UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS
GCE Ordinary Level
MARK SCHEME for the October/November 2006 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 instructed to award marks. It does not
indicate the details of the discussions that took place at an Examiners’ meeting before marking began.
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.
The grade thresholds for various grades are published in the report on the examination for most
IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses.
•
CIE will not enter into discussions or correspondence in connection with these mark schemes.
CIE is publishing the mark schemes for the October/November 2006 question papers for most IGCSE,
GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level
syllabuses.
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Page 2
1
7
(b)
(a)
(b)
(a)
8
(b)
(c)
(a)
1
8
o.e.
15
1.77(0….)
147
5x6
1
1 or −2
2
80
1
62
2
7
7
, 0.7,
0.72,
9
11
400
34
−9
13
o.e.
18
70 c.a.o.
8 c.a.o.
22 x 3 3
(b)
2 3 x 33 x 5
(c)
(a)
(b)
75 or 3 x 52
−1 (Yx <) 2
−1, 0, 1 √
2
3
4
5
6
9
10
11
(a)
(b)
Mark Scheme
GCE O LEVEL - OCT/NOV 2006
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(a)
(b)
(a)
(b)
12
13
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1*
B1 + B1
NB: 0 must be included
5:2 c.a.o
2.1 x 108
4
o.e.
15
 2 1
 −  C = 1600 o.e.
5 3
($)24 000
(a)
3a − 2c o.e.
(b)
Establishing k OP = l BA
(c)
3
o.e.
2
Correct, ruled, line (and no others)
correct method to produce 900 (7 sided)
or
correct method to produce 720 (6 sided)
or
correct method to produce 540 (5 sided)
or
360 − their 54
or 6x = 360 – 54
6
(ext < method)
129
(a)
(b)
Syllabus
4024
1
2
1√
1
2
1
M1
A1
Paper
01
Accept 0.53 or better
Accept
3
, 1.5
2
125
Accept 62.5
2
Accept any equivalents
Not
Accept –34, ±34
6.5
9
Accept –70, ±70, 7 x 10, 10 x 7
Accept –8, ±8 Not 8 x 1
Accept 2 x 2 etc. condone x1n
throughout
Answer 1080 look back. Give mark if
correct prime factors seen
Not
Reversed answers – SC1
Given −p Y x < q in (a), allow
√ if p and q are positive integers
Inclusion of units ⇒ no marks
SC1 for figs. 21; Condone –2.1 x 108
4x
Allow
15
1
s.o.i.
SC1 for
15
2*
1
1*
Must be numerical
1
Accept 1.5, 3:2
1
Accept if line dotted. 3 mm tolerance
M1
A1
2*
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Page 3
14
(a)
(b)
15
16
(a)
(b)
(c)
(a)
(b)
17
(a)
18
(b)
(a)
(b)
Mark Scheme
GCE O LEVEL - OCT/NOV 2006
16
27
2 1 1 4
x + x
3 9 3 9
6
27
9
3π
π
60o or
3
Syllabus
4024
Paper
01
1
M1
A1
2*
1
Both correct 3
*
1
One correct 2
(i)
2
(ii)
5√ 3 their (a) −1
 1 
 − ,0  and (5,0 )
 2 
(i)
2
(ii)
1
4
2 pairs of angles stated equal
Reasons + conclusion (dep on 1st B1)
1
1
1
B1
B1
(i)
(ii)
M1
12
x
2
= o.e.
14 − x 3
28
o.e.
BX=
5
In (b) condone 3, k = 3, 3kπ.
If no marks:- M1 for
circum = 18π or 2π x their (a) √
Must be numerical
Condone 2p
Condone 5q or 5x
1
1
2
Accept (y α ) x2 or (y =) kx2
Accept (y α ) x1 or (y =) kx1
2
Lost for wrong or irrelevant
statements
1
A1
2*
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Page 4
14
15
(a)
(b)
(a)
(b)
16
(a)
(b)
17
18
(a)
(b)
Mark Scheme
GCE O LEVEL - OCT/NOV 2006
1550 (Y distance <) 1650
5.5 (Y speed <) 6.5
300 sec o.e.
 − 4 2
 o.e.

 − 6 0
B1
B1
1  2 3
 o.e.

B1 + B1
2  4 5 
(i)
4p + 7 c.a.o
(ii)
−1√ solution of (their 4p + 7) = 3
2
(a−1) −1
M1
a2 − 2a or a(a – 2)
A1
y = 2x + 3 o.e.
(i)
Lines x = 1 and y = 3 drawn
B1
Lines x + y = 2 drawn
B1
(ii)
Correct region identified
dept. on all 3 lines correct condoning
minor inacc.
–
Syllabus
4024
2
1
2
2*
Paper
01
SC1 for any 2 seen
SC1 for 3 correct elements
condone intrusive letters
seen and isw
1
1
2*
1
2
1
Part of region below the x axis should
be indicated
1
(a)
(b)
P ∩ Q/ o.e.
(c)
25 − x + x + 20 − x + 4 (= 36)
13
1
M1
A1
2*
(P ′ ∪ Q )′
Diag. with x, 25 − x, 20 – x, 4 all
marked earns the M1
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Page 5
19
20
(a)
(b)
(c)
(d)
(a)
(b)
(c)
21
(a)
Mark Scheme
GCE O LEVEL - OCT/NOV 2006
20
110
20
50 or 180 – [their (y + z)] √
3
c.a.o
3:5 c.a.o. or
5
9:25 or (their (a))2
22
A1
8
95
(a)
Fully correct graph or √ to their 95
St. line (+ve gradient) from t = 0-6
correct curvature
from t = 6-8
horiz line (not on axis) from t = 8-12
correct curvature
from t = 12-20
(i)
15
(a)
(b)
2*
1*
1
1
Graph from (0,0) to (20, 95) √
(10,9)
Accept fraction: condone inclusion of
units
Accept 9π: 25π
3
Allow 1.88 but not 1.9; Not
7.5
4
Graph must be continuous and non
decending
2
If graph not fully correct:SC1 for 2 or 3 parts correct
1
Not –15
[but allow √ mark in (c) for –30]
1
1
30 √ 2 x their 15
6
o.e.
10
k 2 − 111
5
− or
10k
k
Arc of circle, centre L, radius 2 cm
St lines, parallel to AB and BC, 2 cm
distance
Fully correct locus
( )
o
1
1
1
B1
+B1 dep
B1 + B1
2
2
(c)
25 (and) 48 or 29 and 48 ± 2
(a)
(b)
∆ drawn (4,4), (8,4) and (10,2)
Rotation
B1
90 o CW, centre (0,0)
B1
2
∆ drawn (−2, 2), (−4, 2), (−5, 1)
B2
2*
(c)
Paper
01
5
NB.   is M1
3
M1
(b)
(b)
24
1
3
Idea of  
5
27:98 c.a.o
(i)
15 o.e. seen
(ii)
(iii)
(iv)
23
1
1
1
1
1
3
(ii)
Syllabus
4024
Accept −
5
61
Allow within 2 mm
Correct locus range 23 → 50 incl.
If sharp loci range 27 → 50 incl.
SC1 if one angle in range or for
reversed angles
√ from their loci (arc or point)
dept. on relevant locus
1
Not turn: extra transf. seen loses both
marks
0
Condone –90°; Allow   or 0.
0
SC1 for 2 points plotted or for 3 pts
stated
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