GCSE MATHEMATICS. NEW PRACTICE PAPER SET 2 Higher Tier Paper 1 Mark Scheme (Published November 2015) 8300/1H. Version 1.0

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1 GCSE MATHEMATICS NEW PRACTICE PAPER SET 2 Higher Tier Paper 1 Mark Scheme (Published November 2015) 8300/1H Version 1.0

2 In Spring 2015, students across the country took this set of practice papers as a Mock Examination. Principal Examiners have marked the papers and these mark schemes have, therefe, been through the nmal process of standardisation. F some questions, Principal Examiners have written based on responses seen. 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 1 [a, b] Accept values between a and b inclusive Allow 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. Page 2 Version 1.0

3 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 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 1 mark unless instructed otherwise. Version 1.0 Page 3

4 Q Answer Mark Comments 1 x² + 3x B ³ B1 3 3 B n + 1 B1 Page 4 Version 1.0

5 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments Alternative method 1 radius = diameter = π their 3 2 9π 4 π their π dep π Alternative method 2 Igne attempts at factisation Do not igne further wk 5 radius = diameter = π their 3 2 9π 36 9π dep 4(36 9π) Igne attempts at expansion Do not igne further wk π = 108π A π = 12(12 4π) (err in factisation) Accept 3.14 better f π f method marks Version 1.0 Page 5

6 Q Answer Mark Comments seen B1 0.33( ) ( )% 40% A crect probability from each bag, with attempt at a comparable fm, with at least one crect eg and ( ) and ( )% and 40% No and both probabilities crect and in the same fmat eg Increct and and seen No and 0.33( ) and 0.4 No and 33( )% and 40% minutes 7(a) their hour 30 minutes 90 minutes dep 2 hours 120 minutes Dependent on 1st subtracting 25 from their distance Page 6 Version 1.0

7 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments (The journey will) take longer B1 7(b) Me time B1 (The journey will) be slower B B1 May be implied by numerat is negative 8 negative negative = positive and No B1 A pair of intersecting arcs of equal radii from ends of line with two intersections 9 Perpendicular line drawn through points of intersection 1 mm tolerance Version 1.0 Page 7

8 Q Answer Mark Comments their their 30 their dep 270 ml SC1 f SC1 f 32 Page 8 Version 1.0

9 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments Alternative method dep 72 < 10 eg 72 is between 8 and 9 12 Alternative method dep 18 < 5 eg 18 is between 4 and % B B1 Version 1.0 Page 9

10 Q Answer Mark Comments and eg and unsimplified crect fraction ( 4) in W only and 14 in B only their 56 + x = 3(their 14 + x) their 56 + x = their x any letter 16 7 in W and B ft ft their 56 and their 14 Award if W total = 3 B total 23 not in W B B1ft ft their 56 and their 14 and 7 Award if the four values total 100 Page 10 Version 1.0

11 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments 3x 2 6x + x 2 3x 2 5x 2 3x 2 + (a their 5)x their 2 + b a their 5 = 8 b their 2 = 5 4 terms with at least 3 crect 17 a = 13 b = 3 a their 5 = 8, a = 13 a their 5 = 8, a = 13 and b 2 = 5, b = 3 13x 3 Version 1.0 Page 11

12 Q Answer Mark Comments Probability of red is not 3 1 B1 Probability of red is (a) He should multiply the fractions, not add them B1 SC1 gives crect answer of ( ) = 1 16 with no reference to Jack s method (b) 360 their 5 1 dep x 2 6 4x x x 6 + = 6 19x B sin x B1 Page 12 Version 1.0

13 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments Alternative method 1 10x = method 100x = and and 9x = x = fraction Alternative method = ft Crect simplification of their fraction and sced method 22 and 100x = 5.55 and 99x = fractions 7 45 ft Crect simplification of their fraction and sced Alternative method ft method fractions with common denominat Crect simplification of their fraction and sced Version 1.0 Page 13

14 Q Answer Mark Comments their dep Dress cost 4 2 ( ) = their 16 - their 8 their16 ( 100) 18 their 8 their16 ( 100) B sces B Page 14 Version 1.0

15 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments 25(a) 1 1 = 0 and After 1 it s all 0s B1 Do not accept a list of zeros 1 ( 1) = 2 B1 4 2 = 2 25(b) and All subsequent values are 2 B1 Do not accept a list of twos Allow one err with four terms 25(c) 2 2 Angle ABC = 90 angle BCA = 30 Angles may be on diagram (x =) Angle DBA = 36 Angle OAD = 54 B1 ( y =) 36 B1ft ft their angle DBA their angle OAD Version 1.0 Page 15

16 Q Answer Mark Comments Alternative method a = 7, b = 3 27 Alternative method a = 7, b = 3 Page 16 Version 1.0

17 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 1 HIGHER Q Answer Mark Comments Alternative method 1 y = 5x 5 2(5x 5) x 2 = 11 10x 10 x 2 = 11 Eliminating a variable x 2 10x + 21 = 0 Collecting terms (x 3)(x 7) (= 0) x = 3 and x = 7 x = 3 and y = 10 x = 7 and y = 30 Crect and accurate method to solve their 3-term quadratic equation 10 (-10)² - 4 x 1x 21 2 x 1 28 x = 3, y = 10 and x = 7, y = 30 Alternative method 2 10x 2y = 10 Equating cfficients 10x x 2 = 21 Eliminating a variable x 2 10x + 21 = 0 Collecting terms (x 3)(x 7) (= 0) x = 3 and x = 7 x = 3 and y = 10 x = 7 and y = 30 x = 3, y = 10 and x = 7, y = 30 Crect and accurate method to solve their 3-term quadratic equation 10 ( 10) Version 1.0 Page 17

18 Q Answer Mark Comments Alternative method 3 x = 5 y y 2y 11 5 Eliminating a variable y 2 40y = 0 Collecting terms 28 ( y 10)( y 30) (= 0) Crect and accurate method to solve their 3-term quadratic equation ( 40) ( 40) y = 10 and y = 30 x = 3 and y = 10 x = 7 and y = 30 x = 3, y = 10 and x = 7, y = 30 Page 18 Version 1.0

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