Version 1.0. abc. General Certificate of Secondary Education. Mathematics Specification A. Paper 1 Higher. Mark Scheme

Transcription

1 Version.0 abc General Certificate of Secondary Education Mathematics 4306 Specification A Paper Higher Mark Scheme 2009 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 2009 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 5 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. eg, accept 0.5 as well as 2 3

4 Paper H Writing at least two fractions with a common denominator oe eg, converting at least two to decimals or % Allow one error as long as the method is sound A oe or [6 7] + [6 2] or better or 2 ( 7 + 2) The first two do not need 3 to be seen for this Allow one sign or arithmetic error Do not allow a conceptual error, eg, ( ) 30 ( 3) or or is sufficient, ( 3) not needed 0 ft ft (max 2 out of 3 marks) from one sign or arithmetic error in st two steps (no further errors) Max B2 For a misread 3(a) 23 Corresponding (angles) 3(b) A 4(a) x 3 Allow x 3 4(b) 2x Allow 2 x or x + x or x 2 but not x2 4(c) x + their (x 3) + their (2x) = 25 ft Their answers for (a) and (b) Must be an equation with expression for each person (x =) 7 Aft SC For x = 7 with no equation or wrong equation SC For correct solution of an equation of the form ax + b = 25 4

5 5 ( ) or 92 oe 480 their 92 or 288 dep scores M2 00 (420 3) or or 40 or oe Not 3 of 420 or use of 30% for their 40 or 280 dep or or scores M2 288 and 280 and Supersave A 6(a) Correct key Correct and ordered B2 One or two errors or omissions or Correct but not ordered 6(b) Only four of these results are greater than 24 most people require significantly fewer lessons than this oe median = 9, this is a better average to use or small sample (not representative) so mean of 24 might be a reasonable estimate 7(a) T = 45w + 20 B2 oe for two of T =, 45w or +20 7(b) 245 (Their )/45 oe eg, (this implies the st ) 5 A 5

6 A cm 2 Independent units mark accept mm 2 only if both lengths are changed to mm or 35 or or their 35 or 400 their A SC For 24 or 86 or 24:86 0(a) Rotation Accept turn 90 clockwise oe Centre the origin oe 0(b) 5 4 (a) 3x 8 2 or 3x 6 Condone = sign for x 2 A x = 2, x < 2, x > 2, x 2 all score A0 (b) 2,, 0, B2 eeoo 2 Correct mid-points correct or correctly rounded frequencies Correct mid-points correct frequencies are 2, 6 23, 0 36, 4 20, 8 0 Correctly rounded frequencies are 0, 20, 40, 20, 0 So 2 0, 6 20, 0 40, 4 20, 8 0 score Allow one error for this st M mark their mid-pt frequency Must be consistent, eg, all lcb or all ucb Their dep Dep on 2 nd M mark 9.8 A 6

7 3(a) Statement 3(b)(i) 08 3(b)(ii) 80 2 their 72 or 08 their 72 Their 72 must be acute (using quadrilateral BCDF) 36 A ft Final answer must be acute 4(a) 2x 3 + 2x 2 + 3x 2 5x Allow error in one term for A Fully correct for A 2x 3 + 5x 2 5x Aft ft If M mark awarded 4(b) 3mh(h 5m) B2 For any of these 3m(h 2 5mh) 3h(mh 5m 2 ) mh(3h 5m) Also for 3mh( ) ie, removing the correct common factor but with mistakes in the brackets. 5 Sight of or or their or their oe must use speed time (need not change either number) A SC2 For 8. 0 x if x 3 or 40 SC For sight of digits 8 6 (gradient =) 3 y = their mx 2 B2 B2 If m = 3, m = 3 or m = other negative value For two of y =, their mx (m as above) or 2 7

8 7(a) 30 2 M0 for 2 9 A 7(b) Median at 26 Quartiles at 8 and 33 Whiskers at 5 and 50 Allow 25.5 to 26.5 (inclusive) Allow 7.5 to 9 and 32.5 to 34 (all values inclusive) 7(c) comparing medians ft From their box plot in (b) for both marks st batch = 26 and 2 nd batch = 3 or on average more growth All remarks must be consistent with their box plot comparing IQR or comparing Range st batch = 5 and 2 nd batch = st batch = 45 and 2 nd batch = 32 or less spread more consistent growth or less spread more consistent growth or or 2 20 oe or oe for inverting their second fraction Clearly showing the division of 45 by or 20 4 or or 2 A oe from 3 27 or 729 from 27 2 or Not 3 3 = oe 27 Complete solution showing all intermediate steps Answer given so precise explanation needed 8

9 20(a) y x or y = k x oe allow y k x but not y = x k = 3 A y = 3 x A oe must make this final statement SC For 3 from 25 and 5 20(b) x is multiplied by 4 B2 for When y = = 3 x 0 = x or x = 00 or Explanation such as When y doubles then x doubles ie, x is multiplied by 2 or x is multiplied by and 4 Both answers required for 73 to 77 and 203 to 207 and total of these two = 380 B2 For 73 to 77 or 203 to = a( ) 2 + b( ) Condone missing brackets 0 = a(4) 2 + b(4) Condone missing brackets 0 = a b or 0 = 6a + 4b A oe a = 2 and b = 8 A Their (2x 2 8x) = x Must attempt to equate the two equations (x =) 4 2 A No need to state that y = 4 2 9

10 23(a)(i) a + c oe c a 23(a)(ii) 2a + 2b oe a a + 2b or 2b 2a 23(a)(iii) 2b + 2c oe 2b + c + c or 2c 2b 23(b) 2 ( 2a + 2b) + 2 ( 2b + 2c) = a + c oe must be clearly shown 23(c) Parallelogram since DG = EF or DG and EF are opposite sides and they are equal and parallel oe DG = EF (not vectors) is not enough Must state equal and parallel 24(a) 290 Accept (b) 0 or 250 Accept 08 or (a) h 2 = h = 32 A Area = ft For their h = ( ) for this M mark only 32 = 6 2 = 4 2 Hence, area = 8 2 A This mark is for simplifying the surd or showing correct surd manipulation Look for complete explanation since answer given 25(b) (length =) 24 2 or oe for division of area by width either at this stage or later A oe rationalising the denominator 4 3 A Fully simplified 0