Version 1.0. abc. General Certificate of Secondary Education. Mathematics Specification A. Paper 1 Higher. Mark Scheme
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1 Version 1.0 abc General Certificate of Secondary Education Mathematics 4301 Specification A Paper 1 Higher Mark Scheme 008 examination - June series
2 Mark schemes are prepared by the Principal Examiner and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation meeting attended by all examiners and is the scheme which was used by them in this examination. The standardisation meeting ensures that the mark scheme covers the candidates responses to questions and that every examiner understands and applies it in the same correct way. As preparation for the standardisation meeting each examiner analyses a number of candidates scripts: alternative answers not already covered by the mark scheme are discussed at the meeting and legislated for. If, after this meeting, examiners encounter unusual answers which have not been discussed at the meeting they are required to refer these to the Principal Examiner. It must be stressed that a mark scheme is a working document, in many cases further developed and expanded on the basis of candidates reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this Mark Scheme are available to download from the AQA Website: Copyright 008 AQA and its licensors. All rights reserved. COPYRIGHT AQA retains the copyright on all its publications. However, registered centres for AQA are permitted to copy material from this booklet for their own internal use, with the following important exception: AQA cannot give permission to centres to photocopy any material that is acknowledged to a third party even for internal use within the centre. Set and published by the Assessment and Qualifications Alliance. The Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number ) and a registered charity (registered charity number ). Registered address: AQA, Devas Street, Manchester 6EX Dr Michael Cresswell Director General
3 Glossary for Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, for GCSE Mathematics papers, marks are awarded under various categories. M A B M dep B dep ft SC oe Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth. Or equivalent. Accept answers that are equivalent. 1 eg, accept 0. as well as 3
4 Paper 1H 1(a) 7.48 B1 1(b) 1.9 B1 1(c) 1 B1 C, A, B B One or two correct B1 3(a) 80. m B1 3(b) (4.9 ) oe eg, or A1 oe eg, 4.9 million or (a) 18 B1 Corresponding angle B1 Allow complete and correct alternative reasons 4(b) ( ) 9 A or 0.7 or 10 or 0 or A1 6 Triangle in correct position (0, 0) (4, 4) (6, ) (± mm) B B1 For correct size and orientation but in wrong position B1 For triangle with two correct vertices B1 Three correct vertices 7(a) x + 3x = 360 B1 oe 7(b) x + 3x = Rearranging linear equation: x terms on one side of equation Allow one error in numerical terms (not 360) 4x = or 4x = 164 or (x =)(their 164) 4 only if (their) 164 > 0 41 A1 4
5 8(a) or 8 3 A A1 1 8(b) 1 7 or 4 (1) or ( +) 0 (8) 0 oe (Their) (their) 0 Allow one error in numerators or ( +) Allow one error in numerators or A1 0 oe Decimal version 3.7 () 1.4 () =.3 (A1) can score M0A0 8(c) 1 oe seen 0. A1 Allow 1 9 Correct key B1 Correct and ordered B One or two errors or omissions B1 or Correct but not ordered B1 10(a) 3 and 7 B B1 For each 10(b) Correct graph between and 4 with good curve through correct points ± mm B1 Allow (4, 6) or (4, 8) or (4, 9) ft From (their)table B1, 6 or 7 of (their) points correctly plotted 10(c) Where the graph crosses the x-axis B1
6 11(a) 70 B1 11(b) 6y = 13 or 3y 1 = 6. 6y = 13 + or 3y = or A oe y = 6 SC (from 6y 1 = 13) 11(c) 16 z = 4 7 or 4 4 z = 7 16 (their) 8 = z z or 4 7 = 4 or z = (their) 8 16 or z 4 = A1 11(d) ( x + 1) B B1 For ( x +1) or 10 ( x + x +1 x + ) x + 10 or ( x + 1) or ( x +1) 1(a) 90 B1 1(b) ft Their 90 or ( ) oe A1 ft 13(a) A1 13(b) 10 6 or or 0.00 seen. 10 A1 SC
7 14(a) π 8 π (their) 8 Must be dimensionally correct, eg, π 16 (not π 8) 30 ( ) π or π ( ) 30 A1 SC 180π or 960 to 1006 cm 3 B1 14(b) (Their)30π = π r 0 or (Their) 30π (0 or 0π) Proceed with ft only if nd scored in part (a) and the answer to part (b) involves π or is 960 r = (their)16 or (their) 16 ft (Their) 30π 4 A1 ft ft (Their) 30π SC Can be awarded if the working in part (b) is unconvincing 1(a) or A1 Not (b) Greater and reason B1 eg, is replaced by a 3b = b + 7 a b = ( b + 7) 3 3a = b + 7 ( b +7) A1 oe eg, 3 ( b + 7) 3 + b or 3. or 6 1 or 6 : 1 PQ 1 PQ = oe eg, = (their) 3. or their 6 1) dep A1 7
8 18(a) 7 B1 Opposite angles (add up to 180) B1 Must see evidence (stated or in working) that opposite angles add up to (b) Angle BAP = (their) 7 DBA = 63 Angle ADB = 4 A1 ADB = 4 19(a) 8 = 7 or 63 = A1 19(b) 30 or 30 6 A1 0(a) 1 h r k or h = r 1 3 or ( ) πr h = k k = 7 A1 k = 4π or 7π from above start ( their) 4. 4 B1 This must be stated for final B1 h = r 0(b) 7 8 = r or r = 8 7 ft Their k if awarded in part (a) 3 A1 ft ft Their k Answer must be in simplest form possible 8
9 or or or or 0.18 (Their)( ) + (their)( ) dep 1 (their)( ) (their)( ) 0.4 A1 (a) 9 or 3 B1 or 9 3 or (=7) B1 or 79 (=7) (b) 9 x = (9 3 ) 4 or (3 ) x = (3 3 ) 4 (for equating powers) (x =) 3 4 x = or A1 Accept or 9 3 BC = a + b + a + 7b or CB = a 7b a b BC = 6a + 9b A1 or CB = 6a 9b Attempt to compare BC and AD ie, One vector is a multiple of the other 4 9 oe 6 eg, 6a + 9b is a multiple of 4a + kb 6 A1 4(a) Sketch showing translation of ( 7 0) B1 Parabola touching x-axis to right of y = x 4(b) Sketch showing one-way stretch (// to y-axis) SF = 3 B1 Parabola touching at origin and inside y = x 9
10 (a) (x +) x + 4x + 4x + 16 (= 6) For expansion (4 terms with 3 terms correct) x + (their) (x + 4) = 6 For substitution (independent of expansion mark) Simplifying to x + 8x 10 = 0 A1 Clearly shown (b) A = (1, ) B = (, 1) B Condone A and B interchanged B1 A = (1, ) or B = (, 1) B1 For x = 1 and x = (from factors of quadratic) but no corresponding y values found 10
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