AQA Qualifications. GCSE Mathematics. Unit H Mark scheme H June Version 1: Final mark scheme

Transcription

1 AQA Qualifications GCSE Mathematics Unit H Mark scheme 43601H June 2015 Version 1: Final mark scheme

2 Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation events which all associates participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every associate understands and applies it in the same crect way. As preparation f standardisation each associate analyses a number of students scripts: alternative answers not already covered by the mark scheme are discussed and legislated f. If, after the standardisation 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 and expanded 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 examination paper. Further copies of this Mark Scheme are available from aqa.g.uk Copyright 2015 AQA and 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 use, with the following imptant exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even f internal use within the centre.

3 MARK SCHEME GENERAL CERTIFICATE OF EDUCATION MATHEMATICS 43601F JUNE 2015 Glossary f Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, f GCSE Mathematics papers, marks are awarded under various categies. If a student uses a method which is not explicitly covered by the mark scheme the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their seni examiner if in any doubt. M A B Q ft SC M dep B dep Method marks are awarded f a crect method which could lead to a crect answer. Accuracy marks are awarded when following on from a crect method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. Marks awarded f Quality of Written Communication Follow through marks. Marks awarded f crect wking following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation 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 independent mark has been awarded. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as 2 1 [a, b] Accept values between a and b inclusive Accept answers which begin 3.14 eg 3.14, 3.142, Use of brackets It is not necessary to see the bracketed wk to award the marks. 3 of 18

4 Examiners should consistently apply the following principles Diagrams Diagrams that have wking on them should be treated like nmal responses. If a diagram has been written on but the crect response is within the 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, and is not, therefe, penalised. Responses which appear to come from increct methods Whenever there is doubt as to whether a candidate has used an increct method to obtain an answer, as a general principle, the benefit of doubt must be given to the candidate. In cases where there is no doubt that the answer has come from increct wking then the candidate should be penalised. Questions which ask candidates to show wking Instructions on marking will be given but usually marks are not awarded to candidates who show no wking. Questions which do not ask candidates to show wking As a general principle, a crect response is awarded full marks. Misread miscopy Candidates often copy values from a question increctly. If the examiner thinks that the candidate has made a genuine misread, then only the accuracy marks (A B marks), up to a maximum of 2 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 gs on to contradict the crect answer. Choice When a choice of answers and/ 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 marks 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 approximation Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark unless instructed otherwise. 4 of 18

5 1(a) Positive Igne any other description Accept eg strong positive, weak positive crelation [28, 29] seen 40 + [24, 30] [64, 70] [28, 29] may be seen on graph 1(b) [68, 69] A1 SC1 Answer [78, 79] with crect point line(s) marked on graph SC1 Answer [91, 92] [28, 29] seen even with other values different answer given A0 Crect wking up to [68, 69] but then gives the answer 70 A etc A etc A1 5 of 18

6 Suitable hypothesis Q1 Strand (i) eg Girls are me likely to study Economics Me boys study Economics Girls are less likely to study Economics than boys 2(a) Must mention girls/ boys and studying Economics Must be a suggested outcome and not a question Condone a crect hypothesis followed by a reason why it may be true May start I think, I predict, I believe and condone should be Condone home economics Two-way table with boys/ girls as row/ column and Yes/ No as column/ row B2 boys/ girls Yes/ No B0 questionnaires intended f individuals to complete 2(b) Condone a list where all four options can be wked out ie you can tell how many: (1) boys planning E, (2) boys not planning E, (3) girls planning E, (4) girls not planning E This may also be seen as two separate lists/ tally charts Condone questions as headings Igne any attempt to fill in cells and allow any extra rows/columns eg Don t know Frequency If the student gives a data collection sheet and a questionnaire, igne the questionnaire Yes/ No could be indicated by a tick cross 6 of 18

7 3(a) 9 : 5 : (white) 30 (brown) 20 (granary) seen implied 50 (white) and 30 (brown) and 20 (granary) seen implied A1 Bar drawn in crect position and shaded (in crect der) with crect length, divisions and width ft ± 2 1 small square ft their 50, 30 and 20 with bar total 100% 3(b) Mark the graph first: a crect bar implies all 3 marks A1 Shading can be incomplete (eg only two parts shaded) as long as unambiguous can use labelling eg white/ brown/ granary W/B/G A bar drawn in the wrong der must have the crect shading Crect bar with increct width position A1B0 A1B0 Condone a bar in the wrong position if it is a replacement f an increct bar in the right position 30, 18, 12 (30 is f white) M0A0B0ft Any crect section in the graph can imply but you must check it is not from increct wking eg = 2 20%, = 3 30%, = 5 50% Then bar drawn 20 : 30 : 50 Do not award f brown = 30 if this method is seen but they can have ft if their bar follows through from their wking and totals 100 M0A0ft 7 of 18

8 (female) (40 10) 2 15 (male female) their 18 their 15 Condone their 15 7 (males sold) (10 (22 their 18)) dep Condone A1 Answer 13 often comes from 18 5 so if 18 is seen award the first mark M0A0 3 should not be awarded full marks if it comes from an increct method 5(a) Point marked at (100, 0.18) ± 2 1 small square B2 answer of (b) A crect answer using any relative frequency from the graph using the average of all of them Answer of 500 out of 5000 Answer The calculation f may be seen in stages eg 100 per 1000 and B2 8 of 18

9 ( ) A1 their A1ft ft their SC A wrong start can still pick up the last two marks eg = = = 1200 Allow 900 f their 2700 eg said No Answer 7200 (either M can be implied) 1350 = 20% Answer 5400 (either M can be implied) M0A0 A1ft M0A0A1ft M0A0 A1ft M0A0 A1ft as a full method, answer A1A as a full method with increct answer A1A0 9 of 18

10 7(a) % A1 3 without % A0 Embedded answer: = 1 (table blank) A0 Table wins unless blank % (b) Accept with wking A1 SC (...) Condone mistakes in number of zeros f and allow recovery f 3 marks Accept answers as eg 7.34 million F the special case allow the marks if they give full values but then round SC B0M0A0 10 of 18

11 8(a) B2 ft 0.013(8...) ft their answer with at least 3 sf given in standard fm to 2 sf SC ( ) ( ) Digits 325 imply 8(b) 32(.5) 3.2(5) 10 (1) (1) A1 SC1 0.03( ) 3( ) 10-2 Crect box plot with min 40, lower quartile 42, median 43, upper quartile 43.5 and max 46.5 B3 B2 any four values crectly plotted lower quartile 42, median 43 and upper quartile 43.5 lower quartile 42 median 43 upper quartile 43.5 Allow ± ½ small square tolerance 9(a) The box plot wins but if blank the stated values may gain up to B2 Mark intention throughout Accept unconventional plots eg line through middle of box arrows/ dots/ longer vertical lines/ no endings on whiskers any depth of box any vertical alignment but not overlapping Ben s (max B2 if it overlaps Ben s) Assume a box without a median line represents the LQ and UQ 11 of 18

12 Z because her inter-quartile range is smaller Z and her inter-quartile range = 1.5 and Ben s = 2 ft Accept Z because her range is smaller Z and her range = 6.5 and Ben s = 7 ft their complete box plot 9(b) If values are quoted they must be crect, but follow through their values from a (completed) box plot They must be using inter-quartiie range (IQR) range. Igne comments about other measures If they do not have a complete box plot, then assume they are using the graph Must use the wds range (inter-)quartile range do not accept a description of the measure If the crect answer is seen but it ds not match their box plot, please escalate the clip Accept eg Z because her IQR is closer/ lower (a) B2 at least two crect probabilities in the crect position Accept decimals percentages equivalent fractions. 3 4 may be % 3 may be 0.6(0) 60% 5 2 may be 0.4(0) 40% 5 12 of 18

13 Alternative method their their their their their their dep % A1ft ft their tree diagram (f probabilities < 1) Alternative method their (b) and 3 3 their their ( 1 their their their ) dep % A1ft ft their tree diagram (f probabilities < 1) 9 20 from 3 3 (and crect tree diagram) M0M0A0 4 5 Allow up to if all four combined probabilities shown next to tree diagram and no wk of further merit seen Students may restart in part (b) and not use their tree diagram Crect method seen f top, bottom middle two probabilities 13 of 18

14 = = Condone 150 [0.36, 0.37] implied by [54, 55.5] 55 A1 11(a) Do not allow 1040 as a misread f 1200 eg = 63 but there is a crect method using 1040 where the student wks out that there are 130 in the sample from the main school and wks out (which evaluated is 55) M0A0 (A1) 14 of 18

15 Alternative method their and seen eg Condone (...) Condone with seen 72 A1 Alternative method (b) (160 their 16) their seen 72 A1 Two numbers with a difference of 16 Allow eg as a misread of 1200 f up to M2 Check table f possible creditwthy wk If they use an increct scale fact in (b) that follows through from (a), then escalate the clip In Alt 1 f the second accept their if their 9 comes from an arithmetic err with full method shown 11 and 9 seen even with other wrong wking M2 15 of 18

16 120 and 100 in crect positions in the table bar 4.5 large squares high bar 1 large square high Strand (ii) 12 Crect vertical scale key shown Q1 1 large square = 20 ribbons 5 small squares = 4 ribbons scale of 2 per cm Only need to show one graduation f scale but if me shown must be crect If crect scale is shown igne any wkings on the histogram Crect frequency on one bar is equivalent to a key as long as the scale ds not contradict Look f key near table but do not allow it written as wking in the wking lines 16 of 18

17 Alternative method 1 Identifying possible totals as 4, 6 and 5, 6 At least three of 4, 6 and 6, 4 and 5, 6 and 6, 5 only dep Igne 5, 5 and 6, 6 f May be in sample space diagram list 3 4 crect totals chosen in sample space list (with outcomes) outcomes stated Denominat of % A1 Alternative method 2 SC2 SC (from all 4 outcomes) 2 (from 4, 6 and 5, 6) 36 Identifying possible totals as 4, 6 and 5, 6 Igne 5, 5 and 6, 6 f May be in sample space diagram list 13 Complete list of 15 pairs with only 4, 6 and 5, 6 chosen dep Condone list with any of 1, 1 and 2, 2 etc included 15 outcomes stated Denominat of % A1 SC2 SC (from all 4 outcomes) 2 (from 4, 6 and 5, 6) 36 The special cases must come from either no wking the methods stated in brackets If a sample space list is used the possible totals must be identified eg ringed f but a crect numerat with a crect sample space list may imply the crect pairs f A sample space diagram may be incomplete if unambiguous In any list diagram allow one err omission repeat and always allow 1, 1 and 2, 2 etc Sample space with 36 outcomes and 6 possible pairs chosen (including 5, 5 and 6, 6) is likely to lead to the answer M0M0A0 17 of 18

18 Alternative method seen Condone (9, 9.5] [0.145, 0.15) 65 A1 Must be using 9.5 and Alternative method seen Condone = [0.145, 0.15) n = a 14 and = 9.57 and [0.145, 0.15) (n + 1) = b where a < 9.5 and b > A1 Must be using (9.5 and) = answer 65 Answer only of 65 A0 B0M0A0 Allow conversion to millilitres throughout 9.49 is equivalent to 9.5 so can sce full marks but do not accept use of eg f the A mark 18 of 18