4024 MATHEMATICS 4024/02 Paper 2, maximum raw mark 100

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level www.xtremepapers.

1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the October/November 009 question paper for the guidance of teachers 404 MATHEMATICS 404/0 Paper, maximum raw mark 00 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. CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 009 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

2 Page Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November Question Number Mark scheme details and sub marks Part Marks Comments and other sub marks available (a) (y =) B Accept seen isw (b) (p =) B p + 4 = 8 p + 6 oe M (c) (q =) ±6 B (q =) 6 SC or (i)8(q + ) 6q soi M q(q + ) soi M (ii)8(q + ) M q(q + 8) M p ± (d) For numerical r p = and r = 0 q seen or used B (not ± p) or (x + ) () 0 q = 4 or q =.8... (accept.9) soi B Final answers.9 www B.09 www B [0] 705 or oe or.87 if completing 500 the square These marks only, if no working seen After B + B + B0 + B0 both.87.. and.087 or.9 and.09 seen B UCLES 009

3 Page Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) Convincing use of AB AP = CD CR B Implied by AB = DC, AP = RC. Ignore ref to AS and QC (ii) PB = RD and BQ = DS stated B ) ) B = D (may be implied) B (iii) Conclusion: (may be at the start) triangles are congruent oe B ) ) BPQ = DRS B Either angle RPB = PRD or ) ) APR = CRP B A S P B Q D R C Dependent on congruency case complete, (i.e. B), but not necessarily named, www. If extra correct facts, case must be identified. Conclusion RPB QPB = PRD SRD or ) ) ) RPQ = 80 ( BPQ + APR) = ) ) ) 80 ( DRS + CRP) = PRS B Dependent on B and www ) ) After 0, PQ// SR and RPQ = PRS alternate angles SC (b) Parallelogram B [8] UCLES 009

4 Page 4 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November d (a) 5 50 = sin soi M (d =).9 (m) A Here and elsewhere accept answers rounding to the given sig. fig. ans. (b) 0 = sin 5 AB soi M 0 AB = sin5 M (AB =) 8.6 (m) A (c) (i) 5(º) B Allow ±0.05 for genuine long methods. (ii) CM cos 0 = their (c) (i) oe (CM =) 9.66 (m) M A Accept 0cos their (c) (i) if triangle BCM is right angled [8] After 0 in (c), B CM ) = 90º seen SC 4 (a) (i) (a) {, 9, 5 } B (b) { 6, } B (ii) 0 5 oe isw B Accept (8 + their n(b)) 5 Dependent on even numbers in (b) and probability Y (b) (i) (a) 4x B (b) 66 4x or 66 their (a) B Accept q + 4x = 66. Their (a) must be in terms of x. (ii) (a) (x =) cao isw B, 66 4x + x = 7 M (b) 90 B [8] Accept (77 + their x ) UCLES 009

5 Page 5 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) B, one error or seen 6 0 or 6 B (ii) Final ans (9 7) B Condone omission of brackets., either correct or final ans a col. vector B SC (b) (i) ± 0 isw B, ½ or deta = ± 0 soi or B (ii) h = 8, k = www B [8] h 0, = 0 k 0 or their (b) (i) seen M 6 (a) 9 : 50 isw B Accept 50 : 9, 9 50 Condone g (b) (i) 9.45 (g) B (ii) (a) 0. (%) B (b) 0.9 (%) B Figs their (b) (ii) (a) M fig 7 independent M (iii).05 (g) isw B.05 seen B (c) 000 B [0], division by 8. M UCLES 009

6 Page 6 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) 9.8 (m) B h = π 0.9 π0.9²h B Their Volume (must be a volume) = figs 5 M 0 oe used correctly at any stage M (ii) (a) 0.45 cos E OD ) = oe seen B 0.9 e.g. sinode = not just ½. NB E O ) D = 60 is AG (b) or 0.498m B π 0.9 (= 0.848) soi M 60 sin 0 oe (= 0.5) M (c) 4880 or 4890 B Figs their (a) (i) their (ii) (b) their(ii)(b) or Figs 5 π 0.9 M (b) (h = ) 5.00 m B 0.00 SC 0 π0.75 = π0.75 h soi M [] UCLES 009

7 Page 7 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) B (ii) All 8 points plotted ft soi. P ( ft at intervals of 0.5) After P0, at least 5 correct plots P Smooth curve through all plotted points C Dependent on P. Straight line graphs or ruled sections will be C0 (iii) 0. to 0.5,. to.4.8 to.95 B, correct value B or clear attempt to read their graph at y = 4 M (b) (i) 5 x and 4 x B (ii) x their 5 x their 4 x M 4x 8x + 0x correctly derived A Accept such as 5 x x Their expressions must be in x AG Expect some intermediate working. Attempts at working back, factorising 4x 8x + 0x must be accurate and convincing. (iii).8 to.95 B Or their value in (a) (iii) > (iv) (a) Their max between 0 and B Accept 6 (b) 0.7 to 0.8 cao B [] UCLES 009

8 Page 8 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) Accurate drawing B Right angles at A and E R C correctly placed in relation to B and D e.g. BC = and DC =, or angle BCD, correct C (ii) 5 ± B Independent. (b) (i) DE : ST :.5 oe B (ii) ( QS² =) ( 7)² + 4² used www B (iii) (cosqrs =) ( their )/ ( 0.5 7) M 5 A (iv) sin R QS ) sin their(iii) = 7 their oe M ( R Q ) S =) 5. to 5.5( ) A [] Accept a correct literal statement that includes DE and ST AG Condone long methods reaching such as 0.7 and rounding to www, ( 7) and 4 seen B soi by After M0 their = 0.5² + 7² ± 0.5 7cos Q R ) S (soi by 0.400) M 65.0 A UCLES 009

9 Page 9 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) () () (80) B Table not copied so values not seen B0 (b) All 8 points plotted ft P After P0, at least 5 correct plots ft P Smooth ogive curve through all plotted points C Dependent on P. Straight line graphs or ruled sections will be C0 (c) (i) 9 98 B Not 00. (ii) 4 48 B in (c), reading their cumulative curve at 40 and 8 M (d) Curve through the points (50,), (50,80), (50,40), (75,60), (00,0) P After P0, correct points plotted P correct points plotted P (e) (i) 7 or 7 B In (e) (i) and (ii), accept non integer values rounding to these given. (ii) 47, 48 or 49 B in (e), M available for reading both graphs at 60 (f) B with some support B Support such as the probabilities or 80 [] The reference must imply a direct comparison of the brands at 50. UCLES 009

10 Page 0 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL October/November (a) (i) 50 (m) B (ii) 5 (m/s) cao B (their (a) (i) + 0 5) 0 M (iii) (t =) (s) B t = 5 0 oe M (iv) t = their (a) (i) + 0( t 5) M ( t = ) 6.5 (s) cao A After M0,A0, a correct area used SC (b) (i) 50 (m) and 50 (m) B Accept their d = their (a) (i) and their d = their (a) (i) + 00 or 0 their (a) (i) (ii) speed B Accept 0 m/s. Not increasing speed (iii) 0 (m/s) cao B (c) 5(.0) (s) B [] 5.0 allows for the use of decimals such as.. Accept values rounding to 5.0. Allow recovery of 5 after decimals, (±) soi e.g. by 5 B 9 UCLES 009

0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

0607 CAMBRIDGE INTERNATIONAL MATHEMATICS UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL