Unit F Mark scheme

Transcription

1 AQA Qualifications GCSE MATHEMATICS Unit F Mark scheme 43602F June 2014 Version/Stage: V1.0 Final

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 2014 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 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. M M dep A B B dep Method marks are awarded f a crect method which could lead to a crect answer. A method mark dependent on a previous method mark being awarded. 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. A mark that can only be awarded if a previous independent mark has been awarded. ft SC [a, b] Follow through marks. Marks awarded following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation which has some mathematical wth. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as Accept values between a and b inclusive of 15

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 15

5 1(a) ( ) , 600, 900, 1200, , 1300, 1000, 700, 400, 100 mixed number allow one err in adding subtracting A1 1(b) 100 B1ft ft only f answer in part (a) not 5 and crect evaluation of 1600 their 1500 from part (a) if 1300 < their (a) B1 condone 30, (b) zero point four three nought point four three point four three fty three hundredths B1 2(c) (nine) hundred(s) (s) B1 5 of 15

6 (0) 2.4(0) (0) 5(.00) 7.40 Q1ft Strand (i) crect money notation ft only if M0 M0 awarded and a crect total of two amounts given in money notation as a multiple of 10p 4(a) 120, 150 and 180 with none increct B2 any der B1 Two crect multiples in range with at most one increct all three crect with any other multiples of 30 another group of exactly three multiples of 30 4(b) 8 B1 5(a) 35 and 65 B1 5(b) 34 and 76 B1 5(c) 76 B1 5(d) 21 B1 6 of 15

7 6(a) (=) 8 B2 B (b) 19 B1 6(c) 2n 2 + 2n 2n 2 2n (n + 1 n ) B1 7 of 15

8 7 Alternative method their their and 1300 A1 No and 1200 and 1300 Q1ft Strand (iii) Alternative method their their and 325 A1 No and 300 and 325 Q1ft Strand (iii) Alternative method 3 and 4 (next page) at least M2 sced and crect decision f their values at least M2 sced and crect decision f their values 8 of 15

9 Q7 continued Alternative method their their their ( ) A1 No and 27.( ) Q1ft Strand (iii) Alternative method their 50 4 their their A1 at least M2 sced and crect decision f their 27.( ) No and 2400 Q1ft Strand (iii) at least M2 sced and crect decision f their of 15

10 8 Crect der and all four crect values seen in same fmat 3, 3.15, 3.25, 3.5(0) , 3, 3, , 3, 3, (%), 315(%), 325(%), 350(%) , 3.15,, 3 after values 4 2 B3 B2 all four crect values in same fmat three crect values in same fmat and crect der f their values B1 three crect values in same fmat 13 1 SC1 9, 3.15,, 3 with no wking 4 2 seen in same fmat 9(a) 90 B1 9(b) 240 B1 10 of 15

11 9(c) Alternative method B is B1 A and 40 A1ft ft their 410 (value indicated f law firm A) A and 40 is B1A1 Alternative method B1 Line from (90, 150) to (270, 450) A and 40 A1ft ft their 410 (value indicated f law firm A) A and 40 is B1A coin value 3(p) 6(p) 15(p) 30(p) 60(p) 150(p) ( )1.50 ( ) 2.(00) their 3 coin value 197(p) 194(p) 185(p) 170(p) 140(p) 50(p) coin value = 1p, 2p, 5p, 10p, 20p, 50p in pounds their (200 their 3 coin value) 4 dep dependent on second A1 igne truncation rounding after crect value seen SC1 any crect trial: chooses cost of one ange and wks out change f four anges A of 15

12 12 Alternative method 1 (8x =) (8x =) 40 5 A1 Alternative method 2 SC x = x = their ( ) 8 5 A1 SC = > > B1 B1 B1 14(a) x = 2 B1 14(b) Crect straight line drawn B1 at least 3 diagonal squares long 14(c) 2, 2 B1ft ft their intersection with line A only if B0 in part (b) 12 of 15

13 15 Alternative method (3 + 1) 619 their 619 (3 1) their (3 1) their their 619 (2476 their 619) their A1 Alternative method 2 (3 + 1) (3 1) 4 2 (3 1) (3 + 1) their their A1 13 of 15

14 (Tablet Wld) A A1 (IT Supplies) 138 B1 (PC Heaven) IT Supplies Q1ft Strand (iii) ft f crect decision based on their values, must have both method marks and a total f PC Heaven 17(a) a 6b 6b + a B2 B1 (1)a 6b 17(b) m(m 2) m (m 2) (m 2)m (m 2) m B1 17(c) 5x 2 15x B2 B1 5x 2 15x 15x + 5x 2 14 of 15

15 23, 25 and 29 B2 any der B1 three crect and one increct 18 two crect and none one increct SC1 any three all four of 21, 22, 26 and 27 with no other number 19 A crect pair of fractions meeting all conditions B3 B2 eg 9 1 and and 4 1 a pair of fractions which add to 3 1 but which do not satisfy all conditions eg, 6 1 and and any fraction less than 3 1 crectly changed to common denominat with at least one numerat crect B1 1 changed to any equivalent fraction 3 2, 6 3, , 1 1 any fraction less than of 15