for price of 1 melon or number of full price melons M1 for revenue from all full price melons sold A1 cao 12 ( 9) '27' ('180' '172.

Transcription

1 International GCSE in Mathematics A - Paper 3H mark scheme or AO M M for or or A 8 (6 ) (=) AO M or use of cancelled ratios (e.g. 3 : 6 : = 0.75 :.5 : ) 3 (=) M (dep) 8 0.5(=56) or cancelled ratios, (e.g ) or M for 8 3 oe 3 A 3 a 5 < d 30 AO3 B B identifies 5 30 class b (.5) + (6 7.5) + (.5) + (6 7.5) + (.5) + ( 8 7.5) or or M AO3 M M for frequency consistent value within interval NB. Products do not need to be added Condone one error 7 A accept 7.3(33 ) 3 c AO3 M 3 60 oe A a 3 for with a < 60 or 60 b with b > 3 Issue June 06 Pearson Education Limited 06 87

2 Working with all boxes 5 (=80) or (=) 3.6 oe ( 7.8) AO M for correct total cost or correct total number of melons (either may appear as part of another calculation) M for revenue from all full price melons sold 5.5 oe (=07) or oe (=7) '07' '7.8' or or 36 '7' ('80' '7.8') A cao M for total revenue or total profit M dep on M3 Alternative working with one box 5 (=.5) or 3.6 oe (.) 3 ( 9) M for price of melon or number of full price melons M for revenue from all full price melons sold 5.5 (=7.5) M for total revenue from one box '7.5' '.' 3 or A cao M dep on M3 88 Issue June 06 Pearson Education Limited 06

3 5 Circular arc, centre B, to intersect both lines AB and BC Equal length arcs, from intersections on each line, meeting to give a point on the bisector AO M correct bisector A dep on M Full construction shown. 6 a AO M Any correct partially factorised expression 9e f (e + 5f 3 ) A b (x ± 6)(x ± ) AO M or correct substitution into quadratic formula (condone one sign error) (x 6)(x + ) M or 6 6, 3 A dep. on at least M 7 PR cos 35 = AO M cos35 M. 3 A. ~ (=.5) or 00 5 (=6.6.) AO M M for ".5" 00 (=50) or 6.6.5(0) 50 3 A M dep Issue June 06 Pearson Education Limited 06 89

4 9 a AO B b Mars AO B c or AO M or oe 7 0 A d :. 0 6 AO M : 00 A or or 3.9 or 3.5 AO M (BC = ) 5.7 A 7.6 "5.7" or.6(6) or.7 M dep on first M or e.g. ACB 7.6 sin ( 53...) "5.7" sin"53.".8 "5.7" or.7(587...) or M dep on first M 3. 5 A for answer rounding to 3. (π ) and 90 Issue June 06 Pearson Education Limited 06

5 e.g. (x + 5x 3x 5)(x + 3) or (x + x 5)(x + 3) or (x 5)(x + 3x 3x 9) or (x 5)(x 9) E.g. x 3 + 3x + x + 6x 5x 5 or x 3 + 5x 9x 5 x 3 + 5x 9x 5 3 A AO M expansion of any two of the three brackets at least 3 correct terms M (dep) ft for at least 3 correct terms in second expansion a ( ) ( ) and ( 3 3 ) 3-7 b Carmelo and reason using IQR AO3 M arrange in order or 6 3 A cao One of (median), 7(LQ), 3(UQ) identified M Identify any two of, 7 and 3 AO3 B ft from (a) Carmelo - he has a lower IQR oe (IQR must be part of the statement) Issue June 06 Pearson Education Limited 06 9

6 3 a m = 5 3 or 3 oe AO M M for gradient for method to find c eg. = 3 + c or y = y = 3 x + 3 (x ) b x y or m = 6 oe 3 3x + y = A AO M M found values of m and c substituted in y = mx + c shown A for conclusion from correct gradients 6 0 (=.3) or or or 30 or 36 or 33 or 30 or or or ( ) 65 or A AO3 M Any one frequency density (without contradiction) or, e.g. cm = 5 or clear association of area with frequency M Any fully correct complete method; condone one error in bar width or bar height 9 Issue June 06 Pearson Education Limited 06

7 5 a (3x + )(x + ) = 00 AO, AO M or (x 3x) + (x + ) + 3x = 00 oe or (x 3x) + ( x ( )) + ) + 3x + + = 00 oe other partitions are acceptable but partitioning must go on to form a correct equation. 6x + 7x 98 = 0 * A Accept 6x + 7x + = 00 if M awarded b (3x + )(x 7) (= 0) AO M * Answer given or x or x If not M then M for (3x ±)(x ± 7) 7 0 or x x = 3.5 A Dependent on at least M Ignore negative root (Area =) or (3 3.5) ( 3.5 ) A 6 M ft Dependent on at least M and x > 0 Issue June 06 Pearson Education Limited 06 93

8 or BAD 77 and ABD 39 or BA " X" 6 where X is on PA produced or a fully correct method to find angle ADB AO M also accept M for BAD 77 or ABD 39 (angles may be stated or marked on diagram) B Opposite angles in a cyclic quadrilateral add up to 80 o 7.5 or.5 or.5 or 3.5 or.5 or 3.5 y ( ) 6 5 A cao AO B B Alternate segment theorem oe M A A accept 83 or 7.55 or 7.5 ( depending on M) NB. Answer must come from correct working 9 Issue June 06 Pearson Education Limited 06

9 8 3x ( x ) ( x ) AO M correct method for divsion (x + )(x ) M correct factorisation of x eg 3( x ) (3 x ) M correct single fraction ( x ) x A l AO M l 30 or l = M For exact expression or answer which rounds to 9. sin (AVO) =.5/ 9.0 (= ) M For a correct expression for sin AVO or cos AVB 58.6 A awrt 58.6 cos (AVB) = ( )/( ) (=0.5...) 0 ai (0, 5) AO B aii (3, 0) B aiii (, 5) B b translation 0 AO B Issue June 06 Pearson Education Limited 06 95

10 d y 8x x d x AO M (M for one term differentiated correctly) 8 x x 0 M dep on M 3 x or x = 0.5 oe 8 M (0.5, 6) 5 A AE AD DE oe AO M may be fully or partially in terms of a and/or b eg. DE = 3 DB or BE = 3 BD M correct use of ratio AE b + a A BC BA AD DC (=3b + 6a) M may be fully or partially in terms of a and/or b eg. AE (b + a) and BC 3(b + a) 5 A NB Correct expressions for BC and AE must be given 96 Issue June 06 Pearson Education Limited 06

11 3 a + 3d = 7 or a + 9d = 35 or 35 7 = 6d AO M M for 7 = p + q and 35 = 0p + q d = 3 A p = 3 and q = 5 a = 8 A ft from d = 3 u = 8 and u50 = ( '8' (50 ) ' 3') oe A M 50(8 55) Issue June 06 Pearson Education Limited 06 97