Mark Scheme (Results) June IGCSE Mathematics (4MAO) Paper 3H

Transcription

1 Mark Scheme (Results) June 0 IGCSE Mathematics (4MAO) Paper 3H

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3 . (a) = M 3 for 0.6 or 5 or (4 figures correct rounded or truncated) or 40 or or A Accept if first 4 figures correct (rounded or truncated) 59 or Also accept.76& or 50 (b).73 B ft from (a) if answer to (a) is a decimal with more than 3 sf Total 3 marks. (5 ) 80 or 3 80 or ( 5 4) 90 or 6 90 or (alternative method) 4 M 360 ( ) Condone incorrect ext angle 540 A 540 seen scores MA ( ) M dep on first M A cao Total 4 marks

4 3. (a) w(w 9) B Award B also for ( w ± 0)( w 9) B for factors which, when expanded & simplified, give two terms, one of which is correct except B0 for (w + 3)(w 3) SC B for w(w 9w) (b) 3x = 6 or 3x = 7 or 5x x = 6 oe 3 M for correct rearrangement with x terms on one side and numbers on the other AND correct collection of terms on at least one side M for 5x x = 7 oe ie correct rearrangement with x terms on one side and numbers on the other A cao dep on M (c) y + 3y 7y M for 3 correct terms out of 4 or for 4 correct terms ignoring signs or for y 4y + n for any nonzero value of n y 4y A cao Total 7 marks

5 4. (a) ( ) M 0. A Also accept 0 or 0% (b) M 8 8 A cao Do not accept 30 Total 4 marks

6 5. 0 and 9 eg 0 9 9, 0 or 9 0 Also accept B B for 5 6 or Alternative method B for both fractions correctly expressed as equivalent fractions with denominators that are common multiples of and 4 eg and or and B (dep on first B) for evaluation as a correct fraction which is equivalent to eg 4 SC B for multiplying both sides by ie 0 9 = Total marks

7 6. (a) Rotation 3 B Accept 90 clockwise B rotate, rotated etc Also accept quarter turn clockwise, 90 or 70 These marks are independent but award no marks if the answer is not a single transformation (0, 0) B Also accept origin, O (b) vertices (4,4), (4,), (5,) R correct B Condone omission of label B for correct vertices Total 5 marks or 5 3 M 5 may be denominator of fraction or coefficient in an equation such as 5x = (3+5+7) or 90 5 or 6 or oe 5 M dep 4 A Also award for 8 : 30 : 4 Total 3 marks

8 8. (i) 3, 5, 7, B cao (ii), 3, 5, 7, 9, B cao Brackets not (B0 if 3 or 5 necessary or 7 or repeated) Total marks 9. 5 eg 8000 = (8000+"400" ) 00 = (8000+"400" + "40" ) = OR M for eg OR 5 M for 8000 or M for completing method (M for or 8400 or or ) Accept ( ) as equivalent to.05 throughout. SC If no other marks gained, award M for oe or A Cao Total 3 marks

9 C = d oe 3 B3 3 d + 7 B for oe B for C = 3 d + 7 oe B for 3 d + 7 B for C = linear expression in d Total 3 marks

10 . (a) or M for finding at least four products f x consistently within intervals (inc end points) and summing them M (dep) for use of halfway values 444 A Cao (b) B Cao (c) Points correct B + ½ sq ft from sensible table Curve or line segments B ft from points if 4 or 5 correct or if points are plotted consistently within each interval at the correct heights Accept curve which is not joined to the origin (d) 5. indicated on cf graph M for 5. indicated on cf graph approx from correct graph A If M scored, ft from cf graph If M not scored, ft only from correct curve & if answer is correct (+ ½ sq tolerance), award M A Total 8 marks

11 . (a) (b) BC = CE 6 = 7. 9 CE or = 7. oe oe or 5. "7.8" CE 7. = oe 6 9 CE oe or = "7.8" oe M for correct, relevant proportionality statement with 3 values substituted 7.8 A cao M for correct, relevant proportionality statement with 3 values substituted 4.8 A cao Total 4 marks

12 3. 0(x ) 0( x ) + = or 5 (x ) + 4( x ) = 40 5( x ) + 4( x ) or = 0 5( x ) 4( x ) or + = 0 0 0x 5 + 4x 4 = 40 0x 5 + 4x 4 or = 0 0x 5 4x 4 or + = x = 49 or 4 x 9 = 40 or 0x + 4x 9 = 40 or 4x 49 = 0 4 M for clear intention to multiply both sides by 0 or a multiple of 0 or to express LHS as a single fraction with a denominator of 0 or a multiple of 0 or to express LHS as the sum of two fractions with denominators of 0 or a multiple of 0 May be implied by first B B expanding brackets (dep on M) B dep on both preceding marks ie for a correct rearrangement of a correct equation 3.5 A dep on all preceding marks Total 4 marks seen M 8 A Total marks

13 5. (a) Splits shape into rectangle & semicircle 4 M May be implied by working π.7 M π.4505 or value rounding to.4 or.5 Also award for equivalent 79π multiple of π eg 3.645π, or M Also accept A for 49.8 or for answer rounding to or (b) P L = πr + r oe 3 M for rearranging with both r terms on one side P L = (π + )r oe M for factorising a correct expression (does not depend on a correct rearrangement) P L A oe π + Total 7 marks

14 6. (a)(i) 4 B cao (ii) eg angle at the centre = angle at circumference B Three key points must be mentioned. Angle at centre/middle/o/origin. Twice, double, or half/ as appropriate 3. angle at circumference/edge/perimeter (NOT e.g. angle D, angle ADB, angle at top, angle at outside) (b) 74 B cao Total 3 marks

15 7. (i) (ii) 7 6 and no other terms M or oe A Also accept 0.05, 0.04, 0.047, etc Sample space method award marks for a correct answer; otherwise no marks 3 or 3 M 3 SC M for or M M for or oe A Also accept 0.6 &, 0.6, 0.7, , 0.67 etc but not 0. Sample space method award 3 marks for a correct answer; otherwise no marks Total 5 marks

16 8. (BC =) 47 sin 3 5 M or for at least 3 sf (may be implied by correct BD) " " tan 5 = or BD BD tan 39 = " " " " (BD = ) or " " tan 39 tan 5 A M 47 sin3 (CD = ) sin9 or for CD = at least sf (may be implied by correct BD) BD or for cos5 = " " M or for (BD = )" " cos5 0. A for answer rounding to 0. (0.686 ) Total 5 marks

17 9. (a) P = kq 3 3 M for P = kq 3 but not for P = Q = k 3375 M for 350 = k 3375 Also award for 350 = k 5 3 P = 0.4Q 3 oe A P = 0.4Q 3 oe Award 3 marks if answer is P = kq 3 oe but k is evaluated as 0.4 in part (a) or part (b) (b) 300 B ft from except for k =, if at least M scored in (a) (at least d.p. accuracy in follow through) Total 4 marks

18 0. n a 0 3 M a A n+ a Award M A A 0 for oe 0 0 a n+ A for 0 for 0 n 0 + oe even if M not awarded. Award M A A0 if a oe seen. 0 Award M A0 A if n 0 + oe seen. Total 3 marks

19 . (a) Use of areas to obtain a correct expression for A, which 3 B B for expression for area of must be correctly punctuated. For example triangle or pair of congruent (A =) 80 x(0 x) x(8 x) triangles, for example x(0 x) or x(8 x) or 0 8 x(0 x) x(0 x) x(8 x) x(8 x) or x( 0 x) or x( 8 x) or 80 x(0 x) x(8 x) Condone omission of brackets for or 0x x 8x x award of B 80 Correct simplification of a correct expression for A to obtain an expression which is equivalent to x 8x + 80 For example (A =) 80 0x + x 8x + x or 80 (0x x ) (8x x ) or 80 (5x x ) (5x x ) (4x x ) (4x x ) B dep on B (b)(i) 4x 8 5 B B for of 3 terms differentiated (ii) 4x 8 = 0 M 4.5 oe A cao (iii) eg positive coefficient of x or U shape d A or = 4 which > 0 dx B correctly Total 8 marks

20 . x + (x 3) = 6 M for correct substitution x + 4x 6x 6x + 9 B (indep) for correct expansion of or x + 4x x + 9 ( x 3) even if unsimplified 5x x + 7( = 0) B for correct simplification Condone omission of = 0 ( 5 x 7)( x )( = 0) B for correct factorisation or for correct substitution into ± 4 4 or or ± quadratic formula and correct evaluation of b 4ac 6 or ± or for using square completion 5 5 correctly as far as indicated x = or x = A for both values of x 5 dep on all preceding marks x =, y = A for complete, correct solutions x =, y = (need not be paired) 5 5 dep on all preceding marks No marks for x =, y = with no working Total 6 marks

21 3. π r + πrh 5 M πr + πrh = Also award for = 4πr 4πr π r + πrh = 4πr oe M for π r + πrh = 4πr oe πr( r + h) or = 4πr If first M awarded for πr + πrh = award this 4πr second M also for π r + πrh = 4πr oe h = 3r oe A If first M awarded for πr + πrh = and second M 4πr for π r + πrh = 4πr oe Award this A also for h = 3.5r oe π r "3r" M dep on first two Ms oe 4 h must be of the form kr 3 πr 3 9 oe A 4 Total 5 marks

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