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GCE O Level
MARK SCHEME for the November 2005 question paper
4024 MATHEMATICS
4024/01
Paper 1
maximum raw mark 80
This mark scheme is published as an aid to teachers and students, to indicate the requirements of the
examination. It shows the basis on which Examiners were initially instructed to award marks. It does
not indicate the details of the discussions that took place at an Examiners’ meeting before marking
began. Any substantial changes to the mark scheme that arose from these discussions will be
recorded in the published Report on the Examination.
All Examiners are instructed that alternative correct answers and unexpected approaches in
candidates’ scripts must be given marks that fairly reflect the relevant knowledge and skills
demonstrated.
Mark schemes must be read in conjunction with the question papers and the Report on the
Examination.
•
s
er
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
CIE will not enter into discussion or correspondence in connection with these mark schemes.
CIE is publishing the mark schemes for the November 2005 question papers for most IGCSE and
GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level
syllabuses.
Page 1
1
2
(a)
(b)
(a)
(b)
3
4
5
6
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
7
8
9
10
(a)
(b)
(c)
(a)
(b)
(c)
(a)
(b)
Mark Scheme
GCE O LEVEL – NOVEMBER 2005
2.44
(0).021
9
20
2
c.a.o.
15
3
6
or
only
8
16
30
M, S, L
20
1
c.a.o.
4
2.4 x 106 c.a.o.
190
1
(n + 1)(n + 2) o.e. (seen)
2
90000
50 x 60
30
73
31 f.t. their 73 − 42
318
Fig. 6
Fig. 4
Fig. 2
75
360
or (2n − 4 ) 90 = 165n
180 − 165
24
11
(a)
(b)
(c)
5 x (x − 2 )
4
0 or −2
12
(a)
AĈB = C D̂ A and BAˆ C = AĈD
(b)
⇒ ∆ s similar
7
4 6
= or
AD 6 9
10½
Syllabus
4024
Paper
1
1
1
1
1
1
1
1
1
1
1
1
1* Accept (n + 1+ 1)
[12]
M1
A1
M1
A1
2*
1
f.t. 1
1
1
1
1
1
1
o.e.
2*
[11]
1
1
1
1 Any irrelevant or wrong
information = 0
1
M1
A1
2*
© University of Cambridge International Examinations 2005
Page 2
13
14
Mark Scheme
GCE O LEVEL – NOVEMBER 2005
(b)
(i)
(ii)
(a)
1
x o.e.
2
−4½ ≤ x < −2
−4 and −3
(a)
(b)
16
17
(a)
(b)
(c)
(d)
(a)
(b)
18
(a)
(b)
19
20
(a)
(b)
(c)
(d)
(a)
(b)
(c)
Paper
1
1
(a)
(b)
15
Syllabus
4024
Squares
1
1 Any clear indication of a set in R
∩ Q’
1
y≥
M1
A1
1
 0


2
−1
 0 − 3


(1− 1)
−17
5
1
(x + 5 )
3
3 f.t.
Idea of 100 ± 2.5 or 75 ± 2.5
340
22.5 or 21.5
2.5 or 3.5
9
x =0
y = −2
(i)
13200
(ii) 500
219 → 221 incl.
13
All 8 points plotted correctly
Smooth curve
A – any comparison using curves
13 − 14
2
or 0.66 − 0.67
3
(i)
500
(ii) 700 f.t. their 500 + 200
Accept as separate statements
2*
[12]
2 SC1 for 4 or 5 elements correct
2 SC1 for a (1 x 2) matrix
1
1
1 Allow y etc.
f.t. 1
M1
i.e. any one of 97.5, 102.5, 72.5
or 77.5 seen
A1
M1
2*
A1
2*
1
1
1
1
[16]
1
1
P1
C1
2
1
1
1
1
f.t. 1
(d)
straight line
L1
curve
C1
A
B
from (30,300) to (40, their 500 f.t.)
2 from (40, their 500 f.t.) to (60,
[11] their 700)
© University of Cambridge International Examinations 2005
Page 3
4024
21
22
Mark Scheme
GCE O LEVEL – NOVEMBER 2005
(a)
(b)
(c)
(d)
(4, 4)
(2½, 2)
y=4
y = ½x − ½
(e)
(a)
(b)
20
(6, 2)
(i)
(− 2, 0)
(ii) 90o AC
(0, −2), (−4, −2) (−6, −6)
(c)
23
(d)
 1
0
−
 2

1
 0 −
2

(a)
(i)
(ii)
Syllabus
4024
B1 + B1






C
(b)
5
1
1
1
2* Mark at earliest ax + by + c = 0
stage
1
1
1
1
2 SC1 for 2 points plotted correctly
or 3 points stated
1
[12]
1
1
1:2 000 000
235 − 237
Constructions
I L bisect
II I bisect
III arc
P
A
I within 2o
II within 2o 2 mm
III within 2 mm
C1
M1
B1
B
The possible positions clearly indicated
P1
Paper
1
4
[6]
© University of Cambridge International Examinations 2005