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CAMBRIDGE INTERNATIONAL EXAMINATIONS
GCE Ordinary Level

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MARK SCHEME for the October/November 2012 series

4024 MATHEMATICS (SYLLABUS D)
4024/12 Paper 1, maximum raw mark 80

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 2012 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

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Mark Scheme GCE O LEVEL – October/November 2012

Syllabus 4024

Paper 12

Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working soi seen or implied Qu. 1 (a) 10.6 (b) 2 (a) (b) 4 cao 3 (a) 34 (b) 10 4 (a) 3 oe (b) oe 5 6 cao Answers Mark 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1
© Cambridge International Examinations 2012

Part Marks

–1, –

,–

, 0,

C1 for 4 correct when one is covered or C1 for reversed answer

(a) 3 (h) (b) 35 or ft

7

(a) 8k + 1 (b) 2x2 + 5x – 12

8

(a) 255° (b) (0)7 h 53 min

9

(a) 6 (b) 11

10

(a) 22 × 32 × 5 oe (b) 11 www

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Mark Scheme GCE O LEVEL – October/November 2012 1 1 2 1 1 1 1 1 1 2 1
A B 5 A C 6 B A 5 B C 7 C A 6 C B 7

Syllabus 4024

Paper 12

11

(a) 6 (b)

12 13

18 (a) 9.45 (b) 1.95 or their (a) – 7.5

B1 for “k” = 2 or B1 for

oe

14

(a) Both p = 6 and q = 4 (b) 33 or f.t. 29 + their q (provided q has a value) (c) 34

15

(a) 4p (4 + p) (b) (x + 2a)(y + 3a)

B1 for any partial factorisation

16

(a) 0 (b)

1

(c) or f.t from table provided (number of 7s) > 0 17 (a) 0.0406 (b) 6.8(00..) × 10– 4 (c) 4 18 (a) 3 (b) 13 (c) 4 19 (a) oe oe

1

1 1 1 1 1 1 2

C1 for 2 or 3 correct elements

2 (b) or oe B1 for det M = 4 or for or B1 for used or seen
© Cambridge International Examinations 2012

× (2 × 2 matrix)

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Mark Scheme GCE O LEVEL – October/November 2012 1 1 1 1 2 1 1 dep. 1

Syllabus 4024

Paper 12

20

(a) (i) 4 (ii) 2 (b) Both a = 1 and b = 2. c=6

21

(a) (b) (one way) stretch Parallel to y-axis/x-axis invariant and (stretch/scale) factor 1 . 2

C1 for 4 or 5 correct elements in a 2 × 3 derived matrix

22

(a) (11, 3)

(b) parallelogram (c) 27

1 2 M1 for their (BC) × their 9 or M1 for 9 × (their BC + 2) – 2 ×

1 2

×9×2

23

(a) 124 (b) 118 (c) 31 (d) 38

1 1 1 1 2

24

(a) 18

M1 for or M1 for (n – 2) × 180 = 160n oe

(b) (i) 10 (ii) 20 25 (a) or any equiv. 1

(b) (i) correct method u=2 (ii) continuous graph from (0, 0) to (10, 40),without any horizontal or vertical lines. Curve, concave upwards

M1 A1 1 1 ind.

e.g. 40 =

× (u + 3u) × 10, × 10 × 2u

or 40 = 10u +

© Cambridge International Examinations 2012

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Mark Scheme GCE O LEVEL – October/November 2012

Syllabus 4024

Paper 12

26

(a) 2011 (b) 36 (c) (i) 9x – 9y, or 9y – 9x , or any equiv. (ii) “123 is not a multiple of 9” oe

2 1 1 1 1 1 1 1 1

B1 for (n = ) 223 seen

27

(a) 126° to 128° inclusive (b) acceptable quadrilateral ABCD (c) (i) acceptable circular arc, centre C (ii) acceptable bisector of angle ABC (d) DP = 2 to 2.5cm with correct P

dep. on an acceptable D and both (c) marks

© Cambridge International Examinations 2012