Mark Scheme (Results) November 2009

Transcription

1 Mark Scheme (Results) November 00 IGCSE IGCSE Mathematics (4400) Paper 4H Higher Tier Edexcel Limited. Registered in England and Wales No Registered Office: One0 High Holbn, London WC1V 7BH

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3 November 00 IGCSE Mathematics (4400) Mark Scheme Paper 4H Except f questions * where the mark scheme states otherwise the crect answer, unless clearly obtained by an increct method, should be taken to imply a crect method. [* Questions (b), 1 and ] Trial and improvement methods f solving equations sce no marks, even if they lead to a crect solution. Q Wking Answer Mark Notes M1 f A1 Accept 1dp better Also accept Total marks. (a) n(n 4) B B1 f facts which, when expanded and simplified, give two terms, one of which is crect except (n + )(n ) and similar SC B1 f n(n 4n) (b) 5x = 8 5x = 8 M1 f 5x + = 8 3 M 5x = 6 5x = oe 5 A1 dep on M Do not accept 6 5 IGCSE Mathematics (4400) Paper 4H November 00

4 Q Wking Answer Mark Notes 3. (a)(i) 6 B1 cao (ii) alternate angles B1 Accept alternate but not Z angles (b) 180 " 6" M A1 cao 4. (a) 1 ( ) M1 (b) 0.1 A1 Also accept n = 0. 4 M A1 cao (a) (b) f oe inc A1 cao M1 1% = $ 65 seen M f % (of amount) = M A1 IGCSE Mathematics (4400) Paper 4H November 00

5 Q Wking Answer Mark Notes 6. (a) Reflection in the line y = 4 B B1 f reflection, reflects etc B1 f y = 4 eg dotted line but, if given, equation must be crect (b) Enlargement with scale fact 1½, centre (1,6) 3 B3 B1 f enlargement, enlarge etc B1 f 1½ oe B1 f (1,6) These marks are independent but award no marks if answer is not a single transfmation. (Second transfmation may be implied) seen 3 M1 May be implied by 1 crect answer A A1 f one crect Total 3 marks 8. Arcs of equal radii > ½AB, centres A, B, which intersect twice M1 Perpendicular bisect within guidelines A1 Total marks IGCSE Mathematics (4400) Paper 4H November 00

6 Q Wking Answer Mark Notes. (a) Crect line B Must be a single straight line passing through at least 3 of (0, ), (3, 0), (6, ), (, 4) B1 f a single straight line with a positive gradient passing through either (0, ) (3, 0) f 3 of 4 points (0, ), (3, 0), (6, ), (, 4) crect with at most 1 point increct Allow ± mm (b) Lines x = 3 and x = 6 drawn 3 B1 Lines y = and y = 4 drawn B1 R shown B1 Condone omission of label Accept shading in shading out, if consistent Award 3 marks f crect labelled rectangle, even if not shaded Award marks f a crect unshaded rectangle without a crect label SC B1 f region bounded by < x < 4 and 3 < y < (a) 6. C = M1 M1 f finding at least 3 products x f consistently within intervals (inc end points) (dep) f use of at least 3 crect halfway values 315 A1 cao isw after 315 (b) 6.1 A B3 B1 f each value cao Total 6 marks IGCSE Mathematics (4400) Paper 4H November 00

7 Q Wking Answer Mark Notes 11. (a) 64 = 6 and 80 = 4 5 1,,4,8,16,3,64 and 1,,4,5,8,10,16,0,40,80 4 (b) 6 5 oe eg 4 4 5, ,18,1,56,30 and 80,160,40,30 M1 Need not be product of powers; accept products lists ie,,,,, and,,,,5 Prime facts may be shown as fact trees repeated division 16 A1 cao M1 30 A1 cao 1. (a) p 4p + 7p 8 M1 f 4 crect terms igning signs f 3 terms with crect signs p + 3p 8 A1 cao (b) 1x 5 y 6 B B1 f any two parts crect (c) q 4 B B1 f either q 4 Total 6 marks 13. (a) (b) eg 15 0, 1 1 0, M f (1.5) oe (1.5) oe seen A1 cao M1 f eg 0 1.5, 0 0.8, & 16 A1 cao IGCSE Mathematics (4400) Paper 4H November 00

8 Q Wking Answer Mark Notes 14. (a) 8 (8) B f all crect (B1 f 3 crect) (b) Points B1 Allow + ½ sq ft from table if at least B1 sced in (a) Curve B1 ft if B1 f points Award f single curve (not line segments) which does not miss me than one plotted point by me than ½ square 15. (a)(i) B1 cao (ii) eg angle at the centre B1 = angle at the circumference Three key points must be mentioned 1. angle at centre/middle/o/igin. twice/double/ half/ 1 / as appropriate 3. angle at circumference/ edge/ perimeter/arc (NOT e.g. angle B, angle ABC, angle at top, angle at outside) (b)(i) B1 cao (ii) eg sum of opposite angles of a cyclic quadrilateral = 180 B1 Accept reason which includes opposite and cyclic and nothing increct Also award if (b)(i) is crect and reason is given as angle at the centre = angle at the circumference oe Igne additional reason(s) IGCSE Mathematics (4400) Paper 4H November 00

9 Q Wking Answer Mark Notes 16. (a) B f completely crect diagram, inc labels (accept First chocolate Second chocolate clear abbreviations eg S and H) 6 soft centre (B1 f branches with at least 3 crect probabilities in the crect place) soft centre hard centre 3 7 hard centre soft centre hard centre (b) (= + + ) (= + ) M1 M1 48 A1 0 f one crect product f completely crect expression M f SC M f f oe inc f f answer rounding to 0.53 SC M1 f SC M1 (dep) f sum of above products f f method marks ft from their tree diagram, provided probabilities < 1 IGCSE Mathematics (4400) Paper 4H November 00

10 17. (a) Q Wking Answer Mark Notes 8.6 (1 + 0.) (1 0.) 10.3 M1 f crect substitution oe A1 (b) T ( 1 e) = n( 1+ e) 5 M1 removes fractions T et = n + en M1 expands brackets en + et = T n M1 collects terms e( n + T) = T n M1 factises T n A1 T + n f T n oe T + n Total 7 marks = = M1 f = 4.1 M1 f " " 3. tan and M M1 f tan and 3. " " Accept CD rounded truncated to at least 1 dp (4.116 ) 46.6 A1 Accept answer rounding to 46.6 ( ) Alternative methods f Q18 appear on the next two pages. IGCSE Mathematics (4400) Paper 4H November 00

11 Question 18 Alternative methods Method 1 Wking Answer Mark Notes = = = = cos and " 5. 67" 5 M1 f M1 f M " 5. 67" M1 f cos and 3. Accept BC rounded truncated to at least 1 dp ( ) 46.6 A1 Accept answer rounding to 46.6 Method Wking Answer Mark Notes = = = = 5.67 " 4. 1" sin and " 5. 67" 5 M1 f M1 f M " 5. 67" M1 f sin and " 4. 1" Accept CD rounded truncated to at least 1 dp (4.116 ) and BC rounded truncated to at least 1 dp ( ) 46.6 A1 Accept answer rounding to 46.6 IGCSE Mathematics (4400) Paper 4H November 00

12 Method 3 Wking Answer Mark Notes Crect method f finding A 5 M1 eg f 7. cos A = ( A =.83 ) cos". 8" M1 f crect Cosine Rule expression f calculating BC 3. " 5. 67" cos and M M1 f cos and " 5. 67" 3. Accept BC rounded truncated to at least 1 dp ( ) 46.6 A1 Accept answer rounding to 46.6 Method 4 Wking Answer Mark Notes Crect method f finding A 5 M1 eg f 7. cos A = ( A =.83 ) cos". 8" M1 f crect Cosine Rule expression f calculating BC 8.3 sin".8" sin B = "5.68" M f crect expression f sinb M1 f crect statement of Sine Rule sin B sin".8" eg = 8.3 "5.68" 46.6 A1 Accept answer rounding to 46.6 IGCSE Mathematics (4400) Paper 4H November 00

13 Q Wking Answer Mark Notes 1. (a) 3t 10t B B1 f 3t 10t Igne further differentiation seen in body on answer line (b) 6t 10 = 0 M1 f linear expression including either 6t 10 5 A1 ft from 6t 10 = 0 if M1 sced 0. (a) 14 1 B1 cao (b) 1 B1 cao (c)(i) B B1 f crect (ii) 11 B1 cao = 18(d 18) 1 1 = 18x 4 M1 f r = 1 + (18 r) 144 = 18d 34 x = 8 M1 f r = r 18r + r 18d = 468 (d=)8+18 M1 f 36r = A1 dep on all method marks Alternative methods f Q1 appear on the next page. IGCSE Mathematics (4400) Paper 4H November 00

14 Question 1 Alternative methods Method 1 Wking Answer Mark Notes Complete, crect method f finding AOM BOM OAB OBA Crect numerical expression f length of OA OM Length of OA OM used to find diameter 4 M1 1 eg tan ALM = 18 ALM = AOM = = M1 eg 1 sin AL = = 468 = 1.63 cm cos ALB = = ALB = ALM = AOM = = sin.6 (= 13) sin tan67.38 M1 eg 13 (18 5 ) dep on both previous M1s 6 A1 dep on all method marks Accept answer rounding to tan ALM = 18 ALM = OAM = =.6 1 tan.6 (= 5) Method Wking Answer Mark Notes AM = 1, OM = 5, OA = 13 and = = 13 4 M3 f use of Pythagean triple use of OM = 5 Pythagas to obtain = 13 f OA 6 A1 dep on M3 and justification IGCSE Mathematics (4400) Paper 4H November 00

15 Q Wking Answer Mark Notes. y = 3x B1 f crect rearrangement x + ( 3x + 4) = 34 M1 f crect substitution x + x + 1x + 1x B1 (indep) f crect expansion of x + x + 4x + 16 (3x + 4) even if unsimplified 34 10x + 4x 18( = 0) B1 f crect simplification Condone omission of = 0 ( 5x 3)(x + 6)( = 0) ( 5x 3)( x + 3)( = 0) ( 10x 6)( x + 3)( = 0) B1 f crect factisation Condone omission of = 0 4 ± ± f crect substitution into the quadratic fmula and crect evaluation of b 4ac 1 ± x = x = ± x =, y = x = 3, y = 5 A1 A1 f using square completion crectly as far as indicated f both values of x f complete, crect solutions Need not be explicitly paired Total 7 marks TOTAL FOR PAPER: 100 MARKS Note The mark scheme f an alternative method f Q is on the next page. IGCSE Mathematics (4400) Paper 4H November 00

16 Question Alternative method Wking Answer Mark Notes 4 x = y 3 y 4 + y = 34 3 y 4y 4y y = 34 y 4y 4y y = 306 o y 8y + 16 r + y = 34 y 8y y = B1 f crect rearrangement M1 B1 f crect substitution (indep) f crect expansion of (y 4) even if unsimplified 10y 8y 0( = 0) B1 f crect simplification Condone omission of = 0 ( 5y )( y + 5)( = 0) ( 5y )(y + 10)( = 0) ( 10y 58)( y + 5)( = 0) B1 f crect factisation Condone omission of = 0 8 ± ± f crect substitution into the quadratic fmula and crect evaluation of b 4ac ± ± y = 5 y = x =, y = x = 3, y = 5 A1 A1 f using square completion crectly as far as indicated f both values of y f complete, crect solutions Total 7 marks IGCSE Mathematics (4400) Paper 4H November 00

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