0607 CAMBRIDGE INTERNATIONAL MATHEMATICS

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1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 010 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL MATHEMATICS 0607/04 Paper 4 (Extended), maximum raw mark 10 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 must be read in conjunction with the question papers and the report on the examination. CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 010 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

2 Page Mark Scheme: Teachers version Syllabus Paper 1 (a) 5h 1 min seen 5.35 h seen seen or [4] Subtracting times (31 ) Converting minutes part to hours (may be later) ( ) 340 their time ( 60 ) (b) (i) 54.0 ( ) B [] If B0, for oe (ii) ft B3 ft [3] ft 340 their (i) changed to hours and minutes added to If B0, for 340 their (i) (6.9 ) or or (dep) for changing decimal part to minutes (a) (i) [1] Accept or (ii) ft ft [1] ft their (i) for 9.331, 9.33 or 9.3 all 10 4 (b) 9.69(0) to B [] for (0) to implied by SC1 for or or [1] (d) 4.7 or 4.7 to 4.73 B [] If B0, for log000 log5 or graph clearly sketched showing intersection 3 (a) Sketch of U-shaped parabola intersecting x-axis twice or full correct use of formula with a = 1, ± 0 b = and c = 4 ( ) use of completing the square 3.4, 1.4 or correct A1 A1 [3] (b) 3.4 x 1.4 ft ft ft [] 4 (a) Line joining 5 on each axis approx Horizontal line roughly through 1 Line through origin at more than 45 to x-axis [3] (b) R in correct region oe dep [1] If A0, SC1 for 3. or 3.36 and 1. or 1.36 If M0, SC for 3.4 and 1.4 or SC1 for 3. or 3.36 and 1. or 1.36 [9] ft only if two solutions to part (a) Condone < used and allow in words, if clear [5] All may be freehand dep on B3 [4]

3 Page 3 Mark Scheme: Teachers version Syllabus Paper 5 (a) (allow.87,.88 or.9) 4 [5] (b) B [] If B0, for attempting to find a fraction with denominator 7 (i) cao B [] If B0, for 7 (ii) 45 ft ft 45 [1] ft their (i) if answer is integer accept 360 [10] 6 (a) 1.15 B3 [3] If B0, for 0t + 8(3t 1) and (dep) for this equal to (b) (i) + = 8 M Allow for l.h.s. y y + 15 ( y + ) + 9y = 8y( y + ) or + 15y y = 8y 16y 8y 8y 30 = 0 4y 4y 15 = 0 o.e. Could still be all over y( y + ) and not expanded or partly or fully expanded E1 [4] Correctly established. Need to see 1 correct line and final answer (ii) (y 5)(y + 3) B [] Allow SC1 for any other (y ± 5)(y ± 3) (iii).5(0) ft ft [1] ft a positive root from (ii) if the only one from two possible roots. [10] 7 (a) Real numbers oe [1] (b) 3, 90 [] Allow either way round (i) Stretch Factor x-axis invariant (ii) Translation 60 0 [3] Independent [] Must be translation Independent Allow description in words [8] 8 (a) (i) Triangle at ( 4, 4), ( 1, 4), ( 1, 5) B [] If B0, SC1 for any translation (ii) Triangle at ( 1, ), ( 1, 5), (, 5) B [] If B0, SC1 if two vertices correct (b) Enlargement, (factor), (centre) (4, 0) Translation 6 3 [3] Each B is independent [] B s independent Must be translation but allow description in words [9]

4 Page 4 Mark Scheme: Teachers version Syllabus Paper 9 (a), 3, 5, 7, 11, 13, 17, 19 [1] (b) All 8 points correctly placed B3 [3] B for 7 correct and for 6 correct isw extras 3, 11, 17, 19 ft ft [1] ft their Venn diagram (d) 3 ft ft [1] ft their Venn diagram (e) B only shaded (i.e. parts in A and C not shaded) [1] 10 (a) (i) One pair of angles equal with reason Second pair of angles equal with reason Angles of triangles equal R1 R1 R1 [3] Reasons can only be angles in same segment oe and vertically opposite oe, the second only used once Accept anything suggesting angles same Each R is independent (ii) 18 B [] If B0, for or 0.5 seen (b) (i) 50 [1] (ii) 98 B [] If B0, for 180 (3 + their (i)) or for angle QPR = 3 seen or for angle PQY = 58 seen (may be on diagram) (iii) 5.14 ( ) B [] If B0, for cos50 = RY 8 oe (iv) 4 [1] [11] 11 (a) 3 points correct mm accuracy P [] P1 for correct (b) Negative [1] Allow description e.g. cold goes down as hot goes up (i) y = 0.565x [] Must be in form mx + c, allow 0.57 or to for m and 58 or for c (ii) 30 or 31 cao B [] Must be integer If B0, for using their linear regression equation with x = 50 1 (a) B3 [3] SC for 6 5, 0.83, 0.833, isw if angle given If B0 and SC0, for (can be implicit) sin C 10 = sin 30 6 oe (b) (i) Two accurate points marked C 1 and C [] mm accuracy (ii) 56.4, 13.6 [] (iii) 67. ft ft [1] ft the difference between their answers in (ii) [8]

5 Page 5 Mark Scheme: Teachers version Syllabus Paper 13 (a) 98 ( ) B [] If B0, for 0.5 π 5 (b) ( ) ft B ft [] ft their (a) 300 If B0, for their (a) 300 (i) ( ) B3 [3] Allow If B0, for cos = 5 oe then dep for (ii) 99.9 to ft B ft [] ft their (i) If B0, for sin(their(i)) or for oe (iii) to 580 ft (iv) ft (v) 83.1 to ft 14 (a) One curve reasonable shape, roughly approaching y = 1 both ends One max in negative x region One minimum just to right of y-axis or on it (b) ( 5.19, 1.4) ( to 5.19, 1.38 to 1.39) to 1.4 ( to and 1.38 to 1.39) B ft [] ft their (i) If B0, for their (i) 360 π 5 ft [1] ft their (iii) their (ii) B ft [] ft their (ii) 0.3 oe If B0, for their (ii) 0.3 oe [3] (d) y = 1 [1] B [] Allow 5. and 1. [14] B3 [3] Allow 0.16 and 1.4 If B0, for top value their y-coord of (b) and (indep) for evidence of finding minimum point (e) 1.6(4 ) B [] If B0, for line with c = 1 and positive gradient added to sketch (may be freehand) [11]

MARK SCHEME for the October/November 2013 series 0580 MATHEMATICS

CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 01 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark