MATHEMATICS (SYLLABUS D) 4024/22 Paper 2 October/November 2016 MARK SCHEME Maximum Mark: 100. Published

Transcription

1 Cambridge International Examinations Cambridge Ordinary Level MATHEMATICS (SYLLABUS D) 404/ Paper October/November 016 MARK SCHEME Maximum Mark: 100 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 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 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 016 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 Cambridge O Level October/November (a) (i).6 1 (ii) 109 B1 for soi or SC1 for oe (b) 70.5 B1 for soi M1 for x = their total amount oe (c) 1000 M1 for 5x x + = 1000 oe and 100 M1 for their 016 price oe (a) (b) ab Final answer M1 for correct transition to multiplication 6 soi 1 5 oe B1 for 5( h k ) (c) (m n)(m+ n) Final ans. 1 (d) ( p )( q ) oe B1 for q( p) or ( p ) seen or M1 if brackets removed and rearranged and extraction of p or or for a correct extraction of a common factor after a sign error. (e) (i) 8 oe 5 B1 for one correct or (ii) 16 cao B1 for either or M1 for (5x 1) = 9 or 8 ( x )( x+ ) = 0 oe ft or 5 Uses e(i) to form simultaneous equations or 1± 9 B ± B 0C x = 5 10

3 Page Mark Scheme Syllabus Paper Cambridge O Level October/November (a).75 1 (b) Correct curve ft ft B1 for 4 correct plots ft (c) ( 0. to 0.5) ft ft M1 for a reasonable tangent at x =.5 (d) 0 cao (.05 to.5) ft ft B1 for either (e) (i) y = 4 x M1 for x ax + b oe + 10x 80 = 0 x x = ( 10) 0 (ii) L drawn on the grid ft 1ft Dependent on at least 1 mark in (e)(i). (iii) (.55) ft 1ft Dependent on at least 1 mark in (e)(i). AD 4 (a) (i).67 M1 = cos 7 oe (ii) 4.57 M for CD = oe or sin 41 M1 for sin 41 CD = oe (b) M1 for 1 5 sinpqr ˆ = 6 oe and A1 for 5.1 or SC1 for supplementary angles from sin ˆ PQR = k. 5 (a) TAB ATB Statement mentions tangent and radius ABT B1 for pairs of equal angles. (b).1 M1 for AC CD = oe soi and AB BT M1 for 7 CD = oe OR 10 B1 for (AB =) 10

4 Page 4 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (b) B1 for entries correct. B1 for entries correct. (c) 4 7 B1 for one correct or x x + seen (d) oe isw B1 for det B = 5 soi or 1 1 soi 7 (a) (i) (ii) (±) x a Final answer M1 for x = a + b oe (b) (i) (PQ =) 17 x (ii) x + 15x 85 (=0) oe shown M1 for (AB =)their(pq) + and M1 for ( their(pq + ) x = 17 or (iii) B1 for 15 4 ( 85) soi and B1 for 15 ± their145 soi and M1 for both real values of p ± r q (iv) 0.8 ft M1 for their(pq) and x + 5 evaluated using x = the positive root from (b)(iii). or for their perimeter in algebraic form

5 Page 5 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (i) Dependent on 4 fig. term calculated using any version of π. M1 for arc length 48 π R soi and 60 M1 for R = oe 48 π (ii) 9 M1 for 48 π R 60 (iii) 0.7 M1 for πr = 1 π R oe 60 (b) (i) 00 M1 for l = oe soi and A1 for (l =) 8.5 (ii).5 B1 for 8 : 5 soi 9 (a) 6 ft 4ft M for 65 = cos ACB soi or M1 for the cosine rule with one error. and A1 for.9 or or 59. and B1 ft for 60 their ACB oe SC for or 7.0 (b) 9. M for AD 110 = sin( ) or(180 ( )) sin 70 soi or oe M1 for or 180 ( ) (c) (i) 1.6 or 1.7 M1 for tan YBC = or tan BYC= (ii) 16.5 M1 for Figs soi and B1 for by oe soi

6 Page 6 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (i) 6b a oe isw 1 (ii) b a oe isw 1ft (iii) : cao NB www 4 M1+ M1 for two of OC = OA + AC CD = CB + BD OD = OB + BD A1 for OC = a + b ft or CD = a + b ft or OD = 5a + 5b (b) (i) (ii) (a) Reflection y = x oe Triangle C with vertices (, ),(, ), (5, 5) B1 for either B1 for two vertices correct or M1 for a correct construction line involving H(, 1) or H(, 0) (b) 1 1 (c) ft

7 Page 7 Mark Scheme Syllabus Paper Cambridge O Level October/November (a) (i) (a) 40 to 41 1 (b) to 7 B1 for 5 ±1 or 7 ±1 (c) 5 to 45 1 (ii) 79 to 80 1 (iii) Paper1 e.g. Paper has median 54 oe Using (i)(a), (i)(c) or (ii) with numerical justification accept reasonable attempts to read the graphs correctly. 1 (b) (i) (ii) 4 oe 1 0 oe 1 (iii) 1 0 oe B1 for or seen (iv) oe B1 for any correct sequence of three coins, 1 or 1 or