
Work out the size of the angle for the adults’ sector.
18 Look at the cylinder on your answer sheet.
It has a radius of ten centimetres and a height of six centimetres.
Draw a ring around the best estimate for the volume of the cylinder.
19 Look at your answer sheet.
Calculate this value.
20 A tank has a volume of one point two five metres cubed.
Work out this volume in centimetres cubed.
Now put down your pen. The test is finished.
Copyright © UCLES, 2018
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 2018
M/S9/03
Cambridge Lower Secondary Progression Test
Mathematics mark scheme
Stage 9
MATHS_S9_01_MS_8RP
© UCLES 2018
2
General guidance on marking
Difference in printing
It is suggested that schools check their printed copies for differences in printing that may affect the
answers to the questions, for example in measurement questions.
Brackets in mark scheme
When brackets appear in the mark scheme this indicates extra information that is not required but
may be given.
For example:
Question
1
Part
Mark
1
Total
Answer
Further Information
19.7 or 19.6(58…)
1
This means that 19.6 is an acceptable truncated answer even though it is not the correct rounded
answer.
The … means you can ignore any numbers that follow this; you do not need to check them.
Accept
•
any correct rounding of the numbers in the brackets, e.g. 19.66,
•
truncations beyond the brackets, e.g. 19.65
Do not accept
•
19.68 (since the numbers in brackets do not have to be present but if they are they should
be correct).
© UCLES 2018
M/S9/MS
3
These tables give general guidelines on marking learner responses that aren’t specifically mentioned
in the mark scheme. Any guidance specifically given in the mark scheme supersedes this guidance.
Number and place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept tailing zeros, unless the question has asked for a specific number of decimal places or
significant figures, e.g.
0.7000
Accept a comma as a decimal point if that is the convention that you have taught the learners, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. Units are provided on the answer line unless finding the units is part of what is
being assessed.
The table shows acceptable and unacceptable versions of the answer 1.85 m.
Accept
Do not accept
If the unit is given on the
answer line, e.g.
............................ m
Correct conversions,
provided the unit is stated
unambiguously,
e.g. ......185 cm...... m (this is
unambiguous since the unit
cm comes straight after the
answer, voiding the m which is
now not next to the answer)
......185...... m
......1850...... m
etc.
If the question states the unit
that the answer should be
given in, e.g. ‘Give your answer
in metres’
1.85
1 m 85 cm
185; 1850
Any conversions to other units,
e.g. 185 cm
© UCLES 2018
M/S9/MS
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4
Money
In addition to the rules for units, the table below gives guidance for answers involving money.
The table shows acceptable and unacceptable versions of the answer $0.30.
Accept
Do not accept
If the amount is in dollars and
cents, the answer should be
given to two decimal places.
$0.30
$0.3
For an integer number of
dollars it is acceptable not to
give any decimal places, e.g.
$9 or $9.00
$09 or $09.00
If units are not given on the
answer line
Any unambiguous indication of
the correct amount, e.g.
30 cents; 30 c
$0.30; $0-30; $0=30; $00:30
30 or 0.30 without a unit
$30; 0.30 cents
Ambiguous answers, e.g.
$30 cents; $0.30 c; $0.30 cents
(as you do not know which unit
applies because there are units
either side of the number)
If $ is shown on the answer line
If cents is shown on the answer
line
All unambiguous indications,
e.g. $......0.30......;
$......0-30......; $......0=30......;
$......00:30......
$......30......
......30......cents
......0.30......cents
Ambiguous answers, e.g.
$......30 cents......;
$......0.30 cents......
unless units on the answer line
have been deleted, e.g.
$......30 cents......
Ambiguous answers, e.g.
......$30 ......cents;
......$0.30 ......cents
unless units on the answer line
have been deleted, e.g.
......$0.30......cents
© UCLES 2018
M/S9/MS
5
Duration
In addition to the rules for units, the table below gives guidance for answers involving time durations.
The table shows acceptable and unacceptable versions of the answer 2 hours and 30 minutes.
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr, hrs),
minutes (m, min, mins) and
seconds (s, sec, secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
Incorrect or ambiguous formats, e.g.
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h (this is because this indicates 0.3 (i.e.
18 minutes) of an hour rather than 30 minutes)
Any correct conversion with appropriate units,
e.g.
2.5 hours; 150 mins
unless the question specifically asks for time
given in hours and minutes
02:30 (as this is a 24-hour clock time, not a time
interval)
2.5; 150
Time
The table below gives guidance for answers involving time.
The table shows acceptable and unacceptable versions of the answer 07:30.
Accept
Do not accept
If the answer is required in
24-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
07:30 with any separator in
place of the colon, e.g. 07 30;
07,30; 07-30; 0730
7:30
7:30 am
7 h 30 m
7:3
730
7.30 pm
073
07.3
If the answer is required in
12-hour format
Any unambiguous indication
of correct answer in numbers,
words or a combination of the
two, e.g.
7:30 am with any separator in
place of the colon, e.g. 7 30
am; 7.30 am; 7-30 am
Absence of am or pm
1930 am
7 h 30 m
7:3
730
7.30 pm
7.30 in the morning
Half past seven (o’clock) in the
morning
Accept am or a.m.
© UCLES 2018
M/S9/MS
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6
Algebra
The table shows acceptable and unacceptable versions of the answer 3x – 2.
Accept
Do not accept
x3 – 2; 3 × x – 2
3x + –2 if it is supposed to be in simplest form
Case change in letters
Changes in letters as long as there is no
ambiguity
Accept extra brackets when factorising, e.g. 5(x + (3 + y)).
Inequalities
The table shows acceptable and unacceptable versions of various answers.
For the following
Accept
Do not accept
For 6 G x 1 8
[6, 8)
61x18
For x G –2
(–∞,–2]
x 1 –2
For x 2 3
(3, ∞)
31x
Just ‘3’ written on the answer line, even if x 2 3
appears in the working.
Plotting points
The table shows acceptable and unacceptable ways to plot points.
Accept
Do not accept
Crosses or dots plotted within ± 1 square of the
2
correct answer
A horizontal line and vertical line from the axes
meeting at the required point.
The graph line passing through a point implies
the point even though there is no cross.
© UCLES 2018
M/S9/MS
7
Stage 9 Paper 1 Mark scheme
Question
1
Part
Mark
2
Total
2
Question
2
Part
Mark
Answer
9.3
−2.1
−18.9
1
Question
3
Part
Mark
(a)
1
(b)
1
Total
2
Question
4
Part
Mark
1
Total
© UCLES 2018
Award 1 mark for two correct.
Answer
1
Total
Further Information
0.6 × 0.6
0.36
0.64 × 0.4
1.6
0.64 ÷ 0.4
0.625
0.4 ÷ 0.64
0.256
Further Information
All lines correct for the mark.
Answer
7.1
14
7.5
2
3
5
7.9
Further Information
28
8
Answer
Further Information
Triangular prism
1
M/S9/MS
[Turn over
8
Question
5
Part
Mark
1
Total
1
Question
6
Part
Mark
Answer
Further Information
Answer
Further Information




(a)
1
6
(b)
1
Any correct description of the relationship,
e.g.
• Positive correlation.
• Heavier cakes take longer to cook.
• As the mass increases, the cooking
time increases.
Do not accept simply
‘positive’.
(c)
1
Any correct explanation, e.g.
• 80 minutes is too long for a cake that
only has a mass of 800 grams.
• 80 minutes would be the cooking time
for a heavier cake.
• Cakes that have a mass of 800g only
take about 40 minutes to cook.
Accept any indication that the
cooking time is too long for
the size of the cake.
Total
3
Question
7
Part
Mark
2
Answer
29 − 5n
Do not accept
Not many cakes take
that long to cook.
•
Further Information
Accept equivalent
expressions, e.g.
24 − 5(n − 1)
Award 1 mark for −5n seen.
Do not award the mark for
just 5n.
Total
© UCLES 2018
2
M/S9/MS
9
Question
8
Part
Mark
2
Answer
164.52
Further Information
Award 1 mark either for
• sight of the digits 16452
in the answer
or
• a correct method leading
to an answer with 2
decimal places with no
more than one arithmetic
error.
e.g.
4 5 7
×
3
6
2
6
4
2
1
3
7
1
0
1
6
3
5
2
so 163.52
Total
2
Question
9
Part
Mark
Answer
(a)
1
1
(b)
1
1
8
Total
© UCLES 2018
Further Information
Do not accept
1
23
2
M/S9/MS
[Turn over
10
Question
10
Part
Mark
(a)
1
(b)
2
Answer
Further Information
15.2 (km)
Allow a tolerance of ±0.2 km.
Award 2 marks if C is within
both sets of tram lines (tram
lines should allow for a ±2°
tolerance).
N
N
087°
C
083°
57°
Award 1 mark if C is within
one set of tram lines.
53°
A
B
Total
3
Question
11
Part
Mark
(a)
(b)
1
2
Answer
Further Information
x
–1
0
2
y
–1
1
5
Both required for the mark.
Award 1 mark for correctly
plotting their 3 points.
Straight line graph correctly drawn
extending at least from x = –1 to x = 2.
y
6
5
4
3
2
1
– 4 –3 –2 –1 0
–1
1
2
–2
–3
–4
Total
© UCLES 2018
3
M/S9/MS
3
4
5
x
11
Question
12
Part
Mark
2
Total
2
Question
13
Part
Mark
2
Total
2
Question
14
Part
Mark
2
Total
© UCLES 2018
Answer
15
9
Award 1 mark for sight of
2
10
90
and
or answer of
3
6
or
for a correct method allowing
one arithmetic error.
Answer
x 2 − 2x − 15
Further Information
Award 1 mark for at least
three of these four terms
seen or implied:
x 2, −5x, 3x, −15
or
for two correct out of x 2, −2x
and −15 in final answer.
Answer
135
Further Information
(cm3)
Further Information
Award 1 mark for sight of a
fully correct method for the
area of the trapezium, e.g.
• 2 × 3 + 0.5 × 2 × 3
• 0.5 × (2 + 4) × 3
• 3 × 4 − 0.5 × 2 × 3
implied by 9 × 15 seen
or
for sight of their area × 15.
2
M/S9/MS
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12
Question
15
Part
Mark
Answer
2
True
400 × 104 = 400 000

0.3 ÷ 10−2 = 0.003

Question
16
Part
Mark
2
Answer
30
Award 1 mark if 3 ticks are
correctly placed.

0.8 × 103 = 0.8 ÷ 10−3
2
False

10−1 = 0.1
Total
Further Information
(cm2)
Further Information
10
or
Award 1 mark for
2
equivalent
or
for an attempt at an algebraic
solution, e.g,
• 12 + 2 x or similar,
which may be part of an
equation
• 2y = 2 x + 10.
Total
2
Question
17
Part
Mark
Answer
Further Information
(a)
1
Any correct explanation, e.g.
• The probabilities do not add to make 1.
• 0.35 + 0.25 + 0.3 = 0.9, not 1.
• The total of the probabilities is 0.1 too
small.
0.35 + 0.25 + 0.3 = 0.9 on its
own is not sufficient for the
mark.
(b)
1
0.05 or equivalent
Total
2
© UCLES 2018
M/S9/MS
13
Question
18
Part
Mark
1
Answer
Further Information
2a or any equivalent fraction, e.g. 4a
5
10 ’
10a
25
Total
1
Question
19
Part
Mark
2
Total
2
Question
20
Part
Mark
3
Answer
39 304
Award 1 mark for an attempt
to work out 4913 × 2 × 2 × 2.
Answer
© UCLES 2018
Further Information
Correct algebraic method seen leading to
(x =) 2
(y =) −1
Do not accept trial and
improvement as a method
here.
Correct methods include:
rearranging one of the equations
to make one variable the subject
and then substituting into the other
equation,
• making the coefficients of x or y equal
followed by addition/subtraction of the
equations.
Award 2 marks for an
algebraic method leading to
either x = 2 or y = −1.
•
Total
Further Information
Award 1 mark for 2 and −1
with no/incorrect working
or
for eliminating either x or y,
allowing one arithmetic error,
e.g.
• rearrange one of the
equations to make one
variable the subject and
then substituting into the
other equation,
• making the coefficients
of x or y equal, followed
by addition/subtraction of
the equations.
3
M/S9/MS
[Turn over
14
Question
21
Part
Mark
2
Total
2
Question
22
Part
Mark
3
Answer
($) 9.60
Further Information
Award 1 mark for 2.40 × 4
or
2.40 ÷ 0.25.
Answer
(a =) 2
Further Information
Award 2 marks for
a2 + 92 = 62 + 72.
This may be implied by
(a2) = 62 + 72 − 92 (= 4).
Award 1 mark for
62 + 72 (= 85)
or
a2 + 92 seen.
Total
© UCLES 2018
3
M/S9/MS
15
Stage 9 Paper 2 Mark scheme
Question
1
Part
Mark
2
Total
2
Question
2
Part
Mark
Answer
($)87.12
(a)
1
6(3a − 2)
(b)
1
c(2c + 5)
Total
2
Question
3
Part
Mark
(a)
1
36
(b)
1
144
Total
2
Question
4
Part
Mark
1
Total
1
Question
5
Part
Mark
Further Information
Award 1 mark for a valid
method,
e.g. 48.40 ÷ 20 × 36
or
2.42 seen
or
1.8 seen.
Answer
Further Information
Answer
Further Information
Accept 180 – their (a).
Answer
Further Information
A minimum of four intervals in the range
100–200(cm) without gaps or overlaps
Answer
Further Information
Both correct for 1 mark.
1
False
True
True
Total
© UCLES 2018
Ignore additional intervals
outside of this range.
Condone unequal intervals.


False
1
M/S9/MS
[Turn over
16
Question
6
Part
Mark
Answer
(a)
1
n3
(b)
1
n
Total
2
Question
7
Part
Mark
Accept n1
(a)
1
(12, 5)
(b)
1
(5, 1)
Total
2
Question
8
Part
Mark
1
Total
1
Question
9
Part
Mark
2
Further Information
Answer
Further Information
Answer
Further Information
Answer
Further Information
12.4(…) (km / l)
1
2 2
4 4
6 6
3
6
12
18
Rows and columns can be
transposed.
The numbers 1, 3, 5 can be
in any order.
The numbers 2, 4, 6 can be
in any order.
5
10
20
30
Award 1 mark for row and
column labels correct.
Total
© UCLES 2018
2
M/S9/MS
17
Question
10
Part
Mark
Answer
(a)
1
Sales are expected to increase as the price
goes down.
Accept equivalents, e.g.
• Less sales as the price
goes up.
• As one goes down the
other goes up.
(b)
2
4 (thousand)
Condone 4000.
Further Information
Award 1 mark for sight of
7 (thousand)
or
3 (thousand).
This can be implied by the
correct lines drawn on the
graph.
Total
3
Question
11
Part
Mark
3
Answer
A complete trial and improvement method
leading to the answer x = 3.4.
This consists of at least one correct trial of
3.4 or lower and a correct 2 decimal place
trial to confirm the first decimal place.
Further Information
Award 1 mark for any trial of
a number between 3 and 4
correctly evaluated.
Award 1 mark for a trial of x
correctly evaluated where
3.35 G x G 3.38.
Award 1 mark for 3.4 in the
answer space.
x
3.1
3.2
3.3
3.35
3.36
3.37
3.38
3.39
3.4
3.5
3.6
3.7
3.8
3.9
Total
© UCLES 2018
x2 + 4x
(Accept rounded or
truncated answers)
22.01
23.04
24.09
24.6225
24.7296
24.8369
24.9444
25.0521
25.16
26.25
27.36
28.49
29.64
30.81
3
M/S9/MS
[Turn over
18
Question
12
Part
Mark
3
Answer
7.5 (%)
Further Information
Award 2 marks for a correct
method for finding the
fractional or percentage
increase, i.e.
0.08 ×1300 + (961 – 900)
2200
(= 0.075)
or
1.08 ×1300 + 961
2200
(= 1.075)
or
2365
2200
Award 1 mark for sight of any
of these:
• 0.08 × 1300 (=$104) oe
• 1.08 × 1300 (=$1404) oe
• ($)165 (increase over
year)
• ($)2365 (total for this
year).
Total
3
Question
13
Part
Mark
2
Total
© UCLES 2018
Answer
(c =) −20
Further Information
Award 1 mark for
5c + 160 = 60
or
c + 32 = 12.
2
M/S9/MS
19
Question
14
Part
Mark
3
Answer
3840 (bottles)
Further Information
Method 1 (Calculating
the total number of litres
produced).
Award 2 marks for
sight of 2880 (litres)
or
180 × 40
2.5
or
7200
2.5
Award 1 mark for
sight of 180 × 40 (= 7200)
or
40
(=16)
2.5
Method 2 (Calculating the
number of bottles produced
per tree).
Award 2 marks for
sight of 21.33… (bottles per
tree)
or
40
÷ 0.75 (= 21.33 ...)
2.5
Award 1 mark for
40
(= 16)
2.5
Total
© UCLES 2018
3
M/S9/MS
[Turn over
20
Question
15
Part
Mark
Answer
Further Information
(a)
1
4.384615..….
Award the mark if these digits
are seen.
(b)
1
4.4
Allow follow through from
an incorrect answer in (a)
as long as their (a) has 3 or
more digits.
Total
2
Question
16
Part
Mark
2
Total
2
Question
17
Part
Mark
Answer
3.6 (litres)
Award 1 mark for 3600
or
for correct conversion to litres
of an incorrect volume in cm3.
Answer
1
Journey A:
180 km in 3 hours
Journey C:
30 km in 0.5 hours
Total
© UCLES 2018
Further Information
Journey B:
140 km in 2.5 hours
Journey D:
10 km in 10 minutes
1
M/S9/MS
Further Information
21
Question
18
Part
Mark
1
Answer
A correct representation, i.e.
Further Information
Accept a drawing with some
visible edges of the individual
cubes shown, e.g.
or
Accept a drawing with hidden
edges shown if hidden edges
are dashed.
Total
1
Question
19
Part
Mark
2
Answer
(t =)
r – 21
r
– 3 or (t =)
7
7
Further Information
Accept equivalent
expressions, e.g.
r÷7−3
(r − 21) ÷ 7
Do not accept r − 21 ÷ 7
Award 1 mark for a correct
first step, i.e.
r
=t +3
7
r = 7t + 21
Total
© UCLES 2018
2
M/S9/MS
[Turn over
22
Question
20
Part
Mark
(a)
Answer
2
History
8
6
5
1
1
(b)
1
Total
3
Question
21
Part
Mark
2
2
0
5
1
Further Information
Award 1 mark if there is one
omission in the 9 leaves
or
if there are 9 unordered, but
otherwise correct, leaves.
Geography
4
5
6
7
3
0
4
2
0
8
4
7
8
A correct comparison, e.g.
• There are more higher geography
marks than history marks.
• History has more marks in the 40s
than geography.
• Geography has more marks in the 70s
than history.
Do not accept just a
description of one subject,
e.g. history had lots of marks
in the 40s.
Answer
Further Information
(Manjit’s number =) 6
(Gabriella’s number =) 39
Total
2
Question
22
Part
Mark
Answer
1
Any correct explanation that indicates that
the original price of the trainers needs to be
taken into account, e.g.
There is a higher percentage/fractional
discount on bargain trainers.
There is a 12% discount on the Alpha
trainers compared to a 20% discount
on the Bargain trainers.
6
6
is less than
(or equivalent).
50
30
Total
© UCLES 2018
1
M/S9/MS
Do not accept references to
averages alone.
Award 1 mark
for one number correct
or
if a factor of 24 (other than
24) and a multiple of 13
(other than 13) are seen.
Further Information
Do not accept, e.g.
• Bargain trainers are
cheaper.
• Alpha trainers are more
expensive.
23
Question
23
Part
Mark
2
Answer
Further Information
50
Award 1 mark if the value 42
is seen (28 + 14) or implied
by the graph.
or
Award 1 mark for correct
method.
40
x+
The point should be plotted at (2012, 42).
60
x
with x misread from
2
the graph.
30
20
10
0
2006 2007 2008 2009 2010 2011 2012
Total
© UCLES 2018
2
M/S9/MS
[Turn over
24
Stage 9 Paper 3 Mark scheme
Question
Mark
1
1
2
1
Answer
Further information
9
Square
Triangle
Hexagon
3
1
x→x−3
4
1
Negative
5
1
22
6
1
18
7
1
Pentagon
Ignore comments about strength.
Answer may be written next to 13.
A
B
8
1
122
61
or
or 61% or 0.61
200
100
9
1
20 (km)
10
1
3
1
or 1 or 1.5
2
2
11
1
18
12
1
2
13
1
3.2
14
1
Accept any equivalent fractions.
Do not accept solid circle.
0
5
15
1
0.4 (m3)
16
1
150(°)
17
1
72(°)
18
1
360 cm3
1800 cm3
180 cm3
3600 cm3
19
1
64
20
1
1 250 000 (cm3)
10
Do not accept 43.
Copyright © UCLES, 2018
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 2018
M/S9/MS
Cambridge Secondary 1 Progression Test
Question paper
55 minutes
*9490275461*
Mathematics Paper 1
For Teacher’s Use
Page
Stage 9
1
2
Name ………………………………………………….……………………….
Additional materials: Ruler
Tracing paper
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
3
4
5
6
Answer all questions in the spaces provided on the question paper.
7
Calculators are not allowed.
8
You should show all your working on the question paper.
9
The number of marks is given in brackets [ ] at the end of each question
or part question.
10
The total number of marks for this paper is 45.
11
12
Total
DC (CW/SW) 93957/5RP
© UCLES 2014
Mark
2
1
Work out the third term of the sequence with nth term 3(n + 2).
For
Teacher’s
Use
.................................................. [1]
2
Work out the size of an exterior angle of a regular pentagon.
NOT TO SCALE
................................................° [1]
3
The table shows the age and value of seven cars.
Age of car
(years)
2
1
9
7
10
5
8
Value ($)
4500
5000
1200
2900
500
2700
2200
(a) Complete the scatter graph.
5000
4000
Value ($) 3000
2000
1000
0
0
1
2
3
4
5
6
7
8
9
10
Age of car (years)
[2]
(b) Write down the type of correlation shown on the scatter graph.
.................................................. [1]
© UCLES 2014
M/S9/01
3
4
For
Teacher’s
Use
Tick (9) to show whether each of these statements is true or false.
Do not do any calculations.
The first one has been done for you.
True
The answer to 20.1 × 1.53 is larger than 20.1
False
9
The answer to 17.4 × 0.82 is larger than 17.4
The answer to 23.8 ÷ 0.74 is smaller than 23.8
[1]
5
(a) A cuboid measures 5 cm by 4 cm by 3 cm.
Draw the cuboid on the isometric grid.
= 1 cm
[1]
(b) Write down the number of planes of reflectional symmetry of the cuboid.
.................................................. [1]
© UCLES 2014
M/S9/01
[Turn over
4
6
Put a ring around the value that is closest to 3 70
3.2
4.1
5.6
For
Teacher’s
Use
8.4
23.3
[1]
7
Here is a pattern.
5
3
15
The rule is to multiply the values in the top two circles to make the value in the bottom
circle.
Complete these patterns using the same rule.
(a)
–8
– 0.5
[1]
(b)
8p4
24p12
[2]
© UCLES 2014
M/S9/01
5
8
Factorise fully.
For
Teacher’s
Use
(a) 2a2 + 5a
.................................................. [1]
(b) 6 – 18x + 24y
.................................................. [1]
9
Draw lines to join each calculation to the correct answer.
One has been done for you.
0.5 + 1.5 × 3
18
3 × (2 + 4)
5
8–1×2
14
10 + 23 – 4
40
(22 + 1) × 8
6
[2]
© UCLES 2014
M/S9/01
[Turn over
6
10 Work out 2 1 + 1 3
6
5
For
Teacher’s
Use
.................................................. [2]
11 Quadrilaterals A and B are drawn on the grid.
y
7
6
B
5
4
3
2
1
–1 0
–1
1
2
3
4
5
6
7
x
A
–2
–3
Describe fully the single transformation that maps A onto B.
.........................................................................................................................................
.................................................................................................................................... [2]
© UCLES 2014
M/S9/01
7
12 Work out 70
For
Teacher’s
Use
.................................................. [1]
13 (a) Work out 24.73 ÷ 0.001
.................................................. [1]
(b) Give your answer to part (a) to 2 significant figures.
.................................................. [1]
14 Here is a circle with centre C.
C
Construct an inscribed regular hexagon.
Use only a pair of compasses and a ruler.
Do not rub out your construction lines.
© UCLES 2014
[2]
M/S9/01
[Turn over
8
For
Teacher’s
Use
20
15 Put a ring around the fraction that is not equivalent to 24
10
12
35
42
14
18
50
60
[1]
16 Expand and simplify.
(x + 5)(x + 3)
.................................................. [2]
17 Put a ring around the correct calculation.
98 ÷ 98 = 9
7 × 73 = 74
68 ÷ 62 = 64
23 × 24 = 47
[1]
18 Bushra writes
480 ÷ 0.4 = 48 ÷ 4
Is Bushra correct?
Tick (9) a box.
Yes
No
Explain your answer.
.........................................................................................................................................
.................................................................................................................................... [1]
© UCLES 2014
M/S9/01
9
19 Ibrahim has some building blocks that are all cubes of the same size.
He uses three of the blocks to make a pile with a height of 43.5 cm.
Then he makes a row with five of the blocks with no gaps.
For
Teacher’s
Use
NOT TO
SCALE
43.5 cm
?
(a) Work out the length of the row of five blocks.
........................................... cm [2]
(b) Ibrahim only has red, yellow and green building blocks.
Ibrahim takes a block at random without looking.
Complete the table.
Number of
blocks
Red
Yellow
10
10
Green
3
5
Probability
[2]
© UCLES 2014
M/S9/01
[Turn over
10
20 The diagram shows the position of two schools, M and P.
The scale used in the diagram is 1 cm is equal to 1 km.
For
Teacher’s
Use
Scale
1 cm = 1 km
North
North
P
M
(a) What is the bearing of school P from school M ?
................................................° [1]
(b) School Q is on a bearing of 120° from school P.
School Q is 4 km away from school P.
Put a cross (8) on the diagram to show the position of school Q.
Label it Q.
[1]
(c) Cheng lives exactly 3 km away from school M.
Draw on the diagram the locus of points showing where Cheng lives.
[1]
© UCLES 2014
M/S9/01
11
21 Solve the simultaneous equations.
For
Teacher’s
Use
7x + y = 50
4x + y = 23
Show your working.
x = .................................................
y = ............................................ [2]
22 Here is a boat’s sail in the shape of a right angled triangle.
12 m
NOT TO
SCALE
15 m
Work out the total distance around the outside of the sail.
............................................. m [2]
© UCLES 2014
M/S9/01
[Turn over
12
23 The back to back stem-and-leaf diagram shows the scores for two different teams in
their last 25 basketball matches.
Team X
For
Teacher’s
Use
Team Y
8
5
0 1 1 2 3 6 9 9 9
4 1
6
1 3 5 5 6 8 9 9
9 9 8 7 5 4
7
1 1 4 7
9 8 8 8 6 5 1 0 0
8
2 3
8 7 5 3 2
9
4
0 0
10
7
Key: 8 | 5 | 0 is a score of 58 for Team X and 50 for Team Y
Tick (9) a box to show which team generally had higher scores.
Team X
Team Y
Explain your answer.
.........................................................................................................................................
.................................................................................................................................... [1]
24 Work out 1 7 ÷ 1 1
8
4
Give your answer as a mixed number in its simplest form.
.................................................. [3]
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.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2014
M/S9/01
Cambridge Secondary 1 Progression Test
Question paper
55 minutes
*4295752272*
Mathematics Paper 2
For Teacher’s Use
Page
Stage 9
1
2
3
Name ………………………………………………….……………………….
4
5
Additional materials: Ruler
Calculator
Tracing paper
Geometrical instruments
READ THESE INSTRUCTIONS FIRST
Answer all questions in the spaces provided on the question paper.
6
7
8
9
10
You should show all your working on the question paper.
The number of marks is given in brackets [ ] at the end of each question
or part question.
The total number of marks for this paper is 45.
11
12
13
14
15
16
Total
DC (NH/SW) 93956/8RP
© UCLES 2014
Mark
2
1
A microwave oven normally costs $160
For
Teacher’s
Use
In a sale there is a discount of 15%.
Work out the sale price of the microwave oven.
$ ............................................... [1]
2
Jamil is conducting a survey to find out how much time students in his school spend
doing homework.
He is going to ask the first 10 students on the register in his maths class.
This may not produce a good sample for Jamil’s survey.
Give two reasons why.
Reason 1 .........................................................................................................................
.........................................................................................................................................
Reason 2 .........................................................................................................................
.................................................................................................................................... [2]
3
Work out
38 – 7
2+5
Give your answer to 2 decimal places.
.................................................. [2]
© UCLES 2014
M/S9/02
3
4
Two shapes A and B fit together to make a parallelogram.
For
Teacher’s
Use
57°
68°
NOT TO
SCALE
B
157°
A
146°
112°
Work out the sizes of the four angles in shape A.
Write them in the correct places on the diagram.
[2]
5
One solution to x2 + 3x = 17 is between 2 and 3
Use trial and improvement to find this solution.
Give your answer to 1 decimal place.
You must record your trials in the table.
x
x2 + 3x
Bigger or smaller than 17
2
3
22 + 3 × 2 = 10
32 + 3 × 3 = 18
smaller
bigger
x = ............................................ [2]
© UCLES 2014
M/S9/02
[Turn over
4
6
Ludwik is an engineer.
He charges a fixed call out fee plus an hourly rate for each job.
For
Teacher’s
Use
The table shows how much Ludwik charges for three jobs that last different amounts
of time.
Amount of time (hours)
1
4
6
Charge ($)
50
140
200
(a) Draw the straight line graph that shows this information.
200
180
160
140
120
Charge
100
($)
80
60
40
20
0
0
1
2
3
4
Amount of time (hours)
5
6
7
[1]
(b) Write down Ludwik’s fixed call out fee.
This is the cost before he has worked any hours.
$ ............................................... [1]
(c) Work out Ludwik’s hourly rate.
$ ............................................... [1]
© UCLES 2014
M/S9/02
5
7
Surinder thinks that regular octagons will tessellate.
For
Teacher’s
Use
135°
Is Surinder correct?
Tick (3) a box. Yes
No
Explain your answer.
.........................................................................................................................................
.................................................................................................................................... [1]
8
Draw lines to join each inequality to the correct solution set.
Inquality
Solution set
–5 –4 –3 –2 –1
0
1
2
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
[1]
© UCLES 2014
M/S9/02
[Turn over
6
9
Here is quadrilateral P.
For
Teacher’s
Use
y
7
6
5
4
3
P
2
1
–6
–5
–4
–3
–2
0
–1
1
2
3
4
5
6
7
8
9
10
x
–1
–2
–3
Draw an enlargement of quadrilateral P with scale factor 3 and centre of
enlargement (3, 2).
[2]
10 Write as a single fraction.
2 3
+
x x
.................................................. [1]
© UCLES 2014
M/S9/02
7
11 Here is a right angled triangular prism.
For
Teacher’s
Use
4.5 cm
NOT TO
SCALE
6 cm
5.2 cm
Put a ring around the correct working for the volume of this prism.
1
(4.5 + 5.2) × 6
2
4.5 × 5.2 × 6
4.5 × 5.2 × 6 ÷ 2
1
× 4.5 × 5.2 × 6
3
[1]
12 Work out the value of 5x2 when x = –3.4
.................................................. [1]
13 Here is a semi-circle with radius 5.5 cm.
NOT TO
SCALE
5.5 cm
Work out the perimeter of this semi-circle.
............................................ cm [2]
© UCLES 2014
M/S9/02
[Turn over
8
14 The table shows some functions and their inverses.
For
Teacher’s
Use
Complete the table.
The first row has been done for you.
Mapping
Function
×4
×2
m
–3
m
÷4
4m
2m – 3
Inverse
function
Reverse mapping
...........
m
...........
m
m
4
...............
[2]
15 Tick (9) whether each set of data is primary or secondary.
Primary
Secondary
Adam collects data about heights by measuring students in
his class.
Bob collects data about cricket scores using the internet on
his computer.
Carol collects data about masses of animals from a book.
[1]
© UCLES 2014
M/S9/02
9
16 The table shows the population of Thailand for 1968 and 2013.
Year
Population
1968
34.50 million
2013
66.93 million
For
Teacher’s
Use
What is the percentage increase in the population of Thailand from 1968 to 2013?
..............................................% [2]
17 In a box the ratio of green to black pens is 5 : 8
Imre takes 20 black pens out of the box.
Now the ratio of green to black pens is 5 : 6
green : black
5:8
green : black
5:6
Take 20 black
pens out
Work out the number of green pens in the box.
.................................................. [2]
© UCLES 2014
M/S9/02
[Turn over
10
18 Make x the subject of this formula.
For
Teacher’s
Use
y = 5(t + x)
x = ........................................... [2]
19 Put these numbers in order, from smallest to largest.
1
....................
smallest
0.3
....................
1
3
....................
9
20
5%
....................
....................
largest
[2]
20 Lucas, Gabriela and Ingrid are solving the equation 4(n + 3) = 8n – 8
They each start the solution in different ways.
Tick (9) whether their statements are true or false.
The first one is done for you.
True
False
Lucas
so
4(n + 3) = 8n – 8
4n + 4 = 8n
9
Gabriela
so
4(n + 3) = 8n – 8
n + 3 = 2n – 2
so
4(n + 3) = 8n – 8
12 = 4n – 8
Ingrid
[1]
© UCLES 2014
M/S9/02
11
21 Mr Green spins two fair spinners.
Some of the possible outcomes are recorded in this table.
For
Teacher’s
Use
Spinner 2
1
3
7, 5
Spinner
1
4
4, 1
7, 9
4, 5
2, 3
2, 2
Complete the diagrams of the spinners by filling in the missing values.
.............
4
.............
1
.............
3
.............
.............
Spinner 1
Spinner 2
[2]
© UCLES 2014
M/S9/02
[Turn over
12
22 (a) Complete this table of values for the equation 2y – x = 4
x
0
y
2
0
For
Teacher’s
Use
6
3
[2]
(b) Here is a graph of the line y + x = –1
Draw the graph of 2y – x = 4 on the same axes.
y
8
7
6
y + x = –1
5
4
3
2
1
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
x
–1
–2
–3
–4
[1]
© UCLES 2014
M/S9/02
13
(c) Use your graph to write down the solution to the simultaneous equations.
For
Teacher’s
Use
y + x = –1
2y – x = 4
x = ............................................
y = ............................................ [1]
23 In a trial, two different light bulbs are being compared.
The trial looks at how long the light bulbs last.
(a) The relative frequency of a low energy bulb lasting 1001–1500 hours is 0.4
Complete the table.
Type of
bulb
Number of
bulbs tested
Standard
bulb
Low energy
bulb
Hours bulbs lasted
0–1000
hours
1001–1500
hours
more than 1500
hours
50
30
20
0
80
36
[1]
(b) Tick (9) whether these statements are true or false.
True
False
The probability of a standard bulb lasting 0 – 1000
hours is the same as it lasting 1001–1500 hours.
The probability of a low energy bulb lasting 0 – 1000
hours is higher than for a standard bulb.
[1]
© UCLES 2014
M/S9/02
[Turn over
14
24 The diagram shows a square.
The square is divided into four rectangles by two straight lines.
The area of the largest rectangle is 48 000 m2.
For
Teacher’s
Use
NOT TO
SCALE
48 000 m2
C
60 m
200 m
(a) Work out the area of the smallest rectangle, C.
.............................................m2 [2]
(b) Complete this sentence.
The area 48 000 m2 is equivalent to .............................. hectares.
© UCLES 2014
M/S9/02
[1]
15
25 A plant grows to a height of 8 cm in 1 week.
Fatima says,
“Plant height and number of weeks are directly proportional.
The height of this plant in 2 years will be about 832 cm, because there are 104 weeks
in 2 years.”
Is Fatima likely to be correct?
Tick (9) a box.
Yes
No
Explain your answer.
.........................................................................................................................................
.................................................................................................................................... [1]
© UCLES 2014
M/S9/02
For
Teacher’s
Use
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.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2014
M/S9/02
Cambridge Secondary 1 Progression Test
Mark scheme
Mathematics
Stage 9
DC (CW/SW) 90762/8RP
© UCLES 2014
2
These tables give general guidelines on marking answers that involve number and place value,
and units of length, mass, money, duration or time. If the mark scheme does not specify the correct
answer, refer to these general guidelines.
Number and Place value
The table shows various general rules in terms of acceptable decimal answers.
Accept
Accept omission of leading zero if answer is clearly shown, e.g.
.675
Accept tailing zeros, unless the question has asked for a specific number of decimal places, e.g.
0.7000
Always accept appropriate tailing zeros, e.g.
3.00 m; 5.000 kg
Accept a comma as a decimal point if that is the convention that you have taught the children, e.g.
0,638
Units
For questions involving quantities, e.g. length, mass, money, duration or time, correct units must be
given in the answer. The table shows acceptable and unacceptable versions of the answer 1.85 m.
Correct answer
Also accept
Do not accept
Units are not given
on answer line and
the question does not
specify a particular unit
for the answer
1.85 m
Correct conversions
provided the unit is
stated, e.g.
1 m 85 cm
185 cm
1850 mm
0.00185 km
1.85
If the unit is given on
the answer line, e.g.
............................ m
......1.85...... m
Correct conversions,
provided the unit is
stated unambiguously,
e.g. ......185 cm...... m
......185...... m
......1850...... m
etc.
If the question
states the unit that
the answer should
be given in, e.g.
‘Give your answer in
metres’
1.85 m
1.85
1 m 85 cm
185; 1850
© UCLES 2014
185 m
Any conversions to
other units, e.g.
185 cm
M/S9/MS
3
Money
For questions involving money, it is essential that appropriate units are given in the answer.
The table shows acceptable and unacceptable versions.
Accept
Do not accept
If the amount is in dollars and
cents, the answer should be
given to two decimal places.
$0.30
$9 or $9.00
$09 or $09.00
If units are not given on answer
line
Any unambiguous indication of
the correct amount, e.g.
30 cents; 30 c
$0.30; $0.30 c; $0.30 cents
$0-30; $0=30; $00:30
30 or 0.30 without a unit
$......0.30......
$......0.30 cents......
$......30......
$......30 cents...... (this cannot
be accepted because it is
ambiguous, but if the dollar
sign is deleted it becomes
acceptable)
If $ is shown on the answer line
Accept all unambiguous
indications, as shown above
If cents is shown on the answer
line
......30......cents
......$0.30 ......cents
Incorrect or ambiguous
answers, e.g.
$0.3; $30; $30 cents; 0.30 cents
......0.30......cents
......$30 ......cents
Duration
Accept any unambiguous method of showing duration and all reasonable abbreviations of hours
(h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, secs).
Accept
Do not accept
Any unambiguous indication using any
reasonable abbreviations of hours (h, hr, hrs),
minutes (m, min, mins) and seconds (s, sec,
secs), e.g.
2 hours 30 minutes; 2 h 30 m; 02 h 30 m
5 min 24 sec; 00 h 05 m 24 s
Incorrect or ambiguous formats, e.g.
Any correct conversion with appropriate units,
e.g.
2.5 hours; 150 mins
324 seconds
Also accept unambiguous digital stopwatch
format, e.g.
02:30:00
00.05:24; 05:24 s
© UCLES 2014
2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3;
2.3 h
2.5; 150
324
Do not accept ambiguous indications, e.g.
02:30
5.24
M/S9/MS
[Turn over
4
Time
There are many ways to write times, in both numbers and words, and marks should be awarded
for any unambiguous method. Accept time written in numbers or words unless there is a specific
instruction in the question. Some examples are given in the table.
Accept
Do not accept
Any unambiguous indication of correct answer
in numbers, words or a combination of the two,
e.g. 07:30
Incorrect or ambiguous formats, e.g.
0730; 07 30; 07.30; 07,30; 07-30; 7.30; 730 a.m.;
7.30am; 7.30 in the morning
07.3; 073; 07 3; 730; 73; 7.3; 7.3 am; 7.30 p.m.
Half past seven (o’clock) in the morning
Thirty minutes past seven am
Also accept: O-seven-thirty
e.g. 19:00
19; 190; 19 000; 19.00 am; 7.00 am
1900; 19 00; 19_00 etc.
Nineteen hundred (hours)
Seven o’clock in the afternoon/evening
Accept correct conversion to 12-hour clock, e.g.
16:42
4.42 p.m.
4.42 am; 0442; 4.42
Sixteen forty two
Four-forty-two in the afternoon/evening
Four forty two p.m.
Forty two (minutes) past four p.m.
Eighteen (minutes) to five in the evening
Forty two (minutes) past sixteen
Eighteen (minutes) to seventeen
Also accept a combination of numbers and
words, e.g.
18 minutes to 5 p.m.
42 minutes past 4 in the afternoon
© UCLES 2014
M/S9/MS
5
Stage 9 Paper 1 Mark Scheme
Question
1
Part
Mark
1
Total
1
Question
2
Part
Mark
1
Total
1
Question
3
Part
Mark
(a)
Answer
Further Information
Answer
Further Information
Answer
Further Information
15
72 ( o )
Tolerance ±1 mm horizontally
±$100 vertically
2
5000
4000
Award 1 mark for at least 3
more correctly plotted points
all within tolerance.
Value ($) 3000
2000
1000
0
0
1
2
3
4
5
6
7
8
9
10
Age of car (years)
(b)
1
Total
3
Question
4
Part
Mark
1
Total
© UCLES 2014
Negative
Ignore words describing the
strength of the correlation.
Accept ‘-ve’ but not ‘-’
Answer
9
Further Information
True
False
True
9
False
True
9
False
Both are required for the
mark.
1
M/S9/MS
[Turn over
6
Question
5
Part
Mark
(a)
1
(b)
1
Total
2
Question
6
Part
Mark
1
Total
1
Question
7
Part
Mark
(a)
Answer
Further Information
Accept in any orientation.
Lines should be ruled.
Ignore hidden edges drawn.
3
Answer
3.2
4.1
5.6
8.4
Further Information
23.3
Answer
Accept any clear indication.
Further Information
1
–8
–0.5
(+)4
(b)
2
8p4
Award 1 mark for 3 and
1 mark for p8
so long as expression is of
form apb where a and b are
non-zero numbers
e.g. 3p16 and 16p8 would
score 1, 3+p8 would score
zero
3p8
24p12
Total
© UCLES 2014
3
M/S9/MS
7
Question
8
Part
Mark
(a)
1
a(2a + 5)
(b)
1
6(1 – 3x + 4y)
Total
2
Question
9
Part
Mark
2
Total
2
Question
10
Part
Mark
2
Answer
Further Information
Answer
Further Information
0.5 + 1.5 × 3
18
3 × (2 + 4)
5
8–1×2
14
10 + 23 – 4
40
(22 + 1) × 8
6
Award 1 mark for 2 or 3
correct matches.
Answer
3
23
113
30 or equivalents such as 30
Further Information
Award 1 mark for correct
common denomitor seen (30
or a multiple of 30) and at
least one correct numerator,
e.g.
2
Total
© UCLES 2014
5
18
48
+ 1 , 65 +
30
30 30
30
2
M/S9/MS
[Turn over
8
Question
11
Part
Mark
2
Answer
Reflection (in the line) y = 2
Further Information
Both reflection and (the line)
y = 2 are required for 2
marks.
Do not accept this as a
drawing on the diagram, it
must be a description.
Award 1 mark for reflection
or y = 2 seen.
Total
2
Question
12
Part
Mark
1
Total
1
Question
13
Part
Mark
Further Information
Answer
Further Information
1
(a)
1
24 730
(b)
1
25 000
Total
2
© UCLES 2014
Answer
Follow through from their (a)
as long as their (a) has more
than 2 significant figures.
M/S9/MS
9
Question
14
Part
Mark
Answer
Further Information
2
Award 1 mark for a regular
hexagon (tolerance ± 2 mm
and ± 2°)
or
6 construction arcs
(must be arcs).
C
Total
2
Question
15
Part
Mark
1
Total
1
Question
16
Part
Mark
2
Answer
10
12
Further Information
14
18
35
42
Answer
x2 + 8x + 15
50
60
Further Information
Award 1 mark for:
x2 + 5x + 3x + 15
or
x2 + ax + 15
or
x2 + 8x + b
(where a and b are numbers
not equal to 0)
Total
© UCLES 2014
2
M/S9/MS
[Turn over
10
Question
17
Part
Mark
1
Total
1
Question
18
Part
Mark
1
Total
1
Question
19
Part
Mark
(a)
2
(b)
2
Total
© UCLES 2014
Answer
98 ÷ 98 = 9
68 ÷ 62 = 64
Further Information
7 × 73 = 74
23 × 24 = 47
Answer
Further Information
No and, reason,
e.g.
•
Bushra has multiplied 0.4 by 10 but
hasn’t multiplied 480 by 10
•
It should be 4800 not 48
•
The correct answer is 1200 but 48
divided by 4 is 12
Answer
Any correct reason with a
decision of ‘no’ scores the
mark.
Further Information
72.5 ( cm )
Award 1 mark for a correct
method, e.g.
(43.5 ÷ 3) × 5
or for 14.5 seen
Red
Yellow
Green
Number of
blocks
10
10
30
Probability
1
5
1
5
3
5
4
M/S9/MS
Award 1 mark for 30 (Green
blocks) correct or both
fractions correct.
11
Question
20
Part
Mark
(a)
1
(b)
1
Answer
Further Information
074(°) ± 2°.
Do not allow 74, must be
three figures.
School Q positioned 4 cm
from School P at a bearing of
120°.
North
North
P
M
(c)
Q
×
1
North
M
Total
3
Question
21
Part
Mark
2
North
2
Question
22
Part
Mark
2
Total
© UCLES 2014
A circle of radius 3 cm
± 2 mm centred on M.
P
Answer
(x = ) 9
Further Information
Award 1 mark for 3x = 27
seen or equivalent correct
method or one correct
answer.
(y = ) –13
Total
Condone if not labelled
providing there is not a
choice of crosses. Award the
mark if the point is
± 2mm and ± 2°.
Answer
36 (m)
Further Information
Award 1 mark for use of
Pythagoras’ theorem, e.g.
152 – 122 = x2 or use of
Pythagorean triples, e.g. 9
seen.
2
M/S9/MS
[Turn over
12
Question
23
Part
Mark
Answer
1
Ticks Team X and gives a suitable reason,
e.g.
•
Team Y have a lower median score
•
Team X have most of their scores in
the 70s and 80s whereas team Y have
most of their scores in the 50s and 60s
Further Information
Any valid comparative
comment.
Condone
• team X have more higher
scores (than team Y)
• team X has a higher
average score
Do not allow comments that
are not comparative, e.g.
• team X has lots of high
scores
Total
© UCLES 2014
1
M/S9/MS
13
Question
24
Part
Mark
3
Answer
1
1
Further Information
For full marks the final
answer must be simplified
and must be a mixed number
2
Award 2 marks for:
a completely correct method,
e.g. converting both fractions
to improper fractions followed
by an attempt to multiply by
the reciprocal of the second
e.g. 15 ÷ 5 followed
8
4
by
15
4
×
8
5
or
sight of a value equivalent to
1 1 but which is unsimplified
2
or that is left as an improper
fraction.
Award 1 mark for:
4
15
or
sight of either
5
8
or
an attempt to multiply their
first improper fraction by the
reciprocal of their second
improper fraction (if there is a
mistake in the conversion).
Total
© UCLES 2014
3
M/S9/MS
[Turn over
14
Stage 9 Paper 2 Mark Scheme
Question
1
Part
Mark
1
Total
1
Question
2
Part
Mark
2
Answer
Further Information
Answer
Further Information
($) 136
Any two reasons from two different
categories:
• sample size too small
• bias relating to selecting from just one
class (e.g. same subject, same age,
same ability level)
• this is not random sampling
Accept equivalent answers,
e.g.
• he should ask more people
• he should ask people from
different classes
Note two marks can be
scored in one sentence e.g.
he should have asked more
students and used more
classes.
Award 1 mark for only one
correct reason or two reasons
from the same category.
Total
© UCLES 2014
2
M/S9/MS
15
Question
3
Part
Mark
2
Total
2
Question
4
Part
Mark
Answer
Further Information
4.43
Award 1 mark for a correct
answer truncated or given to
the wrong number of decimal
places or for 31 seen.
7
Answer
2
Further Information
57°
68°
55°
157°
B
A
68°
Total
© UCLES 2014
146°
203°
Degree symbols are not
necessary.
112°
Award 1 mark for 2 or 3
correct answers.
34°
2
M/S9/MS
[Turn over
16
Question
5
Part
Mark
2
Answer
2.9 with working
The minimum amount of working for 2
marks would be evidence of correctly
evaluating x2 + 3x for two values of x
between 2.85 and 2.94 that result in
answers either side of 17 (likely to be 2.85
and 2.9).
Total
© UCLES 2014
2
M/S9/MS
Further Information
Award 1 mark for evaluating
two values of x (2 < x < 3)
possible values are given
below for reference
or
an answer of 2.9 with no
working.
x
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.85
2.86
2.87
2.88
2.89
2.9
2.91
2.92
2.93
2.94
x2+ 3x
10.71
11.44
12.19
12.96
13.75
14.56
15.39
16.24
16.6725
16.7596
16.8469
16.9344
17.0221
17.11
17.1981
17.2864
17.3749
17.4636
17
Question
6
Part
Mark
(a)
1
Answer
200
180
160
140
120
100
80
60
40
20
0
0
Further Information
(6, 200)
(4, 140)
(1, 50)
1
2
3
4
5
6
Line must be ruled for the
mark. It is not necessary
to see the points plotted
provided the line passes
through all three points. The
line does not need
to pass through the point
(0, 20).
7
(b)
1
($) 20
Follow through using the
intercept from their single
straight line graph as long as
their answer is greater
than 0.
(c)
1
($) 30 (per hour)
Follow through using the
gradient from their single
straight line graph.
Total
3
Question
7
Part
Mark
Answer
1
No and a correct reason, e.g.
• 360° ÷ 135° is not an integer
• putting two 135° angles together leaves
a remainder of 90°
• an octagon needs a square to tessellate
with
• the only regular shapes that tessellate
are triangles, squares and hexagons
Total
© UCLES 2014
Further Information
Do not accept “there will be
gaps” without supporting
evidence, e.g. a correct
calculation or diagram.
1
M/S9/MS
[Turn over
18
Question
8
Part
Mark
Answer
1
Inequality
Further Information
Both lines must be correct for
the mark.
Solution set
–5 –4 –3 –2 –1 0
1 2 3 4 5
–5 –4 –3 –2 –1 0
1 2 3 4 5
–5 –4 –3 –2 –1 0
1 2 3 4 5
–5 –4 –3 –2 –1 0
1 2 3 4 5
x>3
x≤3
Total
1
Question
9
Part
Mark
Answer
2
Further Information
Award 1 mark for 3 out of the
4 vertices correctly plotted or
for a quadrilateral enlarged
by a scale factor of 3 but in
the wrong place.
5
4
3
P
2
Labels are not required.
1
–3
–2
–1
0
1
2
3
4
5
6
–1
Total
2
Question
10
Part
Mark
1
Total
© UCLES 2014
Answer
5
x
1
M/S9/MS
Further Information
19
Question
11
Part
Mark
1
Total
1
Question
12
Part
Mark
1
Total
1
Question
13
Part
Mark
2
Answer
1
2 (4.5 + 5.2) × 6
4.5 × 5.2 × 6
4.5 × 5.2 × 6 ÷ 2
1
× 4.5 × 5.2 × 6
3
Answer
Further Information
Accept any clear indication.
Further Information
57.8 or equivalent
Answer
28.3 (cm)
Further Information
Award 2 marks for an answer
in the range 28.27 to 28.3
Award 1 mark for
2 × é × 5.5 (+11)
(2)
or é=× 5.5 (+11)
Total
2
Question
14
Part
Mark
Answer
2
÷2
Total
© UCLES 2014
+3
m+3
2
Further Information
Award 1 mark for each
correct completed cell or their
inverse function matching
their reverse mapping.
Condone any letter in place
of the m.
2
M/S9/MS
[Turn over
20
Question
15
Part
Mark
1
Answer
Primary
Secondary
9
Further Information
All three must be correct for
the mark.
9
9
Total
1
Question
16
Part
Mark
2
Total
2
Question
17
Part
Mark
2
Total
2
Question
18
Part
Mark
2
Total
© UCLES 2014
Answer
94 (%)
Award 1 mark for
66.93 – 34.5 or 0.94
34.5
Answer
50
Further Information
Award 1 mark for
20 ÷ 2 seen or implied
Answer
(x =)
Further Information
y
y – 5t
– t or (x =)
5
5
2
M/S9/MS
Further Information
Award 1 mark for a correct
first step that affects both
sides of the equation, e.g.
y
=t+x
•
5
• y – 5t = 5x
21
Question
19
Part
Mark
2
Answer
5%
0.3
1
3
Further Information
9
20
1
Accept numbers in same
form in correct order for 2,
e.g.
0.05 0.3 0.33(...) 0.45 1
Award 1 mark for values
correctly converted to the
same form allowing one error
or omission:
1, 0.3, 0.33.., 0.05, 0.45
or
60 18 20 3 27
60 , 60 , 60, 60, 60
(other denominators
are possible providing
denominators are equal)
or
100%, 30%, 33.3..%, 5%,
45%
or for values correctly written
in reverse order
Total
2
Question
20
Part
Mark
Answer
1
True
Total
© UCLES 2014
9
Further Information
False
9
True
False
9
True
False
Both are required for the
mark.
1
M/S9/MS
[Turn over
22
Question
21
Part
Mark
Answer
Further Information
2
9
4
7
5
1
3
2
2
Spinner 1
Award 2 marks for all five
numbers correct. Numbers
can be in any position in the
correct spinner.
Spinner 2
Award 1 mark for
three correct numbers
or
for a correctly completed
sample space diagram:
7
4
2
Total
© UCLES 2014
2
M/S9/MS
1
5
3
2
9
7,1 7,5 7,3 7,2 7,9
4,1 4,5 4,3 4,2 4,9
2,1 2,5 2,3 2,2 2,9
23
Question
22
Part
Mark
(a)
2
(b)
Answer
x
y
1
–4
0
2
6
0
2
3
5
8
7
6
5
4
3
(2, 3)
2
(0, 2)
1
(–4, 0)
–6 –5 –4 –3 –2 –1 0
–1
–2
(c)
1
Total
4
Question
23
Part
Mark
(a)
1
(b)
1
Total
© UCLES 2014
Further Information
Award 1 mark for 2 correct
values in the table.
Line needs to extend
between at least 3 out of the
4 points and must be ruled
for the mark.
(6, 5)
Follow through their values
as long as they are in a
straight line.
1 2 3 4 5 6
x = –2
y=1
Both are required for the
mark and depend on graph
values seen.
If incorrect, follow through
from any single line
intersecting
y + x = –1 (must be within the
grid).
Algebraic solution not
evidenced by graph scores
zero.
Answer
Further Information
32 and 12
Both are required for the
mark.
True
9
False
True
9
False
Both are required for the
mark.
2
M/S9/MS
[Turn over
24
Question
24
Part
Mark
Answer
(a)
2
6000 (m2)
(b)
1
4.8 (hectares)
Total
3
Question
25
Part
Mark
Answer
1
A decision of no and any correct
explanation, e.g.
• Height and number of weeks are unlikely
to be directly proportional
• The plant is unlikely to continue growing
at the same rate
Further Information
Award 1 mark for:
finding one of the missing
lengths 240, 100 or 300 (may
be marked in the correct
place on the diagram)
or
60 P 100
or
48 000 ÷ 200
or
90 000 (m2) or
24 000 (m2)
Further Information
Allow 832 cm is an unlikely
height in just 2 years.
or
There is no basis for her
initial assertion as she has
only one measurement (or
words to that effect)
Do not accept “yes, because
104 × 8 = 832”.
Total
© UCLES 2014
1
M/S9/MS
25
Stage 9 Paper 3 Mark Scheme
Question
Mark
1
½
5.1
2
½
x(3x – 4) or 3x2 – 4x
3
½
4
4
½
6
5
½
(Customers are) increasing or going up or rising
6
½
11
7
½
($) 3.30
8
½
Angle, centre and direction (of rotation)
9
½
3.6
10
½
63 (°) and 4 (cm)
11
½
6x5
12
½
1
10
13
½
Thursday and Friday (or Thurs and Fri)
14
½
2x – 4 or 2(x – 2)
15
½
280 (km)
16
½
3n – 1
17
½
1 or 0.25
4
18
½
c = 2n or n = c
2
19
½
12
20
½
3200 (mm3)
© UCLES 2014
Answer
10%
0.01
10–1
M/S9/MS
26
BLANK PAGE
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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.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local
Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
© UCLES 2014
M/S9/MS