Nov 2005 P1

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS 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. •

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 Dˆ 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