GCSE MATHEMATICS. Practice Papers - Set 1- Teacher Booklet. New Specimen Papers published June 2015 Paper 1 Higher - Mark Scheme 8300/1H. Version 1.

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1 ΑΒ Practice Papers - Set 1- Teacher Booklet GCSE MATHEMATICS New Specimen Papers published June 2015 Paper 1 Higher - Mark Scheme 8300/1H Version 1.0

2 Principal Examiners have prepared these mark schemes f specimen papers. These mark schemes have not, therefe, been through the nmal process of standardising that would take place f live papers. 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. 1 eg accept 0.5 as well as 2 [a, b] Accept values between a and b inclusive Accept 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 UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT 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 B B cm 2 B1 4 B B1 Straight ruled line of best fit B1 Through (1, 9000) to (1, ) and (8, 800) to (8, 1800) Reads crectly from their straight line of best fit with negative gradient B1ft Within 2 1 square SC1 [3200, 3800] with no straight line of best fit drawn = 3 1 = 2 and crect B1 Condone No, they should be 1 and 2 f B1B1 SC1 w = 2 3 ( 1) ( 1) 3 = = 2 and increct B ( ) 4 7 Converts both fractions to improper with at least one crect 7 their 11 their 12 their 4 their dep fraction Page 4 Version 1.0

5 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT 8 5x 3x > x > 13 x > 6.5 SC1 6.5 Lists at least three terms from first sequence between 20 and 40 eg 21, 23, 25,... 9 Lists at least three terms from second sequence between 20 and 40 eg 20, 23, 26, SC2 f any two crect with at most one increct SC1 f any one crect with at most two increct Version 1.0 Page 5

6 Alternative method 1 18 (3 + 2) 3.6 their (0) 30.24(0) dep their (0) 25.2(0) dep dep on first Alternative method (0) (0) 15.4(0) (3 + 2) 3.6 their 3.6 their 15.4(0) dep dep on Alternative method (0) (0) 15.4(0) their 15.4(0) their dep dep th value identified 6 Page 6 Version 1.0

7 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT Alternative method 1 (x + 3) 2 x 2 + 3x + 3x (x + 3) x 2 + 3x + 3x x = x 2 + 9x + 27 Alternative method 2 (x + 6)(x + 3) x 2 + 6x + 3x + 18 their (x 2 + 6x + 3x + 18) x 2 + 6x + 3x = x 2 + 9x + 27 Alternative method 3 (x + 3) 2 x 2 + 3x + 3x (x + 6) x 2 + 3x + 3x x + 18 = x 2 + 9x + 27 Alternative method 4 (x + 6) 2 x 2 + 6x + 6x (x + 3) x 2 + 6x + 6x x 9 = x 2 + 9x + 27 Version 1.0 Page 7

8 13(a) 0.64 B1 13(b) x = cos 50 4 x = their their ft their 0.64 from (a) ft their 0.64 from (a) 14(a) (0) (b) 0.4(0) B1 Alternative method number (c) Alternative method their x Attempt to wk out how many prime numbers in the range 361 n < n < n < B2 B1 (a =) and value calculated that is crectly converted to standard fm Page 8 Version 1.0

9 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT Alternative method 1 x x + 35 = x = 40 2 their and 5 their = 115 and = 115 and cresponding angles Alternative method 2 dep 5x 85 = 2x + 35 x = 40 2 their and their their = 115 and their = 65 dep and angles on a straight line Version 1.0 Page 9

10 Alternative method (a) their their their dep 16 Alternative method their dep 16 17(b) If one person wks at a slower rate the answer will be higher If some of the people wk at a faster rate the task will take less time to complete B1 Page 10 Version 1.0

11 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT x x 2x 2x 3 x x x used as radius eg π seen π x x x πx 3 2x πx 3 Accept a = 2 and b = 8 Condone if subsequently factised to ( π)x 3 cos 30 = 3 tan 60 = k = 48 B1ft ft value seen in the fm a a and b are integers > 1 b where 0.8 Q Q = Qualifies 20(a) DNQ 0.2 Q DNQ 0.8 Q B2 D N Q = Ds not qualify B1 0.2 on DNQ branch All branches included labelled crectly with Q and DNQ but probabilities not all crect 0.2 DNQ Version 1.0 Page 11

12 Alternative method 1 their 0.2 their Look on tree diagram f wking 20(b) 0.96 Alternative method 2 (their 0.2) Look on tree diagram f wking angle ABC = x angle BAC = x and alternate segment theem angle ABC = x and angle BAC = x and alternate segment theem and two equal angles so isosceles (AC = BC) Either gives a crect solution eg divide area by 6 (to wk out area of one face of cube A) calculate the square root of the answer (to wk out length of one edge of cube A) halve this length (to wk out length of edge on cube B) 22 Full evaluation B2 then cube this answer (to wk out the volume of cube B) states implies that if Steph s der is maintained eg would need to quarter the surface area (to wk out surface area of cube B) B1 f partial evaluation eg der is increct 1 st line is increct Page 12 Version 1.0

13 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT 23(a) 0 B1 23(b) 1 B1 23(c) 2 B B1 fraction Accept 36 m/s per min 24(a) m/s 2 B1 Accept m/s per min only if their acceleration is 36 m/s per min 24(b) Chd from (0, 0) to (50, 30) and attempt at tangent to curve that is parallel to chd [11, 14] Must see wking on the graph 2(cx + 5) + c 2cx c 25 their 2cx = 6x their 2c = 6 c = 3 Must have attempted fg(x) 13 SC2 f 11 Version 1.0 Page 13

14 Must multiply numerat and denominat eg 10 is M is Alternative method 1 (n = and) 100n = n = n = dep eg 10n = and 1000n = eg 990n = n = Alternative method = ( + =) dep Page 14 Version 1.0

15 MARK SCHEME GCSE MATHEMATICS UPDATED SPECIMEN PAPERS PAPER 1 HIGHER PMT Alternative method 1 P (1, 3) y = 3 grad OP = 3 B1 grad PQ = 1 their y = (their 3 1 ) x + c and substitutes (1, their 3) dep their 3 x 1 their 3 x 1 y their 3 = (their 3 1 )(x 1) 28 Substitutes y = 0 in their equation dep their 3 1 = their x 1 3 (10, 0) Alternative method 2 P (1, 3) y = 3 grad OP = 3 B1 their 3 1 = QN their 3 dep their 3 their 3 9 their 3 tan PON = 1 dep N is on the x-axis PN is perpendicular to the x-axis (10, 0) Version 1.0 Page 15

16 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/02/15