0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.

Transcription

1 CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the March 206 series 0580 MATHEMATICS 0580/42 Paper 4 (Extended), maximum raw mark 30 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 March 206 series for most Cambridge IGCSE and Cambridge International A and AS Level components. IGCSE is the registered trademark of Cambridge International Examinations.

2 Page 2 Mark Scheme Syllabus Paper Cambridge IGCSE March Abbreviations 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) (b) oe With no errors seen 300 and 80 2 B for each or SC for answers reversed (c) 0 nfww 2 M for implied by 0.5 or nfww (d) (a) Correct perpendicular bisector of AB with 2 pairs of correct arcs isw (b) Correct angle bisector at A with two pairs of correct arcs isw 3 M for 3 + oe 8 3 Mdep on previous M for their ( 3 + ) oe B for accurate with no/wrong arcs or M for correct intersecting arcs with no or wrong line 2 B for accurate with no/wrong arcs or M for two pairs of correct arcs with no or wrong line (c) Circle centre E radius 5 cm isw 2FT FT circle centre their E radius 5 cm provided (a) and (b) attempted (d) 2 cao M for oe soi e.g. from arc If 0 scored SC for circle centre their E R R B for each If 0 scored, SC for two correct regions but in part (c), centre correct but radius incorrect Cambridge International Examinations 206

3 Page 3 Mark Scheme Syllabus Paper Cambridge IGCSE March (a) (i) 3 B for each M P B (ii) 46 FT FT 29 + their 3 values from (a) (iii) (iv) (b) (i) 7 9 oe 2 M for n (0 < n < (6 + their 3)) 6 + their3 or 4+ their 3 (k > (4 + their 3)) k or (ii) M2 for ½ ( ) 9 oe or M for method of finding a relevant area (iii) 7.2 FT FT (their 0800) (a) (i) 64 (ii) 6 to M for UQ = 7 to 7.5 or LQ =55 (iii) 62 2 B for 24 indicated (iv) 6 2 B for 54 seen (b) [8] 2 23 [ 4] 2 3 B2 for incorrect reading FT others (c) Blocks of height with correct widths 4FT B for 2 correct FT their (b) for heights BFT for each correct block If B0, SC for blocks of widths 20, 0, 0, 0 or for their correct frequency densities 5 (a) M2 for oe or M for 6000 associated with 96 [%] (b) B2 for 444. to or 4440 or M for Cambridge International Examinations 206

4 Page 4 Mark Scheme Syllabus Paper Cambridge IGCSE March (c).58 or M for oe A for or to 3 sf or better or or rounded or truncated to 3 sf 8 6 (a) (i) Rotation 90 [anticlockwise] oe and M2 for { ( ) 6000} 00 their oe or M for 6000 r 8 oe 00 (ii) ( 4, 4 ) Enlargement [centre] ( 5, ) [scale factor] 2 5 k (b) (i) Image at ( 2, 5) ( 2, 7) (, 7) 2 B for translation by or k 3 (ii) Image at ( 2, ) ( 2, ) (, ) 2FT FT their triangle P reflected in line y = 3 B for reflection of triangle P in the line x = 3 or y = k (c) Image at ( 2, 3) ( 4, 3) ( 4, 4) 3 B2 for 2 vertices correct in triangle or 3 correct co-ordinates soi in working or B for vertex in triangle correct soi or M for shown or statement rotation 90 [ anticlockwise] about (0, 0) 7 (a) 3.5[0] B for each (b) Fully correct curve 5 B3 FT for 0 or points or B2 FT for 8 or 9 points or B FT for 6 or 7 points B indep two separate branches not touching or cutting y-axis (c) 0.7 to 0.6 SC4 for correct curve, but branches joined Cambridge International Examinations 206

5 Page 5 Mark Scheme Syllabus Paper Cambridge IGCSE March (d) (i) 2.5 If 0,0, M for y = 2.5 x oe seen in working (ii) 0.6 to 0.5 with correct ruled line 3 B2FT for drawing their ruled line from (d)(i) (e) Correct tangent and 0.5 grad 0.85 or M for ruled line through (0, 2.5)FT or gradient FT 3 B2 for close attempt at tangent at x = 2 and answer in range OR B for ruled tangent at x = 2, no daylight at x = 2 Consider point of contact as midpoint between two vertices of daylight, the midpoint must be between x =.8 and 2.2 and M (dep on B or close attempt at tangent [at any point ] for rise run 8 (a) 5 nfww 3 M for y = k ( x +2) oe (b) x + 6 x 2 A for k = 3 nfww final answer 5 B2 for ( x + 6) 2 oe or SC for ( x + a)( x+ b ) where ab = 36 or a + b = 2 or x(x + 6) + 6( x + 6) X (c) 2 W + B2 for ( x 2)( x + 6) or SC for ( x + a)( x+ b ) where ab = 2 or a + b = 4 or x(x + 6) 2( x + 6) or x(x 2) + 6(x 2) 2 nfww final answer 5 M for W = X a or W a = X a a M for next productive step 7x (d) or 2 x 7x ( x )( x+ ) final answer M for 2nd productive step M for 3rd productive step M for final step leading to a = 5 M for common denominator ( )( + ) M for ( x 2)( x ) ( x+ 3)( x + ) x x isw 2 2 B2 for x 2x x+ 2 ( x + 3x+ x+ 3) oe or B for either expansion Cambridge International Examinations 206

6 Page 6 Mark Scheme Syllabus Paper Cambridge IGCSE March (a) (i) y (ii) x + y (iii) x + 2y 2 M for a correct unsimplified route or identifying OS (b) (½ x + y) oe 2 M for a correct unsimplified route or GR = ½ x or RG = ½ x (c) (i) MG = 2x + 2y 2 M for a correct unsimplified route e.g. 2 PQ (ii) MH = x + y or HG = x + y M Accept HM = x y or GH = x y MG = 2 MH oe 0 (a) 5.2[0] or M2 for [h 2 =] (b) (i) 7.2[0] or FT FT their (a) + 2 A Dep on (c)(i) correct, arrows essential or better or M for h 2 + 3² = 6² or B for PR (or PQ or QR) = 6 (ii) 62.4 or M4 for 2 6 ½ tan 60 oe (a) (i) (ii) 4x + 3 final answer (b) 7 2 (c) or M3 for 6 ½ tan 60 oe x final answer 2 M for ( x) 9 or M2 for realising that ½ base = tan60 oe or B for angle 30 or 60 in correct position on diagram or in a calculation If 0 scored, SC for volume = an area 2 seen oe 3 M for ( x) 32 3 = 7oe M for correct first step (d).3 3 M for ( ) 2 3 x+ 4 (7x + 3) = 0 M for 0x 3 = 0 oe If 0 scored, SC for answer 0.7 oe after 2 3 x+ 4 7x+ 3= 0shown previously ( ) Cambridge International Examinations 206