S7/01 Mathematics Stage 7 Paper 1 Mark Scheme 2022

Mathematics
Stage 7

Paper 1 2023
Cambridge Lower Secondary Progression Test
Mark Scheme

3141_01_MS_5RP
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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 Part marks Guidance

5 19.7 or 1
19.6(58…)

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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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 Correct conversions, provided ......185.. . .m

answer line, e.g. the unit is stated ......1850.. . .m etc.
.........................m 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)
If the question states the unit 1.85 185; 1850
that the answer should be 1 m 85 cm Any conversions to other
given in, e.g. ‘Give your units,
answer in metres’ e.g. 185 cm

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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 $0.30 $0.3

and cents, the answer
should be given to two For an integer number of $09 or $09.00
decimal places dollars it is acceptable not
to give any decimal places,
e.g.
$9 or $9.00
If units are not given on the Any unambiguous indication 30 or 0.30 without a unit
answer line of the correct amount, e.g.
30 cents; 30 c $30; 0.30 cents
$0.30; $0–30; $030;
$00:30 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, $......30......
line e.g. $......0.30.. ;
$......0-30.. .; Ambiguous answers, e.g.
$......030.. ; $......30 cents.. ;
$......00:30...... $......0.30 cents......
unless units on the answer
line have been deleted, e.g.
$......30 cents......

If cents is shown on the ......30....cents ......0.30.. .cents

answer line
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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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 Incorrect or ambiguous formats,

reasonable abbreviations of hours (h, hr, e.g. 2.30; 2.3; 2.30 hours; 2.30 min;
hrs), minutes (m, min, mins) and 2 h 3;
seconds (s, sec, secs), e.g. 2.3 h (this is because this indicates 0.3 of
2 hours 30 minutes; 2 h 30 m; 02 h 30 m an hour (i.e.18 minutes) rather than 30
minutes)
Any correct conversion with appropriate
units, e.g. 02:30 (as this is a 24-hour clock time, not a
2.5 hours; 150 mins time interval)
unless the question specifically asks for
time given in hours and minutes 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 Any unambiguous indication 7:30

24-hour format of correct answer in 7:30 am
numbers,
words or a combination of 7 h 30 m
the
two, e.g. 7:3
07:30 with any separator in 730
place of the colon, e.g. 7.30 pm
07 30; 07,30; 07-30; 0730 073
07.3

If the answer is Any unambiguous Absence of am or pm

required in 12-hour indication of correct 1930 am
format answer in numbers, words 7 h 30 m
or a combination of the 7:3
two, e.g. 730
7:30 am with any separator 7.30 pm
in place of the colon, e.g.
7 30 am; 7.30 am; 7-30 am
7.30 in the morning

Half past seven (o’clock) in

the morning

Accept am or a.m.

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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

(3, ∞) Just ‘3’ written on the answer line, even if x

For x  3
3x  3 appears in the working

Plotting points

The table shows acceptable and unacceptable ways to plot points.

Accept Do not accept

1
Crosses or dots plotted within  square A horizontal line and vertical line from the
of the axes meeting at the required point
2
correct answer

The graph line passing through a point

implies the point even though there is no
cross

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Question Answer Marks Part Marks Guidance

1 0.04 1 Accept .04

2 0.08 1 Accept .08

3(a) –16 1

3(b) 17 1

4 5 and 15 1 Both answers correct for the mark.

Accept any clear indication.

5 Perpendicular line to AB drawn. 1 Accept ± 2º

6 –2 and 3 2 Award 1 mark for each correct

add 5 sentence. Accept equivalents,
e.g. plus 5, + 5

7 scatter graph 1 Accept any clear indication.

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Question Answer Marks Part Marks Guidance

8(a) Choice Likelihood 2 Award 1 mark for two correct Accept any clear indication.
answers.
likely
A tuna
sandwich is
chosen.
unlikely

A chicken sandwich
is chosen.
certain

even
chanc
e
An egg
sandwich is
chosen.
impossible
8(b) 3 1 Accept equivalent fractions,
decimals or percentage.
40

9 (x =) 140 1

10 A demonstration that the sum of the 1 Do not accept a division

digits of 14 107 is not divisible by 3 calculation.
e.g.
1 + 4 + 1 + [0] + 7 = 13 (and 1 + 3 =
4)
which is not a multiple of 3
11(a) 24 (cm) 1

11(b) A correct explanation, e.g. 1 Accept equivalents, e.g.

They are not the same • They are similar

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but not
size.
congruent.
• The (corresponding)
sides are different
lengths.

Question Answer Marks Part Marks Guidance

12(a) 11 1

12(b) –3 1 Accept any clear indication.

13 Two lines of symmetry (one 2 Award 1 mark for two lines of

vertical and one horizontal). symmetry or rotational
Rotational symmetry order 2 symmetry order 2

14 7.25 hours 1 Accept any clear indication.

15 (8, –8) 1

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Question Answer Marks Part Marks Guidance

16(a)
y
8
1
7

A 1

–8 0 x
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
–1

–2

–3

–4

–5

–6

–7

–8

16(b) Award 1 mark for shape drawn

y
8
2
7 with correct size and orientation
6 but wrong position
5 or for rotation 90° anticlockwise
4
B
around (4, 2).
3

–8 0 x
–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8
–1

–2

–3

–4

–5

–6

–7

–8

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Question Answer Marks Part Marks Guidance

17 42 44 2 Award 1 mark for one correct 2 marks for two correct answers
63 and 66 answer. and no extras.

Maximum 1 mark if more than two

answers given.

18 20 : 3 1

19 0.625 2 Award 1 mark for 5 ÷ 8 Accept .625 for 2

or marks.
answer 0.62 to 0.63

20 A ruled line drawn from (0, 0) to (16, 2 Award 1 mark for two correct plots 1
Accuracy of line  small square
360), i.e. seen or implied, e.g. (0, 0) and (4,
90) plotted or a short correct line at
400 drawn. 2
(0, 0) and (16,
350
360).
300

250

Number 200
of boxes
150

100

50

0
0 2 4 6 8 10 12 14 16
Time (minutes)

21 3.42 (m) 2 Award 1 mark for 1.28 or for 342

(cm)

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or for 4.7 – their (4 × 0.32)
correctly evaluated.

Question Answer Marks Part Marks Guidance

22(a) 180 2 Award 1 mark for correct

method to find 60% of 300
e.g. 0.6 × 300 or 10% of 300 = 30
then 6 × 30

22(b) 20 000 2 Award 1 mark for recognising 14

000
7
is of 20 000
10 14000
7 Or better, e.g. × 10
e.g. 14 000 = T or better. 7
10
23 3 Award 8k 89
5 2 marks for (4) + (2) 2 marks implied by or
7 12 9k
equivalent.
12k 12k 12
or 17
(6 +)
12

56k
+
or 33k 12k

12k

or Note the same denominator

needed for both fractions.
Award 1 mark for attempt to
convert to common denominator
with one

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8k 9k
fraction correct (4) or (2)
or
12k 12k
56k 33k
12k or
12k
24 8 2 Award 1 mark for 3a + 2 – a =
18 or equivalent.

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Question Answer Marks Part Marks Guidance

25 6 2 15 5 Or 15 8
Award 1 mark for ÷ or better, e.g. 
7 28 5
better.
28 8 120
1 mark implied by or
equivalent,
140
e.g. 3
3.5
26 8 2 Award 1 mark for 2 × 20 × 0.2 or Implied by 10.92 or (–)2.92
2 × 40 × 0.1
or
2.73 × 4 or 0.73 × 4 or better. Or better, e.g. (2.73 – 0.73)

27 900 (ml) 3 Award 2 marks for Or 4 360

1 equivalent, e.g. =
360 ÷ (1 – – 35%) or 10 x
equivalent.
4

or

6
Award 1 mark for or Or 4
equivalent, e.g.
equivalent
10
10
1
or 1 – – 35% or equivalent.
4

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