# Working

Topics: General Certificate of Secondary Education Pages: 22 (1353 words) Published: January 15, 2013
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
GCE Ordinary Level

MARK SCHEME for the May/June 2012 question paper
for the guidance of teachers

4024 MATHEMATICS (SYLLABUS D)
4024/22

Paper 2, maximum raw mark 100

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 must be read in conjunction with the question papers and the report on the examination.

• Cambridge will not enter into discussions or correspondence in connection with these mark schemes.

Cambridge is publishing the mark schemes for the May/June 2012 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2

Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012

Syllabus
4024

Paper
22

Abbreviations
cao
cso
correct solution only
dep
dependent
ft
isw
ignore subsequent working
oe
or equivalent
SC
Special Case
www
without wrong working
soi
seen or implied
SECTION A
Qu
(a)

pentagon

1

x Y 5 oe
x + y Y 6 oe

1
1

(c)

line passing through (5, 0) and (8, 3)

1

(d)
2

Mark

(b)

1

–1 cao

1

(a)

x=

(b)

y= ±9

(c) (i)

h ( h + 6) = 33.25
Rearranging correctly to give
4h2 + 24h – 133 = 0

3
5

oe

(ii)

h = 3.5 oe and –9.5 oe

(iii)

9.5 cm or their (positive h) + 6

2

Part marks

After 0 + 0, C1 for x ... 5 oe and x + y ... 6 oe
with incorrect (in)equalities for “...”.

M1 for 14x + 2 – 4x – 8 (= 0) or better

1
M1
A1
3

p ± (or + or −) q
r
B1 for p = –24 and r = 8 (or 2 × 4)
B1 for q = 242 – 4 × 4 × (–133), or 2704
or q = 52
Using factors
B2 for (2h – 7)(2h + 19) (= 0)
or B1 for (2h ... 7)(2h ... 19) (= 0)
where ... are not both the correct signs

Using

1 ft

© University of Cambridge International Examinations 2012

Page 3

Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012

(a)

36 minutes cao
5 km/h cao

1

(c)

\$5.2(0)

2

(d)

Horizontal line from (1800, 4) to
(2000, 4)

Paper
22

1

(b)

3

Syllabus
4024

1

M1 for 85% = 4.42 oe

Line from (2000, 4) to (2030, 2.5) or
ft from (their 2000, 4) to
((their 2000) + 30, 2.5)
(e)

1 ft

(a)

279° to 283°

1

Y correctly positioned with two
correct construction arcs

2

(c)

Z on a bearing of 072° from W
Z is due North of X
27 to 29 km

1
1
1

(a) (i)

25, 9

1

(ii)

7.15 to 7.25

1

(iii)

1.1 to 1.3

2

M1 for 7.75 to 7.85 and 6.55 to 6.65 seen

(iv)

5

20 30 or (their 2000) + 30

(b)

4

1 ft

22
oe, or 0.36 to 0.37, or 36 to 37%
60

2

B1 for 22 seen
38
oe
or C1 for
60

5.65 cm

3

M1 for 3.5 × 4 + 4.5 × 15 + 5.5 × 20 +
6.5 × 13 + 7.5 × 5 + 8.5 × 3
i.e. 14 + 67.5 + 110 + 84.5 + 37.5 + 25.5
(= 339)
M1 for ÷ 60 (or 4 + ..... )

35%

2

B1 for 65%, or for 21 seen

4, 8, 10, 14

1

(ii)

1

1

(iii)

3 out of {2, 5, 7, 11, 13}

1

(b)

1

(c)

16

2

(b) (i)

(ii)
6

(a) (i)

M1 for correctly positioned Y with one correct
construction arc, or with no construction arcs
or M1 for Y above WX and two correct
construction arcs

B1 for Venn Diagram and 17 in (G ∪ S)′

© University of Cambridge International Examinations 2012

Page 4

Mark Scheme: Teachers’ version
GCE O LEVEL – May/June 2012
b–a

1
(b + c)
2

1

(iii)

1
1
1
b + c or their (aii) – b
4
2
4

Paper
22

1

(ii)

7