Published. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Transcription

1 Cambridge International Examinations Cambridge Ordinary Level MATHEMATICS (SYLLABUS D) 404/ Paper May/June 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 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 May/June 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 6 printed pages. UCLES 06 [Turn over

2 Page Mark Scheme Syllabus Paper Cambridge O Level May/June (a) 4 47 or or cao (b) $65 ( not from rounded ) M for.05x = 68.5 soi (c) [M for oe] or M for their 65 [= 6 500] and M their [= ] (a) (i) 5 6 (ii) or 4.5 or 0 or 5 M for ((±4) + (±) ) (b) (i) (a) b a or (b a) or equivalent two term answers final answer (b) b a or ( b a) or b 6a or equivalent two term answers final answer (ii) : cao Dependent on correct (b)(i)(a) and (b)(i)(b) (a) (i).64 or 6 5 M for (ii) (iii) 0 (b) appropriate reason (c) 0 cao M for 5 4 oe 5 4 (d) Correct bar chart with axes labelled B if only one error (eg incorrect height, scales missing / incorrect, inconsistent bar widths, or 4 correct bars) (e) (a) (i) Correct triangle with arcs shown B for correct triangle with no arcs or triangle with one side correct length with arcs or triangle with BC = 7 and AC = with arcs (reflection) (ii) 04 to 08 Cambridge International Examinations 06

3 Page Mark Scheme Syllabus Paper Cambridge O Level May/June (b) 50 o M for 80 (60 ) or (80 ( )) (c) (i) 0 o (ii) 65 o ft ft their p provided p < 0 and p 90 B for 0, 5 or 75 seen (d) 7 4 x final answer EITHER B for (6 ) x x+ x oe or B for PQ = x OR B for x (area of small trapezium) B for their x oe OR If AB = x used 7 7 SC for x or SC for (a) 4 x (y x ) final answer (b) x = 6.5 or or 6 M for 4x x 0= or better (c) y >.6 or y > 5 M for 5y < 0 7 oe or better Or SC for.6 or.6 oe seen or y > 5 final answer (d) (i) EITHER Width = 8 4 x oe OR Width = 0 x oe M 8 4x x = 0 oe 0 4x + = 8 oe x A isw (ii).85 and 0.65 cao B for.850 to.85 and to or one correct answer or.9 and 0.6 Or if in form p ± q or p + q or r r p q r B for p = 9 and r = 4 or q = 4 Cambridge International Examinations 06

4 Page 4 Mark Scheme Syllabus Paper Cambridge O Level May/June (iii) 6.5 to 6.45 or 6.45 to 6.5 oe 6 (a) (i) (a) 0 (b) 9 (c),5,7, (ii) 4 oe isw ft ft from their (a)(i)(c) (b) (i) 8 0 final answer B for correct elements (ii) 4 oe isw B for k or a 4 c b d SECTION B 7 (a) 58, 88, 04,, 8 (b) Correct cumulative frequency graph B for at least 6 correct plots Tolerance small square for plots B for at least correct plots If 0 SC for consistent horizontal translation to the left of all points or SC for consistent horizontal translation to the left of all points with one slip (c) (i) 0 < their answer ft (ii) 5 their answer 55 ft (d) Correct graph through (0, 6) (5, 0) (4, 60) (44, 90) (60, 0) B for at least 4 correct points plotted B for at least correct points plotted (e) garage A 44 to 48 04/.6 = 40 garage B at 8 to 44 B B B Dep on nd B; an answer of 40 needs to be confirmed by checking graph 8 (a) 0.5 (b) Correct graph with smooth curve B for at least 4 correct points (c) Tangent drawn and gradient =. to.0 B for tangent drawn at x = 4 or B for gradient. to.0 (d) (i) Correct method to eliminate y and reaching the given equation without error including at least one intermediate line Cambridge International Examinations 06

5 Page 5 Mark Scheme Syllabus Paper Cambridge O Level May/June (ii). to.4 dep on line drawn B for x + y = 6 drawn (e) (i) or 0... (ii) Tangent gradient roughly (iii) y = x + k oe where 0 < k < 0.5 ft Ft from their e(i) B for x + k oe where 0 < k < 0.5 or y = x + k oe (any k outside range) 9 (a) 7.8 to 74 m B for 9 and 5 soi AB 0 M for = or better sin 5 sin 9 (b) 5.4 to B for 8.5 to 8.6 or M for cos DFE = or M for 0 = cos F (c) (i) 88 to 89 (ii) 69 to 70. km / h M for 5 their 88 seen (iii) 5.67 to 6.0 M for 90 (= 4.) π 0 (a) a = b = 5 B for one correct (b) 6 or (c) Reflection, y = x B for reflection or B for y = x only (d) Enlargement, Scale factor, centre ( 4, ) B for enlargement / negative enlargement B for scale factor B for centre ( 4, ) (e) 0 0 oe Cambridge International Examinations 06

6 Page 6 Mark Scheme Syllabus Paper Cambridge O Level May/June (f) (i) ( h, g) (ii) Reflection y = x B for reflection or B for y = x only (a) (i) 5.06 to B for r +.5 seen B for π(r +.5) πr or 0π(r +.5) 0πr B for 0π(r +.5) 0πr = 000 or better (ii) Solid II by B.5 to. cm or M for π r r = 000 or better and M for r = 000 ( = 4) π (b) 60 to 6 4 M for 8 8 sin 60 or 8 48 oe M for 8 4 soi or 9 soi M for their (triangle area) Cambridge International Examinations 06