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 MATHEMATICS 0580/41 Paper 4 (Extended) May/June 017 MARK SCHEME Maximum Mark: 130 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 befe 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 Rept f Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes f the May/June 017 series f 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 May/June 017 Abbreviations cao crect answer only dep dependent FT follow through after err isw igne subsequent wking oe equivalent SC Special Case nfww not from wrong wking soi seen implied 1(a)(i) M1 f oe 1(a)(ii) M f oe M1 f oe 1(b) 17.[0] to M1 f (c)(i) M f [ 100] oe oe 1(c)(ii) to M f oe 5.5 x 3 = 7.7 oe 1(d) 150 [million] oe M1 f 390 [million] ( ) 1(e) 50 nfww 3 M f 58.5 (( ) 100) 58.5 associated with 103.3[%] (a) 71 < t 7 1 (b) to 7.8 nfww 4 M1 f midpoints soi (condone 1 err omission) M1 f use of fx with x in crect interval including both boundaries M1 (dep on nd M1) f fx 90 (c)(i) 41, 6, 80, 90 B1 f crect values UCLES 017 Page of 7

3 May/June 017 (c)(ii) Crect curve 3 B1FT their (c)(i) f 5 crect heights B1 f 5 points plotted at upper ends of intervals B1FT (dep on at least B1) f increasing curve increasing polygon through 5 points (c)(iii) 7.1 to If zero sced, SC1FT f 4 crect points plotted (c)(iv) 1.9 to. M1 f UQ = 73. to 73.4 LQ = 71. to 71.3 (d) 180 cao nfww 4 B3 f 50 [m/s] nfww M3 f M f seen f (3715 to 375) (74.5 to 75.5) M1 indep f multiply by 3.6 oe 3(a)(i) Image at (5, 1), (7, 1), (7, 4) B1 reflection in y = 4 x = k 3(a)(ii) Image at ( 1, 1), ( 4, 1), ( 1, 3) B1 crect size and crect ientation wrong position f rotation 90 clockwise around (0, 0) 3(a)(iii) Image at (, 4), (4, 4), (, 1) 1 B1 f translation by k k 5 3(b) Enlargement 1 [sf] 0.5 oe 1 (5, 5) 1 3(c) B1 f one crect column row 3(d)(i) (4, ) M1 f 0 1 oe UCLES 017 Page 3 of 7

4 May/June 017 3(d)(ii) ( 4, ) M f (d)(iii) oe isw 3 0 M f det = soi k 0 1 soi recognition that Q is inverse matrix of G GQ = I QG = I 4(a) 1.6 to (b) (c) k > 4 B1 f identifying the 4 f hizontal line drawn y = 4 4(d) y = x 5 ruled and.3 to.1 1. to to B f crect line and crect values no line and 3 crect values B1 f no line and crect values B1 f crect line 4(e) Tangent ruled at x = 1 B1 No daylight at point of contact. Consider point of contact as midpoint between two vertices of daylight, the midpoint must be between x = 0.8 and 1. 6 to 4 Dep on B1 close attempt at tangent at x = 1 5(a)(i) to M1 f π M1 f rise/run f their tangent at x = 1 UCLES 017 Page 4 of 7

5 May/June 017 5(a)(ii) to B f answer to π 18 oe M f ( ) ( ) (figs 50.9 figs 30) ( π figs18 ) ( ) = ( π 18 ) h oe alternative method M f 50 oe π 18 M1 f figs 30 π figs 18 ( 50 ) figs 30 f oe π figs18 alternative method ( ) M f 50 oe = h oe 50.9 ( ) 50.9 (figs 50.9 figs 30) figs oe oe (a)(iii) 334 nfww 4 M f figs 30 π oe and B1 f π oe 3 5(b)(i) 3.8[6..] M f [ r = ] 95 3 oe 8.4π 1 π 8.4 [ 95] 3 r = 5(b)(ii) 93.1 to M3 f π M f (a)(i) 7x + 55 final answer M1 f 8x x + 35 answer 7x + k kx (a)(ii) x 14x + 49 final answer M1 f 3 of x 7x 7x + 49 UCLES 017 Page 5 of 7

6 May/June 017 6(b)(i) 18 3 M1 f a crect first step ie crectly multiplying by 3 crectly dividing by f crectly subtracting 5 M1 f crectly reaching ax = b from their first step 6(b)(ii) 15 3 M f 6x 4x = oe M1 f 6x 1 crect division by 3 f crectly reaching ax = b from their first step 6(b)(iii) 5 and 5 3 B f 5 5 [x =] (74 + 1) 3 better 7(a) ( 0.5, 3) B1 f one crect value 7(b) [y = ] x + final answer 3 8 M1 f better 3 M1 f substitution of ( 3, 8) (, ) their midpoint into y = mx + c with their m 7(c) y = x + 7 oe FT FT their (b) M1 f y = (their )x + k ( k ) y = kx + 7 (k 0) their x + 7 If zero sced, SC1 f ( ) 7(d) x y + 9 = 0 y x 9 = 0 oe 4 B3 f any crect equivalent in wrong fm Or M f y = ½ x + k oe (FT negative reciprocal of their gradient in (b)) grad = ½ (FT negative reciprocal of their gradient in (b)) M1 f substitution of (1, 5) into y = mx + c oe with their m 8(a)(i) 90 M1 f oe 8(a)(ii) [9..] 5 B1FT f CBA = 10 (their (a) 80) and B3 f [angle ACB = ]13. 50sin( their10) M f [sin C] = = oe sin C sin ( their10) UCLES 017 Page 6 of 7

7 May/June 017 8(a)(iii) to M f [ x = ] 50sin( their 10) oe 8(b)(i) x (x 5) = 00 1 and no errs seen sin ( their 10) = x oe 50 a crect right-angled triangle drawn with 50 as hypotenuse 8(b)(ii) ( 5) ± ( 5) 4(1)( 00) (1) better B B1 f ( 5) 4(1)( 00) better f x 5 oe B1 f both f ( 5) + q (1) ( 5) (1) q and final answer B1,B1 If B0B0, SC1 f values in ranges to and to seen f answers 36[.0] to and 61[.0] to and seen in wking f and as final ans 9(a)(i) 5 and (a)(ii) 8n 3 = 03 M1 Evaluation of 5th 6th term with suppting evidence explanation A1 Second evaluation of 5th 6th terms with suppting evidence explanation If zero sced, SC1 f and 05 with partial evidence explanation 9(b)(i) 6n + 7 oe final answer B1 f 6n + c kn + 7 k 0 9(b)(ii) n + n + oe final answer B1 f a quadratic expression second difference = 9(c) [y = ] 10 M1 f 5(0 y) = 50 [First term = ] 14 M1 f 5(x their y) = 0 f their y UCLES 017 Page 7 of 7

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

Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education MATHEMATICS 0580/43 Paper 4 (Extended) 017 MARK SCHEME Maximum Mark: 130 Published This mark