MARKING SCHEME

Higher Tier GCSE MathematicsPaper 1 Autumn 20087. (a) Least = 975Greatest = 1025(b) Use of 50 × "their greatest volume"= 50 × 1025= 51250 (cm 3 ) (= 51·25 litres)51·5 (litres) ≤ tank (≤ 52·5 litres)50 of the largest jugs will always fit into the tankbecause 51·25 is < minimum tank (51·5 litres).8. (a) 20c 9 d 5(b) 2a(3b – a)9. 4x ≥ – 22 OR equivalentx ≥ – 22/4 (I.S.W.) (–5·5)10. 131211.52(4x – 1) – (2x + 7) = × 628x – 2 – 2x – 7 = 156x = 24x = 24/6 I.S.W. (= 4)12. (a) largest = 18 = (1·5)largest 12middle = 15 = (1·5)middle 10smallest = 9 = (1·5)smallest 6(All same ratio, therefore similar triangles)(b) For example, QR = 1510 12MarkB1B1M1A1B1E27B2B24B2B13B22M1M1A1A14B2M1CommentsC.A.O.C.A.O.F.T. providing 1000 < "their greatest volume" ≤ 1100C.A.O. No need for upper bound.Note also the correct division arguments:51·5/1·025 gets M1, and evaluated as 50·2(4) gets the A1.The 51·5 gets the B1OR 51·5/50 gets M1 and 1·03 gets the A1.E1 for an explanation that only uses 52 litres for the tank andstates that it is always possible.B1 for 20c 9 d k OR 20c n d 5 OR kc 9 d 5Ignore any extra × signs.B1 for a(6b – 2a) OR 2(3ab – a 2 )B1 for each side provided there is a correct inequality sign.F.T. until 2 nd error.F.T. equivalent difficulty if B1 has been awarded.0 marks if they only use = sign. Condone use of the > sign.For all 4 correct.B1 for any 3 correct.Must clear fractions by a valid methodFor handling 2 of the 3 terms correctlyFor the Ms, 2x+ 7 is acceptable, but the first A mark is A0.For handling all 3 terms correctlyCollecting terms. F.T. until 2 nd error if at least M1 awardedUnsupported answer of x = 4 gets all 4 marks.B1 for finding any 2 corresponding ratiosB2 for ‘The triangles have been multiplied by 3/2 OR 2/3’OR‘the scale factor is 3/2 OR 2/3’, etcOR‘both cancel to 3:5:6’ – must be all 3 correct values.Any correct equation with only QR unknownRQ = 12·5 (cm)A14C.A.O.13. (a)3 2 and on the first branch5 5B1C.A.O.(b)2 and 97 on the second branches92 7 ×5 9=1445B1M1A14C.A.O. Accept only on one branch provided the other branch isempty.F.T. their tree if probabilities are between 0 and 1 exclusive andNOT all ½.10