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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
for the guidance of teachers
0444 MATHEMATICS (US)
0444/21
Paper 2 (Extended), maximum raw mark 70
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.
om
.c
MARK SCHEME for the May/June 2012 question paper
s
er
International General Certificate of Secondary Education
Page 2
Mark Scheme: Teachers’ version
IGCSE – May/June 2012
Syllabus
0444
Paper
21
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
186 cao
2
(a)
64
1
(b)
1
27
1
3
3p(5p + 8t) final answer
2
B1 3(5p2 + 8t) or p(15p + 24t)
SC1 for correct answer seen in working
4
a = 11
b = –2
2
M1 for 4x2 + 4x + 1 or 4x2 + 11x – 2 seen in
working
5
(3, 0)
2
M1 (3, k) or (k, 0)
SC1 (2, 2)
6
1.4 × 1010
2
M1 for 14 000 000 000
7
25
2
M1 for
8
7
2
9
9
2
M1 125 = 53
10
x = –2
y=3
3
M1 consistent multiplication and
addition/subtraction
A1 one correct
11
2
3
82
oe
30
55 27
oe
or M1
+
30 30
1
2
11
cao
15
M1 for 0.619 × 300
M1
y = 5 or 4y = 100
8+4+8+9+ y
= 7.2 oe
5
M2
52
oe
30
25 27
oe
(1)
+
30 30
(1)
If M0 scored then SC1 for common denominator
of 30k seen
215
1
(b) (i) (c =) 40 + 35h
1
12 (a)
(ii) 10
1
© University of Cambridge International Examinations 2012
Page 3
13 (a)
(b)
Mark Scheme: Teachers’ version
IGCSE – May/June 2012
−
1
2
2
y=−
1
x+2
2
1ft
14
0.75
3
15 (a)
angle of 67° at B
1
perpendicular bisector of AB
2
(b)
16
Syllabus
0444
Paper
21
M1 for attempt at rise / run
or y = (a)x + 2
M1 y =
k
B1 k = 18
x2
B1 correct line B1 correct arcs
3
M1 clearing denominator and removing brackets
M1 collecting terms in w on one side only
M1 factorising correctly
M1 divide by coefficient of w
(3, 0) (0, 12)
2
(0, 3) and (12, 0) or (0, 12) and (3, 0) score one
mark
1
x
4
2
M1 gradient of
w=
18 (a)
(b)
4 − 3c
www
c −1
4
17
y=
π × 4 × 10
1
192
3
20 (a)
–p + t
1
(b)
p + 2t
2
(c)
2(p + t) or 2p + 2t
19 (a)
(b)
2ft
1
1
or y = x + c or y = kx (+ 0)
4
4
1
× 4 × π × 42 or better
2
B1 for cylinder = π × 2 × 4 × 15 or better
B1 for hemisphere =
M1 for a correct route from P to R or unsimplified
answer
M1 for OR or a correct route or ft p + their (b)
unsimplified provided their (b) is a vector
© University of Cambridge International Examinations 2012
Page 4
Mark Scheme: Teachers’ version
IGCSE – May/June 2012
PT
PR
or
oe
5
5
B1 tan 60 = 3
21
Syllabus
0444
Paper
21
Alternative methods:
Enlargement
B1 right angles triangle with 1, 3 and 60° in
correct place
B1 PR = 5 3 as an enlargement operation
M1 tan 60 =
E1 PR + PT = 10 3
6
B1 PR + PT = 10 3
or similar triangles
B1 right angles triangle with 1,
correct place
x
3
B1 =
5
1
B1 PR + PT = 10 3
240
× 10π or M1 for 240 soi
360
20π
E1
3
M2
22 (a)
1
12
2
M1
(b)
5
18
3
M2 their (a ) +
(c)
5
9
3
M2 2 ×
3
2
×
3 + 2 + 4 (their 9) − 1
2(×1)
4×3
+
their 72 their 72
2(×1)
4×3
or
or M1
their 72
their 72
4
5
×
3 + 2 + 4 (their 9) − 1
4
5
or M1
×
3 + 2 + 4 (their 9) − 1
© University of Cambridge International Examinations 2012
3 and 60° in