Set 1 Teacher Booklet GCSE H November

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1 AQA Qualifications Practice Papers Set Teacher Booklet GCSE MATHEMATICS Unit 460H Mark Scheme 460H November 0 Final version.0

2 Mark schemes are prepared by the Lead Assessment Writer considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the stardisation events which all associates participate in is the scheme which was used by them in this eamination. The stardisation process ensures that the mark scheme covers the students responses to questions that every associate understs applies it in the same crect way. As preparation f stardisation each associate analyses a number of students scripts: alternative answers not already covered by the mark scheme are discussed legislated f. If, after the stardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer. It must be stressed that a mark scheme is a wking document, in many cases further developed eped on the basis of students 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 eamination paper. Further copies of this Mark Scheme are available from aqa.g.uk

The stardisation process ensures that the mark scheme covers the students responses to questions that every associate understs applies it in the same crect way.

3 Glossary f Mark Schemes GCSE eaminations are marked in such a way as to award positive achievemena nt wherever possible. Thus, f GCSE Mathematics papers, marks are awarded under various categies. M A B Q ft SC M dep B dep oe Method marks are awardedd f a crect method which could lead to a crectt answer. Accuracy markss are awarded when following on from a crect method. It is nott necessary to always see s the method. This can be implied. Marks awarded independent of method. Marks awarded f Quality of Written CommunicaC ation Follow through marks. Marks awardedd f crect wking following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretationn which has some mathematical wth. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous p independent mark has been awarded. Or equivalent. Accept answers that aree equivalent. eg, accept 0.5 as well as [a, b] Accept values between a b inclusive..4 Allow answers which begin.4 eg..4,.4,.49. Use of brackets It is not necessary to see the bracketed wk to award the marks. Version.0 Page of 4

It is nott necessary to always see s the method. This can be implied. Marks awarded independent of method. Marks awarded f Quality of Written CommunicaC ation Follow through marks.

4 Eaminers should consistently apply the following principles Diagrams Diagrams thatt have wking on them should bee treated like nmal responses. Iff a diagram has been written on but the crect response is within thee answer space, the wk within the answer space should be marked. Wking on diagrams that contradicts wk within the answer space is not to be considered as choice but as wking, is not, therefe, penalised. Responses which appear to come from increct methods Whenever there is doubt as to whether a cidate has used an increct methodd to obtain an answer, as a general principle, the benefit of doubt must bee given to the cidate. In casess where there is no doubt that the answer has come from increct wking then the cidate should s be penalised. Questions which ask cidates to t show wking Instructions on marking will be given but usuallyy marks are not awarded to cidates who show no wking. Questions which do not ask cidates to show wking As a general principle, a crect response is awarded full marks. Misread miscopy Cidates often copy values from a question increctly. If the eaminer thinks that the cidate has made a genuine misread, then only the t accuracy marks (A B marks), up to a maimum off marks are penalised. The method marks can still be awarded. Further wk Once the crect answer has been seen, further wking may be igned unless it goes on to contradict the crect answer. Choice When a choice of answers / methods is given, mark each attempt. If both methods are valid then M marks can be awarded but any increct answer method would result in markss being lost.. Wk not replaced Erased crossed out wk that is still legible should be marked. Wk replaced Erased crossed out wk that has been replaced is not awarded marks. Premature approimation Rounding off too early can lead to inaccuracy inn the final answer. Thiss should bee penalised by mark unless instructed otherwise. Page 4 of 4 Version.0

Wking on diagrams that contradicts wk within the answer space is not to be considered as choice but as wking, is not, therefe, penalised.

5 MARK SCHEME GCSE MATHEMATICS 460H NOVEMBER 0 Q Answer Mark Comments oe 4 = 8 A 4.5 Aft oe ft their rearrangement with one err if awarded (a) A SC 480 SC 860 SC 79 SC any table value rounded to sf SC 75 SC 70 without awarded (b) ( ) ( their increct total of eact values f July in part(a)) 40 Aft ft 855 their increct total of eact values in part(a) Alternative Method their Aft ft 860 their 70 from rounding in part(a) Page 5 of 4 Version.0

to sf SC 75 SC 70 without awarded (b) (49 + 49 + 59 + 59 + 9 855) (99 + 99 + 49 + 49 + 9 75 their increct total of eact values f July in

6 Q Answer Mark Comments (a) = 5 B oe 5 = Condone 5 = (b) a = 4 b = B B a = 4 b = a = 5 b = 00 (both in either der) a = 55 b = 00 (either der) B crect list of square numbers to 00 allow one err omission 4 Crect method to change 5 8 into fractions with common denominat with at least one crect numerat eg 6, (eithe er way around) Crect fractions No A Alternative method Crect method to calculate 5 8 of a chosen value of the t same value eg Crect evaluations No A Page 6 of 4 Version.0

$fractions with common denominat with at least one crect numerat eg 6, 5 4 4 (eithe er way around) Crect fractions No A Alternative$

7 MARK SCHEME GCSE MATHEMATICS 460H NOVEMBER 0 Q Answer Mark Comments Alternative method Crect method to change 5 8 into decimals percentages 5 = (%) 8 = 0.66(6 ) (.6 )(%) 67(%) No A Crect consistent decimals percentages 5(a) 8 () () 9 () () () () 4 () () 6 Allow on prime fact tree repeated division Condone 8 () () etc. f this mark () () () A Allow on prime fact tree repeated division Aft ft any product of prime numbers in inde fm if awarded 5(b) 9 B B answer 8 = 4 () () () Page 7 of 4 Version.0

6 )(%) 67(%) No A Crect consistent decimals percentages 5(a) 8 () () 9 () () () () 4 () () 6 Allow on prime fact tree repeated

8 Q Answer Mark Comments 6 Line (0900,0) to (00,80) Hizontal line 4 squa res long fr stage Hizontal line square across f stage 4 Line squar re across squares down f stage line squa ares across down to time ais to represent arriving homee f stage 5 B Bft Bft Bft need not be straight, but gradient must be positive f all points on the line ft fromm the end off the preceding part of the journey each stage must be in crect der The sections f stages 5 need not be straight, but gradient must be negative f all points on the line 7(a) 0 B B 0 0 multiplies out simplifies with one err 7(b) a (a + b + ) B B a + a (b + ) ) a (a + b) + a a (a + b + ) three terms in bracket with two crectt 7(c) oe 5 A SC ( =) 5 < together Page 8 of 4 Version.0

part of the journey each stage must be in crect der The sections f stages 5 need not be straight, but gradient must be negative f all points on the line 7(a) 0 B B 0 0 multiplies out

9 MARK SCHEME GCSE MATHEMATICS 460H NOVEMBER 0 Q Answer Mark Comments 8 0 0( %) ( %) ( %) 0( %) 44( %) 44( %) A oe Crect method to calculate comparable values A Qft Any indication Str (iii) crect decision based upon their values after awarded 9(a) 4n + B 9(b) (4n, their 4n + ) Bft ft their (a) 9(c) y = + 4n circled in (a) y = 6n circled in (a) y = 6n + circled in (a) y = + B oe all equations B y = m + c with m = c = B B B (a) four terms, three crect with a term in + k with k A (b) 8a 7 b 9 B B two crect from 8, a 7 b 9 B crect answer with multiplication sign(s) Page 9 of 4 Version.0

in (a) y = 6n circled in (a) y = 6n + circled in (a) y = + B oe all equations B y = m + c with m = c = 0 445 544 B B 445 544 450 540 450 549 B 450 540 545 549 (a) 5

10 Q Answer Mark Comments (0) 0 9 A SC their , with digits 454, crectly converted to stard fm SC 4.54(0) 00 (million) SC (a) oe Condone numerat as = r = A SC chooses c a value f, evaluates the crect c numbers of each colour bead a shows that the fraction of blue beads b can be written in the fm eg. =, red =, white = 6, blue = (b) = 0.9 oe = =.7 ( =) 7 A Alternative method Chooses a value f, evaluates the crect numbers of each colour bead the crect proption of blue beads. eg, 6, 9 (oe fraction, decimal percentage) Chooses a value f, evaluates the crect numbers of each colour bead the crect proption of blue beads, f a proption closer to 90% eg, 6, 9 (oe fraction, decimal percentage) 4, 8, 6 4 (oe fraction, decimal percentage) 7 ( =) 7 A Page 0 of 4 Version.0

$eg, 6, 9 (oe fraction, decimal percentage) Chooses a value f, evaluates the crect numbers of each colour bead the crect proption of blue beads, f a proption closer to 90% eg, 6, 9 (oe fraction,$

11 MARK SCHEME GCSE MATHEMATICS 460H NOVEMBER 0 Q Answer Mark Comments Alternative method ( =) 7 A 4 ( y)( + y) B B ( y)( y) ( + y)( + y) ( y) ( + y) (4 + y)( y) (4 y)( + y) 5 Crect equation of any line associated inequality Crect equations of all four lines associated inequalities y y + y 8 Use of included inequality f at least one of the solid lines Use of strict inequality f at least one of the dashed lines A Qft Igne increct inequality signs Igne increct inequality signs Str (i) crect use of notation Page of 4 Version.0

of all four lines associated inequalities y y + y 8 Use of included inequality f at least one of the solid lines Use of strict inequality f at

12 Q Answer Mark Comments 6 9 = (7) = B 8 = 8 8 r 8 oe im mplies r 8 = 8 = 8 = A All three numbers crectly evaluated in crect der (7) A 8 9 Page of 4 Version.0

13 MARK SCHEME GCSE MATHEMATICS 460H NOVEMBER 0 Q Answer Mark Comments 7 ( + ) 4( ) Igne RHS denominat Allow one err Igne RHS denominat this also implies first mark ( )( + ) ( )( + ) ( + ) ( + ) + 4 = 0 A As denominat Igne LHS this also implies third mark ( + 7)( ) (= 0) Crect method to solve their quadratic equation by Crect substitution into the quadratic fmula Crect completion of the square Crect factisation 7 Aft ft their quadratic but must be eact values (integers, fractions, decimals surds) SC = 7 = Page of 4 Version.0

$of the square Crect factisation 7 Aft ft their quadratic but must be eact values (integers, fractions, decimals surds) SC = 7 = Page of 4$

14 Copyright 0 AQA its licenss. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges f AQA are permitted to copy material from this booklet f their own internal i use, with the following imptant eception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to t a third partyy even f internal use within the centre. SP//

internal i use, with the following imptant eception: AQA cannot give permission to schools/colleges to

General Certificate of Secondary Education November 2012. Mathematics (Linear) B 4365 Paper 1 Foundation Tier. Final. Mark Scheme

General Certificate of Secondary Education November 2012 Mathematics (Linear) B 4365 Paper 1 Foundation Tier Final Mark Scheme Mark schemes are prepared by the Principal Examiner and considered, together