Unit H Mark scheme

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1 AQA Qualifications GCSE Mathematics Unit H Mark scheme 43602H November 204 Version/Stage: v.

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 204 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 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 [a, b] Accept values between a and b inclusive. 3.4 Allow answers which begin 3.4 eg 3.4, 3.42, Use of brackets It is not necessary to see the bracketed wk to award the marks. 3 of 9

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 mark unless instructed otherwise. 4 of 9

5 Q Answer Mark Comments (a) B any clear indication (b) 34.6 B any clear indication (0) their.2(0) dep 4 00 ( ) 2.80 Q Strand (i) Must have crect units do not accept 2.80p 280p of 9

6 (Nisha) 5 their 2800 their dep (Nisha) (Dipen) their their 4 40 their 2800 their dep dependent on 3 rd method mark (Dipen) 2660 and 2240 A 420 and No Qft Strand (iii) crect comparison f their values, with at least one crect value 3 Additional Guidance implies minimum first and second Method marks implies minimum third and fourth Method marks 6 of 9

7 4(a) 5, 9, 3, 7, 2 seen allow one err omission = 65 A 4(b) 4n + B2 B 4n (± k) 4(b) Additional Guidance 4 n + is B2 4 n (+ k) is B 7 of 9

8 5 Alternative method x + x + 30 = 0 ( x representing Ann) (x =) 40 A their Aft fraction Alternative method 2 x + x 30 = 0 ( x representing Tom) (x =) 70 A their Aft fraction Alternative method 3 (0 30) A their Aft fraction Alternative method 4 (0 + 30) A their Aft fraction Alternative method A their Aft fraction 5 Additional Guidance 85 0 is M0 A0 A0ft 8 of 9

9 6 6x + 5 2x + 8 allow one err 6x + 5 2x + 8 A fully crect 4x + 23 Aft do not igne fw SC2 4x Additional Guidance Do not allow fw eg. 4x + 23 = 27x sce A0 f final accuracy mark Allow fw in trying to solve equation after 4x + 23 seen to sce A f final accuracy mark 6x + 5 2x 8 4x + 7 4x + 7 alone on answer line is A0 Aft is SC2 Two independent expanded brackets (shown one underneath the other) 6x + 5 2x 8 with 4x + 23 on answer line is A A Two independent expanded brackets shown remotely (same line) 6x + 5 2x 8 with 4x + 23 on answer line is A A Two independent expanded brackets shown remotely without crect answer on answer lines sces zero marks 6x + 5 2x 8 with answer line blank is M0 A0 A0 9 of 9

10 7(a) 5x 29 + x x 40 5 x 8 A SC 8 SC x 3.6 x (b) B x < 4 B2 4 4 condone missing arrow f B2 B 7(b) Additional Guidance Intention must be clear to indicate x < 4 with minimum of a line drawn to the left of hollow circle positioned at 4. 4 Is B2 implies 4 is B 0 of 9

11 8 Alternative method and A both fractions crectly written with common denominat eg. and Y and their and their Alternative method Qft Strand (iii) and crect decision based on their fractions written with common denominat, with at least one crect 0.55 and (%) and 56(%) A Y and their 55(%) and their 56(%) Y and their 0.55 and their 0.56 Alternative method 3 Qft Strand (iii) and crect decision based on their decimals percentages, with at least one crect 0 : : : 50 and 28 : 50 A both ratios crectly written with common right side left side f comparison Y and their 27.5 : 50 and their 28 : 50 Qft Strand (iii) and crect decision based on their ratios crectly written with common right side left side f comparison, with at least one crect of 9

12 8 Alternative method 4 (cont) and A both fractions crectly written with common denominat eg. and Y and their and their Qft Strand (iii) and crect decision based on their fractions written with common denominat, with at least one crect Alternative method and (%) and 44(%) A Y and their 45(%) and their 44(%) Y and their 0.45 and their 0.44 Alternative method 6 (200 0) : 200 (200 40) : 250 Qft Strand (iii) and crect decision based on their decimals percentages, with at least one crect 22.5 : 50 and 22 : 50 A both ratios crectly written with common right side left side f comparison Y and their 22.5 : 50 and their 22 : 50 Qft Strand (iii) and crect decision based on their ratios crectly written with common right side left side f comparison, with at least one crect 2 of 9

13 9(a) (x + a)(x + b) where ab = ±24 a + b = 0 (x + 4)(x + 6) A 9(b) x = 4 and x = 6 Bft ft their factisation from part (a) 0 Alternative method dep A mixed number Alternative method Full method to evaluate 4.5 x 3.75 dep allow one err A condone rounding truncation after crect answer seen 3 of 9

14 3y = 2 4x 4x + y = x 3 2 4x y = 3 y = 4(3 x) 3 A 4x y = 4 3 2(a) 5 B 2(b) (0, 4) B x 0 (5-2) 0.8 x x x x 0 4 A SC. x of 9

15 4 Alternative method 8f + 4c = 40.2(0) 6f + 3c = 30.5 and and allow one err 3f + 4c = 9.2(0) 6f + 8c = 38.4(0) 5f = 2(.00) 5c = 8.25 dep crect elimination of one unknown f their equations (f =) 4.2(0) (c =).65 A 2.75 A Alternative method 2 3f + 4(0.05 2f ) = 9.2(0) 9.2(0) 4c 2 + c = allow one err 5f = 2(.00) 5c = 8.25 dep crect elimination of one unknown f their equations (f =) 4.2(0) (c =).65 A 2.75 A Alternative method 3 5f + 5c = f + c = f + c = 5.85 dep (f =) 4.2(0) (c =).65 A 2.75 A Alternative method 4 5f + 5c = f + c = f + c = f + 2c = 0.7(0) dep A 2.75 A 5 of 9

16 5 x(x 2) x 2 2x any crect common denominat seen 4x 3(x 2) 4x 3x + 6 dep crect numerat seen f their denominat, may be written as separate fractions x + 6 x( x 2) x x + 6 Q 2 2x Strand (ii) crect answer with no errs in wking 6 ( 0 = ) ( 20 = ) ( 3 20 = ) ( 50 = ) dep A allow Additional Guidance First method mark is f any useful first step 6 of 9

17 7 5x 2 6xy 20xy + 8y 2 allow one err 5x 2 6xy 20xy + 8y 2 A fully crect 5x 2 26xy + 8y 2 Aft ft their four terms do not igne further wk f final mark 8 x 2 + ax + ax + (a 2 ) x 2 + 2ax + (a 2 ) 2a = 8 a 2 + b = 7 (x + 4) 2 a = 4 b = 9 A (x + 4) 2 9 A allow a = 4 and b = 9 7 of 9

18 9 Alternative method R = R = dep R = 4.8 ( R = ).8 4 dep 0.45 A fraction decimal Alternative method 2 R = + = 6 8 R dep R = 40 = 8 R 20 9 dep Alternative method 3 A fraction decimal R R + R 2 = RR2 RR2 R + R 2 R = dep dep 0.45 A fraction decimal 8 of 9

19 ( ) = = A 2 m = 5 B p m ( ) = p 3 2 = 3 m p 2 their 5 ( ) 3 = 3 2 p 3 = 3 their their 5 = ( ) their = their 5 3 crectly evaluated 9 m p = p their 5 9 = 3 p 9 = p = 243 their 5 p 2p = m 2p = their 5 9 = 9 2 p = 2.5 Aft ft f values of m and p where m p = 2 9 of 9

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