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 007/4 Paper 4 Paper 4 (Extended) October/November 0 MARK SCHEME Maximum Mark: 0 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 0 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 Abbreviations awrt answers which round to cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied (a) 7 (b) 0 (c) 7 (d) 4 B for 70 or 74 seen (e) 7. M for attempt at fx soi by 4099 or 7 or 7... (a).8 or B for 8 or final answer or M for + or M for correct sketch (b) 5 cao B for 45 soi by e.g. 5 If 0 scored SC for 4.9 to 5. (c) 8 cao M for oe (a) Positive (b) (i).5 (ii) (c) (i) y = 7.+.7x Range 7.0 to 7. and.9 to.70 B for 7. + kx, or a +.7x, If 0 scored, SC for 7 +.4x (ii) 8 or 8... FT their (i)

3 Page Mark Scheme Syllabus Paper 4 (a) 48 (b) 84 FT (80 their (a)), their (a) 45 M for (80 their (a)) their (a) 45 (c) 4 FT their (b) (d) 9 cao B for angle OBC or OAC = or angle ABC = 9 (e) 55.5 FT their (d) M for (80 their (d)) 5 (a).7 or.8 to.9 B for at least of (7.5, 7.5, 0, 4.5, 70) soi by Accept 7. or 7.8 to 7.9 for full marks and of (8, 8, 0.5, 4, 70.5) soi for B (b) 0.8,.,.,.7,.47 or.4 to.47, 0.7 B for 4 or 5 correct or B for or correct (a) Reflection y = x (b) Rotation, centre (, ) 90 [anticlockwise] or 70 clockwise (c) Translation 4 (d) Enlargement, centre (0, 0) [SF] oe Allow reduction 7 Correctly equating one set of coefficients Correct method to eliminate one variable x = y = M M B Equation = or = from one equation Note a correct sketch showing intersection in third quadrant scores M (other sketches may score the M for y = seen) Correct substitution into other equation If zero scored SC for correct substitution into one of original equations and evaluation to find other variable

4 Page 4 Mark Scheme Syllabus Paper 8 (a) 8 or or 8 9 M for or M for If 0 scored, SC for 0.94 or or (b) (i) [cosb] = oe M for = cos B (ii) their exact (a) M M for their (a) (their (a) must be < ) Leading to 0 A Cancelling seen or 80 seen or 90 or 0 9 (a).5 or.45 to.4 M for 00 π 5 oe (b) (i) 5.77 or 5.77 to M for tan0 = 0 x oe (ii).5 or.54 to.55 M for 0 + their (b)(i) oe 0 or 0 + sin 0 oe (iii) 00 to 0.0 nfww 4 M for their (b)(i) their (b)(i) sin 0 oe or M for any of these or M for any of these OR M for 0.5 (their(b)(ii)) sin0 0 oe or M for 0.5 (their(b)(ii)) sin0 oe or M for their attempt at area of triangle ABC 00

5 Page 5 Mark Scheme Syllabus Paper 0 (a) Fully correct curve 0 y f(x)=-/(x-) B for both branches but with serious 'curl back' and/or overlap. or B for branch x - -0 (b) x = y = (c) [x = ] 4 [x = ] (d) x < 4 < x < FT their 4 from (c) FT their from (b) and their from (c) (e) (i) (ii) Translation 0 Translation 0 (a) n oe (b) 4 n + n + oe M for pn² + qn + c p, q, c 0 or M for second differences = or pn² + c or pn² + qn (c) 7 n n n oe FT their (a) their (b) FT their (a) their (b) M for pn + qn + rn+ c p, q, r, c 0 or n their (b) or M for third differences = or for pn + qn + c or pn + qn + rn or pn + rn+ c

6 Page Mark Scheme Syllabus Paper (a) (i) 44π M for π (ii) 08π M for π + π If 0 scored SC for 7π their ( a)( i ) (b) (i) or.99 to.0 nfww M for oe 4 π or M for 4 π r = their(a)(i) (ii) : or : cao nfww M for 4 π (their(b)(i)) : their(a)(ii) oe or M for 4 π (their(b)(i)) or their(a)(ii) (a) p q final answer M for correct use of alogb M for correct use of loga ± logb (b) (i).9 or.9 M for log log 4 or log 4 or sketch of and y = oe or M for xlog4 = log or sketch of (ii) x² 5x 7 = 0 B or B for terms correct in expansion x 9x+ 4x y = 4 x y = 4 x ( 5) ± ( 5) 4 ( 7) x = x =.57 or x = 0.74[0...] M B FT their three term quadratic or for sketch of parabola with minimum point Alternative If sketch of parabola with minimum point and y = and no three term quadratic seen, allow B

7 Page 7 Mark Scheme Syllabus Paper 4 (a) Fully correct curve y f(x)=^x-x^/ x B for correct graph for x < 0, minimum point seen above x-axis B for correct graph for 0 < x <, maximum point seen higher than minimum point B for minimum point seen below x-axis, < x < 8 If 0 or scored, SC instead for correct curve except stationary point of inflexion instead of LH minimum and maximum (b) 0.79 or or 0... (c) (. or. to.,.7[0] ) co-ordinate (d).8, 0.4, 4., 5.7 or.84 to to to If 0 scored SC for.8, 0., 4., 5.8 or SC for three of these.

MARK SCHEME for the October/November 2014 series 0580 MATHEMATICS

CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 04 series 0580 MATHEMATICS 0580/4 Paper 4 Extended, maximum