GCSE MATHEMATICS. Practice Papers - Set 1- Teacher Booklet. NEW PRACTICE PAPER SET 2 Higher Tier Paper 2 Mark Scheme (Published November 2015) 8300/2H

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1 Practice Papers - Set 1- Teacher Booklet GCSE MATHEMATICS NEW PRACTICE PAPER SET 2 Higher Tier Paper 2 Mark Scheme (Published November 2015) 8300/2H 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 oe 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 1.2

3 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 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 goes 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 8n 3 B B1 3 2 B1 4 y = kx B1 5 Obtains an equivalent ratio writes out multiples of 11 (to 33) 33 A1 eg 8 : : 21 11, 22, 33 Page 4 Version 1.0

5 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments 3x 9 2 x x 3 9 6(a) x 6 A1 x 6 in wking lines and 6 on answer line A1 x + 2 > x + 8 > 12 6(b) x > 1 A1 SC1 > 1 SC1 x 1 Wking uses = but recovery to x > 1 x > 1 in wking lines and 1 on answer line A1 A1 6(c) B1ft Crect ft their two inequalities from (a) and (b) Condone dotted line Version 1.0 Page 5

6 Q Answer Mark Comments Alternative method = 0.2(E ) oe dep oe A1 Alternative method = 0.2(E ) oe dep A and 5.5 oe B2 B1 f each ± 5.5 B2 Page 6 Version 1.0

7 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments Alternative method oe their oe 1000 A1 SC Alternative method oe eg : 7 9 their oe 1000 A1 SC Alternative method [95.2, 95.4] oe 10.5 their [95.2, 95.4] 1000 A1 SC (a) B and C B1 10(b) SAS B1dep Must have (a) crect Enlargement (scale fact) 3 1 B1 B1 oe 11 (centre) igin B1 oe Version 1.0 Page 7

8 Q Answer Mark Comments 4 π oe 12(a) [2143, 2145] 2048 π A (.1) M May be seen on diagram 8 6 their May be seen on diagram 12(b) their 16 their 16 their 48 oe A1 SC Page 8 Version 1.0

9 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments 2(3x 9) = 5x 11 oe Must be crect and have x on both sides 6x 18 = 5x 11 oe their bracket(s) expanded crectly x = 7 2 their and 5 their A1 Substitutes their value of x in 2x + 4 and 5x : 24 and 3 : 4 A oe eg and x 9 = 2(5x 11) 3x 9 = 10x x = and M0 A0 A0 T & I leading to x = 7 A B1 15 y = 1 B1 Version 1.0 Page 9

10 Q Answer Mark Comments 1 x 2 = x = 8 oe any letter May be implied (28...) 2.83 (hypotenuse =) 2 their 8 their (1) 32 A1 Condone ± 8 and ± 16 etc f 2 nd and/ 3 rd Page 10 Version 1.0

11 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments Alternative method their their dep A1 SC (.25) Alternative method x 1000 oe 17 their (1.025x 1000) = dep oe x = oe x = A1 SC (.25) Version 1.0 Page 11

12 Q Answer Mark Comments 18(a) 0.54 B1 oe 18(b) 0.9 and and (1 0.2) 0.72 (1 0.9) (1 0.2) 0.72 and (1 0.9) Pairs must be linked eg on a tree diagram May be seen on a tree diagram May be seen on a tree diagram 0.79 A1 oe Page 12 Version 1.0

13 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments Smooth curve passing through the points (± 0.5 square) (2, 0), (3, 11), (4, 20), (5, 27), (6, 32), (7, 35), (8, 36), (9, 35), B3 Accept a line drawn from (0,0) to (2,0) Condone no line drawn from (0,0) to (2,0) B2 At least 7 crect points wked out plotted (± 0.5 square) 19(a) (10, 32) B1 At least 4 crect points wked out plotted (± 0.5 square) Crect points may be implied by curve passing through the points Condone curve continued beyond t = 10 their 35 their (b) 6 A1ft ft their points oe 20 their their dep dep on their 3402 their (...) A1 Version 1.0 Page 13

14 Q Answer Mark Comments Alternative method [1, 12] [14, 25] oe dep A1 Alternative method 2 21(a) and and 8400 [1, 12] [168, 2016] dep oe A1 Page 14 Version 1.0

15 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments 21(b) Any appropriate explanation B1 eg1 this is only a sample eg2 it may not reflect the whole population eg3 it may be different on another day eg4 it may be different at another time 22(a) (x 5) 2 2a = 10 a = 5 a 2 + b = 29 (x 5) a = 5 and b = 4 A1 Alternative method 1 (x 3) x 2 3x 3x x 2 6x + 14 c = 6 and d = 14 Alternative method 2 A1 Crect expansion of their (x + m) 2 + n 22(b) 2 2 c c x d 2 4 c c 2 = 3 and d = Equates coefficients f their x a b 2 c = 6 and d = 14 A c + d = 5 M0 Version 1.0 Page 15

16 Q Answer Mark Comments Alternative method 1 y cos 40 = 100 y sin 50 = (0...) x sin 40 = 100 x cos 50 = cos sin sin cos 50 Any letter y is the vertical side May be seen on diagram Any letter x is the hizontal side May be seen on diagram tan 40 = x their y 23 their y tan 40 tan 50 = their y tan 50 their y x their y 2 [64.27, 64.3] their their cos 30 [5169, ] their 5169, [71.8, 71.92] dep dependent on third May be seen on diagram their 76.6 their [64.27, 64.3] their [71.8,71.92] dep 50 9 A1 Page 16 Version 1.0

17 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 2 HIGHER Q Answer Mark Comments Alternative method 2 x sin 40 = 100 x cos 50 = 100 [64.27, 64.3] y cos 40 = 100 y sin 50 = sin cos cos sin 50 Any letter x is the hizontal side May be seen on diagram Any letter y is the vertical side May be seen on diagram tan 40 = tan 50 = their x y y their their x tan their x 76.6(0...) x 2 their x tan 40 their their cos 30 [5169, ] their 5169, [71.8, 71.92] dep dependent on third May be seen on diagram their 76.6 their [64.27, 64.3] their [71.8,71.92] dep 50 9 A1 First 2 M marks Sides have been transposed M0 M0 Third is not dependent Version 1.0 Page 17

18 Q Answer Mark Comments (cf values) 8, 56, 100, 110 and 120 Allow one err but no omission Allow inclusion of 0 May be implied by crect frequencies 24 (frequencies) 8 ( 0) 8 and their 56 their 8 48 and their 100 their and their 110 their and their 120 their (class widths) 20, 20, 40, 40 and 100 (frequency densities) 0.4 and 2.4 and 1.1 and 0.25 and 0.1 A1ft ft their cf values Must have 5 frequencies All crect ft their frequencies and their class widths Must have 5 frequency densities Must have first and second Suitable axes and scaling on grid B1ft ft their frequency densities Bars of crect width and height A1 Must be fully crect Igne any polygon drawn with a histogram Page 18 Version 1.0

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20 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. SP/03/15