Practice Papers - Set 1- Teacher Booklet GCSE MATHEMATICS. PRACTICE PAPER SET 3 Higher Tier Paper 1 Mark Scheme 8300/1H. Version 1.

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1 ΑΒ Practice Papers - Set - Teacher Booklet GCSE MATHEMATICS PRACTICE PAPER SET 3 Higher Tier Paper Mark Scheme 8300/H Version.0

2 Further copies of this Mark Scheme are available from aqa.g.uk 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 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. 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] [a, b) Accept values between a and b inclusive. Accept values a value < b 3.4 Allow answers which begin 3.4 eg 3.4, 3.42, 3.46 Use of brackets It is not necessary to see the bracketed wk to award the marks. Page 2 Version.0

3 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER 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 student has used an increct method to obtain an answer, as a general principle, the benefit of doubt must be given to the student. In cases where there is no doubt that the answer has come from increct wking then the student should be penalised. Questions which ask students to show wking Instructions on marking will be given but usually marks are not awarded to students who show no wking. Questions which do not ask students to show wking As a general principle, a crect response is awarded full marks. Misread miscopy Students often copy values from a question increctly. If the examiner thinks that the student 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. Continental notation Accept a comma used instead of a decimal point (f example, in measurements currency), provided that it is clear to the examiner that the candidate intended it to be a decimal point. Version.0 Page 3

4 Q Answer Mark Comments 8π B 2 6x 3 5x 2 B 3 x > 2 B B x = (2 + 9) 3 3 x = 2 5 x 9 3 = 2 3 x 27 = A = 39 M0A0 Page 4 Version.0

5 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method A Alternative method at least eight 0.2s at least eight 0.2s 6(a) 2 A Alternative method and A Version.0 Page 5

6 Q Answer Mark Comments It will take fewer days B the answer would be lower eg it will be less than 2 6(b) Quicker/faster than 2 days Quicker/faster alone B B0 DAE = ABC = 65 DAB = 72 EDB = BAE = BAC = ADB = and ACD = 5 May be on diagram in crect position May be on diagram in crect position 7 BAC = 50, BAE = 5 and ADB = CAE = 65 and DAE = 43 DAB = 72 and BAC = = = = = 22 A eg 5 A = 50 is ambiguous Written wk takes precedence over diagrams if contradicty. M0 Page 6 Version.0

7 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method seen 5 3 (= 2) 2, 3 and 5 A 8(a) Alternative method 2 x + 2y = 28 and 2x + 3y = 43 equations Solves equations crectly obtaining x = 2 A If setting up two equations, they must be crect b a Second term 8(b) 2b a 3b a dep A Fourth term Version.0 Page 7

8 Q Answer Mark Comments The method will sometimes give an answer which is a whole number B 64 = 8 eg 5² 4² = 9 and 9 is a square number crectly evaluated example where the answer is a whole number B 5² 4² = 3² 9 Crectly evaluated example where the answer is not a whole number B eg 3² 2² = 5 and 5 is not a square number 2 marks can be gained f example(s) even if the decision is increct = 5 and 5 is between 4 and 9, implies 5 is not square B0B0B Page 8 Version.0

9 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method ( 60) 30 minutes 2 h ( 60) 40 minutes 2 3 h ( 60) 45 minutes 3 4 h Two of ( 60) 30 minutes 2 h and ( 60) 40 minutes 2 3 h and 0(a) ( 60) 45 minutes 3 4 h ( 60) 30 minutes 2 h and ( 60) 40 minutes 2 3 h and ( 60) 45 minutes 3 4 h C with all wking crect A Condone missing units, but note that 30 is given as both a distance and a speed in the question Mark scheme f 0(a) continues on the next page Version.0 Page 9

10 Q Answer Mark Comments Alternative method ( 60) 40 minutes 2 3 h ( 60) 45 minutes 3 4 h ( 0) 30 minutes 2 h (.3..) miles miles miles miles (a) 26(.6..) miles 26.7 miles 22.5 miles (.3..) miles and (.6..) miles 26.7 miles miles and miles C with all wking crect A Condone missing units, but note that 30 is given as both a distance and a speed in the question and 40 appears as both a time and a speed Page 0 Version.0

11 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments time = 30 minutes 2 h 5 minutes difference scale fact 2 B 0(b) mph faster A 20 mph with no box ticked BA0 20 mph with slower ticked BA0 (a) 6 and 5 6 on each pair of branches B In crect der (b) 36 B Version.0 Page

12 Q Answer Mark Comments Alternative method their Aft ft from part (b) provided probabilities < (c) Alternative method Aft ft from part (a) 5 B 2(a) 2(b) A is negative B B (0, 2) and D (6, 5) B f one crect 3(a) B (4, 4) and D ( 2, ) B2 f one crect and one increct B and D reversed crect diagonal drawn of any length eg B(0,2) and D( 2, ) B 3(b) B f vect of same size B2 f any perpendicular vect Page 2 Version.0

13 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments from crect rounding to sig fig dep A 9 2 = (no other wking) M0M0 5 2x + x B 6 A B 9 2 = (no other wking) Version.0 Page 3

14 Q Answer Mark Comments Alternative method (0) dep their 4.4(0) (0) (0) and Yes A and 4.4(0) and Yes 9 ( =) 8.3(3...) and Yes 5 7 Alternative method (0) (3 ) dep and 4.4(0) and Yes 8.3(3 ) and Yes A Page 4 Version.0

15 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments At least point from ( 2, 8) (, ) (0, 4) (, ) (2, 8) (3, 23) (4, 44) Seen implied If only seen plotted allow ± 0.5 square 8 At least 3 crect points from ( 2, 8) (, ) (0, 4) (, ) (2, 8) plotted crectly (± 0.5 square) and attempt to join their points with a smooth curve (± 0.5 square) [ 0.75, 0.95] A [.45,.65] A F first allow (3, 23) (4, 44) even though they cannot be plotted 4 B 9(a) Allow one err 9(b) A Version.0 Page 5

16 Q Answer Mark Comments B2 B F B responses 2 can be 0.5 F final two B responses can be Page 6 Version.0

17 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method ( 2 BE ) 0 sin 30 May have BE = x ( any letter) 2 5 BE 2 (perpendicular height of triangle =) 5 BE 0 sin 30 = BE BC 2 dep May have BE = x and BC = x 2 ( any common letter) BC = BE = dep Must divide by BE and substitute sin 30 = 2 May have BC = x 2 ( any letter) 4 2 A Mark scheme f 2 continues on the next page Version.0 Page 7

18 Q Answer Mark Comments Alternative method 2 ( 2 (BC + 2) ) 0 sin 30 May have BC = x ( any letter) 2 5 (BC + 2) (perpendicular height of triangle =) 5 2 (BC + 2) 0 sin 30 2 = (BC + 2) BC BC = BE = dep dep May have BC = x ( any common letter) Must divide by (BC + 2) and substitute sin 30 = May have BC = x ( any letter) 4 2 A Any one fd class width dep A Page 8 Version.0

19 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method = 3k 4 ( 3 6 = 4 27 =) ( =) dep 6 dep on Any crect common denominat with at least one numerat crect = 3k but must be k 3 3 A Alternative method 2 ( = =) ( =) 2 3 dep Any crect common denominat with at least one numerat crect ft their dep but must be k 3 3 A 6 6 Alt first and alt 2 third 2 Multiplying by eg Version.0 Page 9

20 Q Answer Mark Comments Alternative method (x =) and (0x =) At least two 8s needed 9x = dep 3 45 A Alternative method 2 (0x =) and (00x =) At least two 8s needed 90x = dep 3 45 A Alternative method 3 24 (x =) and (00x =) At least two 8s needed 99x = dep 3 45 A Alternative method fractions dep Crect conversion to a common denominat 3 45 A 3 Any fraction equivalent to 45 A0 Page 20 Version.0

21 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments 25(a) B 25(b) 4 43 B x in Histy only (and 3x in English only) 25(c) expressions inside circles such that the number who take English is twice the number who take Histy x + their x + their 3x + 25 = 295 equation Must have three expressions inside circles 34 A 2x in Histy only and 5x in English only ( 5) 2 = 25 (0 2 +) y 2 = 25 and y = 5 B 26(a) radius of the circle is 5 B is on the y-axis B is below the Origin B0 B0 Version.0 Page 2

22 Q Answer Mark Comments 26(b) Tangents from an external point are equal in length B Alternative method (a 3) 2 + ( 5 4) 2 = a 2 PA 2 = PB 2 a 2 3a 3a = a 2 6a = 90 Expands brackets Allow one err Rearranges their quadratic equation to ka = c (a =) 5 and (b =) 5 A SC b = 5 26(c) Alternative method 2 (grad AP =) y 4 = 4 3 (x 3) y = 4 3 x + c and substitutes (3, 4) 3 25 eg y = x ft their gradient AP = x ft their equation AP (a =) 5 and (b =) 5 A SC b = 5 Mark scheme f 26(c) continues on the next page Page 22 Version.0

23 MARK SCHEME GCSE MATHEMATICS PRACTICE PAPER - SET 3 PAPER HIGHER Q Answer Mark Comments Alternative method 3 XP 4 = May be seen on diagram X is foot of perpendicular from A to BP 26(c) XP = 3 4 (4 5) XP = Must have calculation value f XP (a =) 5 and (b =) 5 A SC b = 5 Version.0 Page 23

24 Copyright 206 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. SP/03/5