MARK SCHEME for the May/June 2009 question paper for the guidance of teachers MATHEMATICS 4024/02 Paper 2, maximum raw mark 100

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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the May/June 009 question paper for the guidance of teachers 404 MATHEMATICS 404/0 Paper, maimum raw mark 00 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the eamination. It shows the basis on which Eaminers were instructed to award marks. It does not indicate the details of the discussions that took place at an Eaminers 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 eamination. CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the May/June 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 May/June (a) 4a + 9 6a final answer 5b(b ) final answer Condone missing final bracket After give sc for both correct forms seen. (c) (i) (6, ) Condone missing brackets ( ± 4) + ( ± 0) 0.7 to 0.8 A Accept 9 (d) p ± ( or + or ) q For numerical r p = and r = 6 (or 3) q = 05 or q = 4.3 to (a) (i) Figs 378/the product of at least of 0, 4, 7 and 60 4 [9] Completing the square 05 for ; for oe 6 36 dep. on correct formula s.o.i or used If final B0 + B0 then sc for 0.5 to 0.6 AND 4. to 4.; or for any two answers given to d.p. $3.5 A Accept $3. $3.3 $ $ million; % cao 945 or A Accept (iii) :5 or m =, n = 5 B sc for partial simplification seen. 6:35, 54:35, 4:05, 8:45, 4:35, 6:5; or for, or :.5, 5 or 5: or m:5m 480 = cao A [8] sc for 9.6(euros) or ($)800 seen. UCLES 009

3 Page 3 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL May/June (a) (i) tan = 4 70 to 70.0 A For any complete methods allow appropriate M and A marks. sc for 9.9 to 0 (a) 4 sin 8 = PX PX or (sin 90) = 8.5 to d =, or PX cos 8, or tan 8 or PX to 7.6 d (= 3.4 to 3.5) 4 sin 8 4sin 6 sin 8 A A 3 GRADIAN ANSWERS (i) sc for. or. (a) (leading to.5) or 7.77 from Sine Rule (leading to 3.3) r 3 96 = or π.84 to.84 4 (a) (i) (a) 3 (lines of symmetry) order 3 A [9] (a) (c) Use of (9 ) 80 etc y = 60 oe y = 40 oe isw Sensible attempt at solving for or y = 36 A AG. Allow if 40 calculated, but not if quoted. The second B mark implies the first. (i) LFEB = 4 LBEA = 4 (iii) LAGD = 63 [0] 5 (a) (i) (a), 0.0 cao 50 (8 + 4) 00 oe 00 m A (c) 5 m/s Accept negatives 50u = u = (= 975) oe A 4 + (their 5) UCLES 009

4 Page 4 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL May/June (i) 95 m 4.5 or (5.4 to 5.5) seen Distance Time 7.64 to 7.65 A 3 90 N.B. = 7.6 scores the 5 only [0] 6 (a) p = q = 30 r = 60 s = 6 all four B sc for or 3 correct = n + oe y = n(n + ) oe z = n(n + ) oe y 3 In, accept any unsimplified form but, once, if not given eplicitly (c) 0 [6] 7 (a) (i) 5 oe fraction Not 40%; 0.4 (a) h = 5 ( ) cm A sc for 3300 or for 9300 cm (i) 0 π to 0 A 0 π 9 (= ) sin40 (= 6.03 ) 8 to 8 A 4 POSSIBLE GRAD ANSWERS 88 to 88.3 from 9 sin40 (= 3.7 ); 77 to 78 from 8 sin70 sin0 (=.3 ) (iii) 4.9 from cos70; 6. from sin0 sc for 4.08 or for If A0, then sc for 55 to 56 seen or for 5.9 to 6. seen (iii) d = 9 9cos 70 = 5.9 to 5.93 A [] } }sc for 3.07 to 3.08 seen UCLES 009

5 Page 5 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL May/June (a) (i) PQ = ( + ) m If AB used instead of, once BC = 68 (iii) QR = 68 + BC + all 3 (condone 0 + for ) B sc for or correct 68 Area = ( + ) ( + ) 68 or PQ QR 68 as an epression in 336 correct working to + + A or ( + ) + 0( + ) + 68 oe Answer given (c) p = 58 to 58 3 (d) Correct scales 7 correct plots (ignore = 9) within mm S P Condone reversed aes, if labelled Accept if curve goes through correct points Smooth curve C 3 Not grossly thick; no straight lines Ignore curve for < 3 and > 8 (e) Clear attempt to draw tangent at (4, 50) gradient = 6 to T G Accept integer fractions (f) (i) 43 Y answer < to 7.6 [] 9 (a) (i) AD 7 = sin 38 sin4 sin 38 AD = 7 dep. sin4.4 to.5 A 3 7 = ± () 9 0 cos } or cos = ± [( )/() 9 0] } cos C = = ( 0.6) to 7 A A GRADIAN ANSWERS (i) 9.7 to to 4 UCLES 009

6 Page 6 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL May/June (i) (a) (c) (d) OQ = p + q RS = p q (a) q OS = p + q (a) OT = 4p In (i),, once, for unsimplified answers (O, P and T are) collinear oe OT = 4OP oe 0 (a) Correct scales and aes Correct bases (width + position) Heights (), 0, 8, 7, 4, S H 3 [] Marks in are dep on a correct (i) (d) Condone reversed aes if clearly labelled 7 < t Y 9 (c) (4 ) + (0 3.5) + (8 4.5) + (4 6) + (8 8) + (6 0.5) (= 90) A 3 8, 35, 36, 84, 64, 63 Condone up to 3 slips Indep of first M (d) (i) 0 Condone 0, none, nil oe 0.56 (e) (i) In (e),, once, for any answer (= ) (0.308 to 0.309) not in lowest terms, or in decimal form (a) (i) 88 4 (= ) (0.50 to 0.503) B [] sc for (0.5 to 0.5) 75 3 B sc for 3 correct elements AB = 0 + or BA = or B 0 3 = oe 3 = 3 dep. 0 e.g. 3, (0.33 or better) 3 UCLES 009

7 Page 7 Mark Scheme: Teachers version Syllabus Paper GCE O LEVEL May/June (i) (a) SF = Centre is (, ) B for each coord. sc for Shear, -ais inv., SF = Mention of a nd transformation loses both marks (iii) (a) k k + 4 = 0 k = 4 ET(L) = E((8, )) = ( 3, ) MA B [] sc for (.5, ) UCLES 009

MARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75

CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9709 MATHEMATICS 9709/11 Paper 1, maximum raw mark 75 This mark