CAMBRIDGE INTERNATIONAL EXAMINATIONS

Cambridge International General Certificate of Secondary Education

MARK SCHEME for the October/November 2014 series

0581 MATHEMATICS
0581/31 Paper 2 – Core, maximum raw mark 104

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of
the examination. It shows the basis on which Examiners were instructed to award marks. It does not
indicate the details of the discussions that took place at an Examiners’ meeting before marking began,
which would have considered the acceptability of alternative answers.

Mark schemes should be read in conjunction with the question paper and the Principal Examiner
Report for Teachers.

Cambridge will not enter into discussions about these mark schemes.

Cambridge is publishing the mark schemes for the October/November 2014 series for
most Cambridge IGCSE®, Cambridge International A and AS Level components and some
Cambridge O Level components.

® IGCSE is the registered trademark of Cambridge International Examinations.

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Cambridge IGCSE – October/November 2014 0581 31

Abbreviations
cao correct answer only
dep dependent
FT follow through after error
isw ignore subsequent working
oe or equivalent
SC Special Case
nfww not from wrong working
soi seen or implied

Qu. Answers Mark Part Marks

Alternative method
1 (a) (i) 540 ÷ 9 M1 M1 540 ÷ 1000
their 60 × (9 + 7 + 4 + 5) M1FT M1FT their 0.54 ÷ 9
1500 ÷ 1000 A1 A1 0.06 × (9 + 7 + 4 + 5)

If 0 scored SC1 for 0.54 + 0.42 +

0.24 + 0.3

(ii) 300 2 M1 for 5 ÷ (9 + 7 + 4 + 5) × 1500

or (540/9) × 5 or 60 × 5

(iii) 210 2FT M1 for 70 ÷ 100 × their (a)(ii) oe

(b) (i) 2.25 1

(ii) 52.6[0] 2 B1 for 14 or (7/8) × 16 × 3.4[0]

(iii) 46.1 3FT M2 for

(their (b)(ii) – 36) ÷ 36 × 100
or M1 for their (b)(ii) – 36

M2 for
their (b)(ii) ÷ 36 × 100 – 100
M1 for their (b)(ii) ÷ 36 [× 100]

2 (a) (i) Trapezium 1

(ii) 16 2 M1 for ½(2 + 6) × 4 oe

cm2 1

(b) Rotation B1 Independent marks

90°[anti-clockwise] oe B1

[centre] (–2, –8) B1

(c) (i) Correct reflection in y = 0 2 SC1 for correct reflection in x = 0

(ii) Translation 5 left and 7 up 2 SC1 for one of 5 left or 7 up

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Cambridge IGCSE – October/November 2014 0581 31

(iii) Correct Enlargement 2 SC1 for enlargement,

SF ½, but incorrectly placed.
(d) Obtuse angle marked 1

3 (a) (i) 4 points correctly plotted. 2 B1 for 1 correct

(ii) Correct continuous ruled line of best fit. 1 Dependent on at least 8 points on
graph

(iii) Distance on their line of best fit. 1FT FT their single straight line in part
(ii).
(iv) Negative 1

(v) Faster the time, the longer the distance oe 1

(b) (i) 11.7 or 11.69... NFWW 2 M1 for Attempt at ∑f ÷ 12

5
(ii) 41.7 or 41.66 to 41.67 2 B1 for seen
12
(iii) 2.45 1

4 (a) x + x + 180 = 480 M1

2x = 300 M1

(b) 1060 [cm] 2 M1 for 2 × 480 + 2 × (20 + 30) oe

(c) (i) 16 500 2 M1 for 30 × 150 + 50 × 180 + 20 ×

150 oe

(ii) 2 805 000 1FT FT their (c)(i) × 170

(iii) 44.9 or 44-88 2FT FT their (c)(ii) ÷ 100³ × 16

M1 for their (c)(ii) × 16

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5 (a) 6 003 076 1

(b) (i) –0.375 1

(ii) –2.2 1

(iii) > 1FT FT their answers to (i) and (ii)

(c) 3945, 3955 1, 1 SC1 for both correct but reversed

(d) 1.667 cao 2 B1 for 1 23 or better

(e) (i) 1 1

1
(ii) 1
125

(iii) 24x9
2 B1 for 24xk or kx9

6 (a) (i) 4, 7, 4 2 B1 for 2 correct

(ii) 7 points correctly plotted 3FT B2 for 5 or 6 correct

B1 for 3 or 4 correct
Correct curve through the points 1

(iii) x = 0 1

(iv) 2.7 to 2.9, –2.7 to –2.9 1, 1

(b) (i) Points correctly plotted and a ruled line 2 B1 for 1 correct plot. (even if line is
through points and beyond them. not drawn)

(ii) [y =] –2x + 4 3 B2 for –2x + j

or B1 for kx + 4 k ≠ 0
or [gradient =] rise
run
correct values
(iii) ( –1.2 to –1.4, 6.4 to 6.6) 1

7 (a) 106 to 110 1

(b) (i) Correct bisector of AB constructed with 2 2 B1 for correct bisector

pairs of arcs.

(ii) Correct bisector of angle ABC with arcs 2 B1 for correct bisector without arcs

(iii) T marked at intersection of their bisectors 1FT

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(c) 24.4[km] to 26.0[km] 2FT FT their AT

B1 for their AT correctly measured.

(d) Circle, radius 7.5(±0.2)cm centre T. 2FT FT their intersection

SC1 for circle centre T, incorrect
radius.

(e) No It is outside the circle. oe 1FT FT their circle.

8 (a) (i) Correct diagram with scale 3 B1 scale correct.

B1 for all widths the same
B1 for all 6 heights correct

(ii) 10 to 12 cao 1

19
(iii) or 0.158[3....] or 15.8[3......]% 1
120

(b) Probability must be between 0 and 1 oe 1

9
(c) (i) or 0.45 or 45% 1
20

(ii) 0 oe 1

9 (a) (i) 18 23 28 1, 1, 1 Allow one mark for each addition

of 5 to the previous answer

(ii) Add 5 oe 1

(iii) 5n – 2 oe 2 B1 for 5n + j or kn – 2 k ≠ 0

(iv) 73 1FT FT their (a)(iii) if linear.

(b) (i) 10 14 1, 1 Allow 1 mark for addition of 4 on

their value for 3rd diagram.

(ii) 4n – 2 oe 2 B1 for 4n + j or kn – 2 k ≠ 0

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