Mark Scheme (Results) Summer 2008

Transcription

1 Mark Scheme (Results) Summer 008 IGCSE IGCSE Mathematics (4400) Paper 3H Edexcel Limited. Registered in England and Wales No Registered Office: One90 High Holborn, London WC1V 7BH

2 Summer 008 IGCSE Maths Mark Scheme Paper 3H Q Working Answer Mark Notes for 17.8 or.4 or seen.4 7. A1 for 7. oe inc Total marks for or 0.4 seen or x where 0 < x < 1 0. oe A1 for 0. oe Total marks 3. (a) Enlargement scale factor centre (1, 3) 3 B3 B1 for enlargement, enlarge etc B1 for,, two,, 1 :, : 1 1 B1 for (1, 3) Condone omission of 1 brackets but do not accept 3 (b) Reflection in the line y = x B B1 for reflection, reflect etc B1 for y = x oe inc eg in line from (,) to (5,5), in dotted line shown These marks are independent but award no marks if answer is not a single transformation Total 5 marks 4400/3H IGCSE Mathematics Summer 008 1

3 or 4 seen for or 4 seen 10 A1 for 10 cao Total marks 5. (a)(i) 1, 9, 17 B1 cao (ii) 1, 5, 9, 13, 17, 5, 33 B1 cao (b) eg No members in common. The intersection is empty. None of the members of A & C are the same. They don t have the same numbers. No numbers are in both A and C. 1 B1 (B0 if 1, 9 or 17 repeated) Brackets not necessary Total 3 marks 4400/3H IGCSE Mathematics Summer 008

4 6. 3 tan x = = for tan or for sin and A1 3 3 for or following 8 "73" correct Pythagoras and A1 for or for cos and 8 following "73" correct Pythagoras and A1 for A1 for 0.6 or better (Accept rounded or truncated to 4 sig figs or more ) Total 3 marks 7. π 7.8 or π 3.9 for π 7.8 or π A1 for 4.5 or for answer which rounds to 4.49, 4.50 or 4.51 (π ) Total marks 4400/3H IGCSE Mathematics Summer 008 3

5 8. (a) n = p + 1 oe 3 B3 for n = p + 1 oe eg n = p + 1, 1 + p = n, n = p + p + 1 B for p + 1 oe B1 for n = linear function of p eg n = p + 1 (b) n 1 n 1 p = n 1 or = p + for p = n 1 or = p + n 1 oe A1 for n 1 oe inc n 1 Total 5 marks 9. (a) 7x 7 = 5 x 7x + x = or 9x = 1 (b)(i) oe A1 for for 7x 7 seen for 7x + x = or 9x = 1 or for 7x + x = or 9x = 6 following 7x 1 = 5 x 1 1 oe inc 4, 1, 1. 3 &, x x x 4 for 16 x 4 A1 for 4 (ii) B B1 for 3 correct and none wrong or for 4 correct and 1 wrong Total 7 marks 4400/3H IGCSE Mathematics Summer 008 4

6 10. (a) or 158 seen 3 or for for or or or for or or or A1 cao (Do NOT award for 5.3) (b) or 8141 M for or or 850 for 983 or or for or for 8141, 105.%= or 67.5(0) seen A1 cao Total 6 marks 4400/3H IGCSE Mathematics Summer 008 5

7 11. (a) 60 < p 70 1 B1 Accept (b) 4 for finding at least four products f x consistently within intervals (inc end points) and summing them or or 4350 (dep) for use of halfway values (55, 65,... ) or (55.5, 65.5,...) (c) " 4350" (or 30½) indicated on graph or stated "4350" (dep on 1st ) 60 for division by 60 "4380" or for if 55.5, 65.5,... used A1 for 7.5 Award 4 marks for 73 if first two M marks awarded for 30 (or 30½) indicated on graph or stated 14 or 15 A1 Accept any value in range inc eg 14, 14.5, 15 (d) Use of p = 131 on graph for use of p = 131 shown on graph or implied by 47, 48 or 49 stated 1 A1 Accept any value in range inc Total 9 marks 1. 3 or 9 or value which rounds to 3.39 seen for 3 or 9 or value which rounds to 3.39 seen 36 A1 for 36 cao Total marks 4400/3H IGCSE Mathematics Summer 008 6

8 13. finds int angle of hexagon ( 6 ) finds ext angle of hexagon ( 6 ) 180 for or A1 for 10 or 60 int angle of polygon = 150 or ext angle of polygon = 30 B1 int angle of polygon = 150 or ext angle of polygon = ( n ( n ) or = 150 oe 360 ) for or = 150 oe 30 n 30 n Award A1 for int angle of hexagon shown as 10 or ext angle shown as 60 on printed diagram or on candidate s own diagram If there is clear evidence the candidate thinks the interior angle is 60 or the exterior angle is 10, do not award these two marks. Award B1 for int angle of polygon shown as 150 or ext angle shown as 30 on printed diagram or on candidate s own diagram 1 A1 for 1 cao Award no marks for an answer of 1 with no working. Award 5 marks for an answer of 1 if at least of the previous 4 marks scored. Total 5 marks 4400/3H IGCSE Mathematics Summer 008 7

9 14. (a) 5(y 3) 1 B1 cao (b) 3pq(3p + 4q) B B1 for 3pq( ) or (3p + 4q) or 3p(3pq + 4q ) or 3q(3p + 4pq) or pq(9p + 1q) or 3(3p q + 4pq ) ie for two factors, one of which is 3pq or (3p + 4q), or for correct, but incomplete, factorisation (c)(i) (x )(x + 8) 3 B B1 for one correct factor or (x + )(x 8) (ii), 8 B1 ft from (i) if two linear factors Total 6 marks 15. (a)(i) 57.5 B1 for 57.5, 57.49, , etc but NOT for (ii) 56.5 B1 for 56.5 Also accept (b) for Accept 6.49, 6.499, etc instead of A1 for 6, 5. 9, etc ft from 56.5 Total 4 marks 4400/3H IGCSE Mathematics Summer 008 8

10 16. (a) (b) 5 for A1 for Sample space method 9 9 award marks for a 5 or 0.31 or better or for or SC for or oe 1 1 for 4 oe for oe A1 4 for or 0.05 or better correct answer, otherwise no marks Sample space method award 3 marks for a correct answer, otherwise no marks Total 5 marks 17. (a) d = k h 3 for d = k h but not for d = h Also award for d = some numerical value 54 = 15k for 54 = 15k Also award for 54 = k h oe A1 for 3.6 h oe Award 3 marks if answer is d = k h but k is evaluated as 3.6 oe in any part (b) B1 ft from except for k = 1, if at least scored in (a) (1 d.p. accuracy or better in follow through) (c) h = for h = except for k = 1 "3.6" "3.6" 89 A1 cao Total 6 marks h 4400/3H IGCSE Mathematics Summer 008 9

11 18. a for correct statement of Sine rule = sin35 sin sin35 for correct rearrangement a = sin A1 for 4.34 or rounded or truncated to 4 figures or more Total 3 marks B1 for use of 8 = or 8 = 16 eg = = = B1 for multiplication of numerator and denominator by or (in either order) = = = 8 1 SC B1 for 1 = or for both = 18 = = = 8 8 = and (3 ) = 9 = = = NB only total of 1 mark for either of these approaches Total marks 4400/3H IGCSE Mathematics Summer

12 0. (a)(i) 59 B1 cao (ii) angle at the centre = twice angle at the circumference or angle at the circumference = half the angle at the centre B1 Three key points must be mentioned 1. angle at centre/middle/o/origin. twice/double/ or half/ 1 as appropriate 3. angle at circumference/edge/perimeter (NOT e.g. angle R, angle PRQ, angle at top, angle at outside) 4400/3H IGCSE Mathematics Summer

13 0. (b) 180 (x + 36) oe seen (possibly marked on diagram as size of ACB ) 5 B1 for 180 (x + 36) oe seen, either on its own or as part of an equation (This mark may still be scored, even if brackets are later removed incorrectly.) x = (180 (x + 36)) or x = (180 x 36) x or 180 ( x + 36) = 1 or 180 x 36 = x SC (Max of M marks) for omission of brackets in (x + 36) or their incorrect removal x = (180 (x + 36)) or x = (180 x + 36) 1 or 180 x + 36 = x or x = 1 x x = 360 x 7 x = 360 x or x + x = or x + x = (Note incorrect simplification results in an answer of x = 144) 3x = or 3x = or x = or x = A1 cao Please note that there is an alternative method on the next page. 4400/3H IGCSE Mathematics Summer 008 1

14 0. (b) OR x oe seen (possibly marked on diagram as size of ACB ) x x = B1 96 A1 cao Total 7 marks 4400/3H IGCSE Mathematics Summer

15 1. (a) tan drawn at (3, 6.5) 3 tan or tan produced passes between points (, 0 < y < 4) and (4, 9 < y < 1) vertical difference vertical difference finds their for two points on tan horizontal difference horizontal difference vertical difference or finds their for two points on curve, horizontal difference where one of the points has an x-coordinate between.5 and 3 inc and the other point has an x-coordinate between 3 and 3.5 inc A1 dep on both M marks inc (b) B1 Accept answer in range (c)(i) line joining ( 1,11) & (1,13) 4 1 A1 cao (ii) produces line to cut curve again 4 A1 ft from line Total 8 marks 4400/3H IGCSE Mathematics Summer

16 first part finds area of BCD and/or length of BD. Area of BCD = 6 B1 for area of triangle BCD for correct start to Pythagoras or trig for BD BD (BD =) + or + = BD finding BD or BD / or = cos 45 or sin45 BD or = cos 45 or sin45 ( BD =) 8 or or.83 or better ( ) A1 BD for lengths BD or correct BD 8 or = or or 1.41 or better ( ) second part method 1 uses Pythagoras to find AM, where M is midpoint of BD AM = BD 10 AM = 98 or 7 or 9.90 or better ( ) A1 for 98 or or better 16 A1 for 16 or answer rounding to 16.0 Total 6 marks 4400/3H IGCSE Mathematics Summer

17 second part method finds angle A either using Cosine Rule or by first finding A using trig BD 19 cos A = or or A BD / 8 or sin = or or or better 10 0 ( ) (A =) 16.3 or better ( ) A1 for angle A correct 16 A1 for 16 or answer rounding to 16.0 Total 6 marks second part method 3 finds angle ABD (or angle ADB) using trig or Cosine Rule BD / 10 + BD 10 (cos ABD = ) or (cos ABD = ) BD or cos ABD = 8 or or better ( ) 0 ( ABD = )81. 9 or better ( ) A1 16 A1 for 16 or answer rounding to 16.0 Total 6 marks 4400/3H IGCSE Mathematics Summer