Cambridge International Examinations Cambridge International General Certificate of Secondary Education. Published

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1 Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/3 Paper (Extended) May/June 017 MARK SCHEME Maximum Mark: 10 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 May/June 017 series for most Cambridge IGCSE, Cambridge International A and AS Level and Cambridge Pre-U components, and some Cambridge O Level components. IGCSE is a registered trademark. This document consists of 7 printed pages. UCLES 017 [Turn over

2 0607/3 Cambridge IGCSE Mark Scheme May/June 017 MARK SCHEME NOTES The following notes are intended to aid interpretation of mark schemes in general, but individual mark schemes may include marks awarded for specific reasons outside the scope of these notes. Types of mark M A B Method marks, awarded for a valid method applied to the problem. Accuracy mark, awarded for a correct answer or intermediate step correctly obtained. For accuracy marks to be given, the associated Method mark must be earned or implied. Mark for a correct result or statement independent of Method marks. When a part of a question has two or more method steps, the M marks are in principle independent unless the scheme specifically says otherwise; and similarly where there are several B marks allocated. The notation dep is used to indicate that a particular M or B mark is dependent on an earlier mark in the scheme. Abbreviations awrt cao dep FT isw nfww rot SC soi answers which round to correct answer only dependent follow through after error ignore subsequent working not from wrong working or equivalent rounded or truncated Special Case seen or implied UCLES 017 Page of 7

3 0607/3 Cambridge IGCSE Mark Scheme May/June 017 1(a) Image at (0, 5), (3, 5), (3, 3) SC1 for translation k 1(b)(i) Image at (, ), (5, ), (5, ) 1 1(b)(ii) Image at (, ), ( 7, ), ( 7, ) 1 or k 7 1(b)(iii) 1(c) Rotation 10 [centre] ( 1, 0) Stretch [factor] x-axis invariant 3 B1 for each 3 B1 for each (a)(i) M1 for [angle BAC or DEC =] 10 6, soi by angle CDE = or M1 for angle BAC = their angle CDE (a)(ii) isosceles 1 (b) M for 10 0 or M1 for (c)(i) Angle sum of triangle 1 (c)(ii)(a) similar 1 (c)(ii)(b) 5. M1 for = QR 3(a)(i) (a)(ii).5 1 3(a)(iii) 3 1 3(b)(i) Positive 1 3(b)(ii) (b)(iii) (0 ) or 0 or 10 (0 ) 3(b)(iv) 7.3t 55.3 (7.3 to 7.33)t (55.5 ) B1 for 7.3t + k or kt 55.3 or SC1 for 7.3t 55 3(b)(v) Correct line (positive gradient and not below the x-axis) B1 for positive gradient UCLES 017 Page 3 of 7

4 0607/3 Cambridge IGCSE Mark Scheme May/June 017 (a)(i) 5 : B1 for any other correct ratio (a)(ii) 1.6 M1 for [0] (a)(iii) 1.5[0] 3 M for or M1 for recognising 11.5 as 90% (a)(iv) 300 nfww M for or M1 for (implied by nfww) (a)(v) M for or M1 for n where n > 1 (b) 17 3 B for 16.5 or 16.5 to log 10 or M for or appropriate sketch log1.057 or n = 300 and at least trials which reach from 50 to 350 or M1 for n [ = 300] 5(a) 0 or 0. to M1 for 16 3 π M1 for 3 π 5(b) 50 or 9.5 to M for π + 16 or M1 for or π their l UCLES 017 Page of 7

5 /3 Cambridge IGCSE Mark Scheme May/June 017 5(c).9 or.9 P is point of contact between slant edge and circle. B for PV = nfww or M1 for 16 = PV M1 for OV OR = + PV B for l = 30 or M1 for l = + 16 M1 for = l OV soi OR x is semi-vertical angle of cone M1 for tan x = 16 M for sin x or M1 for = sin x OV 6(a) Correct sketch B1 for correct shape 6(b) (.17, 0.) or (.171, 0.77 ) B1 for each 6(c) 0. f ( x ) 1.51 or f ( x ) FT their 0. B1 for 0. f ( x ) or f( x ) (d) 0.50 or or 5.7 B1 for each 6(e) 0.50 < x < 5.3 or < x < FT their (d) 6(f)(i) 15.[0] or [0] or [0] or (f)(ii) [an] asymptote 1 UCLES 017 Page 5 of 7

6 0607/3 Cambridge IGCSE Mark Scheme May/June 017 7(a) 9.77 or M for cos35 or M1 for cos35 = AB 7(b) 60.6 or M for 6 9 or M1 for = cosC (a) 10 1 (b) 1 M1 for [h(1) =] or for 1 [gh(x) = ] 3 + x + 1 (c) 5x + 1x M1 for (3 + x) + 1+ x + 1 B1 for 9+ 6x + 6x+ x or better for (3 + x ) (d) 1 1 x or 1 x x final answer 3 M1 correct first step M1 correct second step (e)(i) 1 M1 for 3 + x = 1 (e)(ii) 5 1 9(a) 15, 7, 1 correctly placed B1 for two correctly placed or M1 for 1 (0 6) seen or correct equation 9(b)(i) 7 1 FT their Venn diagram 9(b)(ii) 1 FT their Venn diagram 9(c) 15 1 FT their Venn diagram 9(d) M1 for (e)(i) FT their Venn diagram 9(e)(ii) their 7 their1 their1 their 7 M for or M1 for one of these products 9(f) 3 their 7+ n 5 M for = 0 + n 16 or M1 for at least two trials UCLES 017 Page 6 of 7

7 0607/3 Cambridge IGCSE Mark Scheme May/June 017 9(g) 1 10(a)(i) M1 for.75, 3.15, 3.5 soi 10(a)(ii) Correct histogram 3 B1 correct widths B1 for two correct heights 10(b)(i) = x x B B1 for 00 x or 00 x ( x+ 10) 60 00x= 0 x( x+ 10) M1 i.e. correctly clearing fractions or all over common denominator x + 10x 6000 = 0 A1 completion with at least one interim line and without any errors or omissions 10(b)(ii) h 5 min B for 7.6 or 7.6 or M1 for correct use of formula or correct sketch M1 for 00 their positive x, implied by (a)(i) a + b 1 11(a)(ii) 1 a + 1 b 1 FT their (i) 11(a)(iii) 3 a + 1 b B1 for correct unsimplified answer or a correct route 11(b) (6.5, 1.5) 3 FT their (a)(iii) 6.5 B for or M1 for OR uuuur B for (5, 3) at M or [ OM = ] or B1 for (k, 3) or (5, k) at M uuuur k 5 or [ OM = ] or 3 k 5 3 UCLES 017 Page 7 of 7