MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 October/November 2016 MARK SCHEME Maximum Mark: 100. Published

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1 Cambridge International Examinations Cambridge Ordinary Level MATHEMATICS (SYLLABUS D) 404/ Paper October/November 06 MARK SCHEME Maximum Mark: 00 Published 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 ds 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 should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 06 series for most Cambridge IGCSE, Cambridge International A and AS Level components and some Cambridge O Level components. IGCSE is the registered trademark of Cambridge International Examinations. This document consists of 7 printed pages. [Turn over

2 Page Mark Scheme Syllabus Paper (a) (i) 33 (ii) 0 (iii) 900 M for (b) or 0 pm (c) 6600 final answer M for (d) 8.93 B for 00.5 or.5 used (a).7 or.7[ ] (b) 3p( 3p q ) final answer (c) 9a + 6ab + b final answer (d) 6t + (t+ )(3t + ) answer 6t + or 6t + 5t+ final 3 M for 4( 3t + ) 3( t + ) soi B for 6t + seen as numerator or (t + )(3t + ) seen as denominator (e) 3, 4, 5 M for n < 9 4 Or SC for answer 3, 4, 5, 6 or answer, 3, 4, 5 (f) 50 3 B for x + (x ) + (x 4) = and B for x = 37 or M correct evaluation of amount for Chuku using their expression and their x 3 (a) (i) [ PBQ = ] 80 a or (90 a) (ii) [ APD = ] 90 a (iii) [ DAP = ] a (iv) [ ADP = ] 90 a (b) (i) 3.3 (ii) 30.4[9..] M for 4.7 sin 54

3 Page 3 Mark Scheme Syllabus Paper 4 (a) 4 or 43 or 4.4 to 4.6 M for 4 (9 0.8) π Or SC for answer to (b) 440 or to B for 8. used 3 B for 3 π r used M for Bowl: π 9 π ( 9 0.8) M for Cylinder: π (a) 3.76 to 3.77 M for 0 π (b) 9.99 to 0.0 3ft FT their (a) [ ] M for [OB = ].8 tan 60 [...] or M for tan 60 =.8 (c) (i) Full calculation, including calculation for OC = 3.6 and radius = TC + OC AG M for.8 cos 60 = OC or OC =.8 + their OB (ii).8 ft FT 5.4 their OB

4 Page 4 Mark Scheme Syllabus Paper 6 (a) [DT = ]0.8 or 0.86 to 0.8 M for DT = (b) 39 or 39. to B for BT = 0 M for sum of areas of four triangles seen, with at least 3 of the following correct: 8 6, 9 6, 8 their DT, 9 their BT (c) 504 M for or (d) 50.7 final answer 3 M for finding an acute angle in triangle THG. e.g. tan [ ] = 9 or tan [ ] = 9 A for 50.7[...] or 39.8 to (a) 83 (b) 055 (c) [AB = ] 5.4 or 5.36[ ] 3 B for ABC = 74 AB 9 M for = sin 5 sin ABC (d) [DC = ] 0.08 to 0. 3 M for [DC =] cos 48 or M for cosine formula with one error (e) Correct working leading to 4 minutes or hour 54 minutes 4 M for AX = 9 cos 48 or for CX = 9 sin 48 M for DX = 7 their AX Or for DX = their DC their CX M for Time = 6 their DX 7

5 Page 5 Mark Scheme Syllabus Paper 8 (a) 0. or 0.[ ] (b) Correct axes B Correct shape curve through 9 correct points B Bft for at least 7 correct points plotted (c) Clear, correct, tangent drawn. to.5 M A (d) (i) Ruled line from ( 0.4, 0) to (, 3.6) (ii) y =.5x or 3 3 y = x + B for m =.5 5 or for c = 0.6 or for correct equation in a different form (iii) 0 and 3. to 3. ft FT intersections of their ruled line with their curve (iv) A =.4 to.6 B = 9 (a) 4 (b) 7 3 B for or for answer 7 or B for 7 8 or and their 494 their 400 M for 00 their 400 (c) (i) (30 y) ( y) isw B for (30 y) or (40 + 4y) soi 00 (ii) Forms equation (30 y) ( y ) = then correct working leading to y + 5y 50 = 0 AG B FT for y + 0y 4y = 4000 or better FT equating their product from (ii) with 40, eliminating fraction and expanding brackets (iii) y = 0, 5 3 B for ( y + 0 )( y 5 ) or B for ( y + a )( y + b ) where ab = 50 or a + b = 5 OR B for 5 soi 5 ± their5 and B for

6 Page 6 Mark Scheme Syllabus Paper (iv) 60 cao 0 (a) (i) Correct histogram with linear scale on frequency density axis 3 B for all 5 heights correct with axis scaled OR B for at least 3 correct frequency densities soi and B for all 5 bars correct widths (ii) 39.4[4 ] 3 B for use of correct midpoints Σfx M for 35 (b) (i) (ii) M for Or SC for answer 4 95 (iii) cao (iv) 9 90 M for k k n n where n > k > (a) (i) 3 M for ( 5) + (ii) (a) [ BD = ] BA + AD = + = k k AG Or [ BD = ] AD AB = = k k (b) 8.5 M for using 6 = k 5 (c) 4.5 or FT their (i) their k (b) (i) Reflection x = 0 or y-axis

7 Page 7 Mark Scheme Syllabus Paper (ii) (a) ( 3½, ), ( 7, ), ( 8, ) B for or correct pairs of coordinates (b) B for used 0 or M for a b = c d