GCSE MATHEMATICS. NEW PRACTICE PAPER SET 2 Higher Tier Paper 3 Mark Scheme (Published November 2015) 8300/3H. Version 1.0

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1 GCSE MATHEMATICS NEW PRACTICE PAPER SET 2 Higher Tier Paper 3 Mark Scheme (Published November 2015) 8300/3H 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 3 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 10 1 x B B B1 4 25x 4 B t < B2 B1 1 crect bound 5 Accept f (a) 3 4 B1 Alternative method (b) Alternative method 2 y = their ft ft their tan x from (a) Page 4 Version 1.0

5 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments 6(b) Alternative method 3 tan -1 (their 4 3 ) [36.8, 36.9] This could be on the diagram seen in part (a) 4.5 ft ft their tan x from (a) F, accept given as a decimal truncated rounded to 2dp better Award both marks f an answer of 8 in part (b) unless an increct statement is made; eg in (a), tan x = 3 4, in (b), 4 3 = 6 y, answer 4.5 M0A0 in (a), tan x = 3 4, in (b), tan x = y 6 (increct), 3 4 = y 6, answer 4.5 M0A0 in (a), tan x = 3 4, in (b), tan x = 6 y, 3 4 = 6 y, answer 8 ft If the answer line is blank, but 4.5 is seen crectly embedded as the crect length on the diagram, award only the method mark A0 In alt 2 and alt 3 their tan x must be a value f tan x and not a value f x Version 1.0 Page 5

6 Q Answer Mark Comments their 150 their 124 dep dependent on M2 26 8(a) 0 B (and 12) and 16 3 May be implied from a diagram as the denominat of a fractional answer May be shown by exactly 3 two-digit outcomes in a list, grid table as the numerat of a fractional answer 8(b) 3 fraction, decimal percentage % 16 F, their (sample space) diagram table may be blank A 4 4 grid with crect values f at least the 3 two-digit numbers seen implied Page 6 Version 1.0

7 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments Alternative method 1 π [117.7, 118] their [ , 118] ( 100) dep [0.785, 0.787] 0.79 [78.5, 78.7] 79 Alternative method 2 9 π [117.7, 118] their [ , 118] dep [21.3, 21.6] 21 [78.5, 78.7] 79 [0.784, 0.785) [78.4, 78.5) implies M2 the value may be outside the limits f due to premature rounding Version 1.0 Page 7

8 Q Answer Mark Comments Alternative method 1 3a (+) 4c (=) 23 and 3a (+) 15c (=) 45 15a (+) 20c (=) 115 and 4a (+) 20c (=) 60 eg wks in pence Multiplies one both equation(s) to equate cfficients of a c Allow one err in multiplication 11c (=) 22 11a (=) 55 Subtracts equations to eliminate one variable Allow one err in subtraction (a =) 5 (c =) 2 (a =) 5 and (c =) 2 Alternative method c a = 3 a = 15 5c c = c = 23 3a 4 15 a 5 Makes a c the subject 23 4c 3 = 15 5c 23 3a 4 15 a 5 = Crectly substitutes their expression to eliminate one variable (a =) 5 (c =) 2 (a =) 5 and (c =) 2 Accept any letters, adult and child, as variables To allow one err in the first mark of alt 1, the equal cfficients must be the same. eg allow 3a + 4c = 23 and 3a + 15c = 15 but not 3a + 4c = 23 and 3a + 5c = 45 Page 8 Version 1.0

9 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments Alternative method their eg 8% 8% and the doct is crect Two crect comparable values and The doct is crect Alternative method 2 eg 0.08 and and : 300 and 24 : their Two crect comparable values and The doct is crect eg 12.5 and and : 48 and 300 : 24 Alternative method their 300 dep 48 from crect method and 24 and The doct is crect In alt 2, 12.5% and 6.25% instead of 12.5 and 6.25 cannot get the accuracy mark A0 Version 1.0 Page 9

10 Q Answer Mark Comments Explanation that in A 10 b the value of A must be range 1 A < 10 B1 eg the first part should be Accept the crect conversion to (a) Igne errs in inequalities given as a range f the acceptable first part of a number in standard fm if the written answer shows clear understanding eg in a b n, a must be less than 10, 0 < a >10 B1 12(b) Explanation that the power should be positive B1 eg the power should be 5, not -5 this gives ( 99 ) Accept the crect conversion to unless awarded in 12(a) Allow an increct conversion with a crect statement eg the power should be positive, -5 gives B1 Page 10 Version 1.0

11 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments 35 : 21 and 21 : : 3 : : : Any crect pair of ratios where the values f women are equal a crect three-part ratio : 7 : 4 : : : their 35 + their 21 + their their 21 + their dep Could be multiples of these numbers = % 35 and (half of 68 is) (men) and 33 (women and children) Version 1.0 Page 11

12 Q Answer Mark Comments Allow one err Condone missing brackets Fully crect Condone missing brackets and and 0.17 Condone the method of completing the square f A0 Square numbers cannot be prime B1 15(a) Accept any crect explanation why square numbers cannot be prime, eg prime numbers have exactly 2 facts and square numbers have an odd number of facts An increct statement, even with a crect statement, sces B0 eg prime numbers cannot be square numbers as prime numbers have no facts B0 15(b) n + 1 B1 2 Page 12 Version 1.0

13 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments Alternative method 1 [3.1415, ] B1 their their dep [0.0018, ]% Alternative method 2 [3.1415, ] B their [ , ] their [0.0018, ]% dep 16 Alternative method 3 [3.1415, ] B and [3.1415, ] and [3.1415, ] and states that value is between lower bound and given value Numbers in the crect range can come from finding a percentage of their value, which can only gain the B mark. Version 1.0 Page 13

14 Q Answer Mark Comments 17 Draws the line x = 3 as a dashed line Draws the line x + y = 2 as a solid line Draws the line y x 1 2 as a solid line Crectly labels shades the region satisfying all three inequalities B1 at least from y = 0 to y = 5 B1 at least from x = 3 to x = 2 B1 at least from x = 3 to x = 2 B1ft ft their three lines Only withhold a mark f an increct line style on the first occasion. With only one two with four me lines drawn it is impossible to sce the last B1 c(d + 3) = 4 d cd + 3c = 4 d dep 18 cd + d = 4 3c d(c + 1) = 4 3c 4 3c d = c 1 dep d = 4 + 3c c 1 19 (1, 4) B B1 Page 14 Version 1.0

15 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments Alternative method 1 (w =) x 2 and ( y =) x + 2 Allow (x =) w + 2 and ( x =) y 2 (x 2)(x + 2) + 4 wy = (x 2)(x + 2) and wy = x 2 4 = x and x = x 2 Alternative method 2 All steps must be seen SC1 crect numerical example with all steps shown (x =) w + 2 and ( y =) w + 4 Allow (x =) w + 2 and ( x =) y 2 (w)(w + 4) = w 2 + 4w + 4 and w 2 + 4w + 4 = (w + 2) 2 and (w + 2) 2 = x 2 All steps must be seen SC1 crect numerical example with all steps shown Alternative method 3 (x =) y 2 and (w =) y 4 Allow (x =) w + 2 and ( x =) y 2 (y)(y 4) + 4 = y 2 4y + 4 and y 2 4y + 4 = (y 2) 2 and (y 2) 2 = x 2 All steps must be seen SC1 crect numerical example with all steps shown x = 3, w = 1, y = 5 and = 9 0 x = 3, w = 1, y = 5 and = 9 and 9 = 3² SC = 9 and 9 = 3² 0 Version 1.0 Page 15

16 Q Answer Mark Comments (C has codinates) (2, 4) B1 (Gradient =) 2 B1 Implied by y = 2x 1 their gradient (Gradient =) 2 1 Implied by y = 2 1 x 22 their 4 = their 2 1 their 2 + c c = 3 y = 2 1 x + 3 y = 2 1 (x + 6) ft ft their codinates of C and their initial gradient if sced (Gradient =) 2 1 y = 2 1 x implies the second B mark and the first M mark. Page 16 Version 1.0

17 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments (With 90 ) sin x = 10 6 (x =) (With 85 ) sin 6 x sin both fractions inverted sin x = 6 sin (x =) 36.7 (with 90 ) (x =) and (with 85 ) (x =) 36.7 and suitable comment eg they are the same to the nearest degree they are different to 1 decimal place his answer will give a (slightly) larger angle 24(a) 4b B1 ( ED =) 3 1 (a + 3b) ( ED =) 3 1 a + b B1 EC = their ( 3 1 a + b) 3 1 a EC = b 24(b) Valid justification eg and ED = 3 1 a + b and EC = b AB = 4EC (so AB is a multiple of EC ) Version 1.0 Page 17

18 Q Answer Mark Comments T = k l 1.6 = k = k 8 k = k = 64 8 k = T = 0.2 l (T =) their (T =) their dep dependent on first two method marks 2.3 ft ft their 0.2 if M0 sced 26 y = (x 2) 2 B1 Page 18 Version 1.0

19 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER 3 HIGHER Q Answer Mark Comments Alternative method and (14 + 6) (9 + 7) (t 14) 2 their 36 + their t 112 = 7.2t 0.8t = Alternative method and (14 + 6) (9 + 7) x 8x any letter using x to denote t 14 2 their 36 + their x = 7.2x x = 10.8 x = 13.5 their Version 1.0 Page 19

20 Q Answer Mark Comments 5f(x) = 4x 3 5f(x) + 3 = 4x 5y = 4x 3 5y + 3 = 4x 5x = 4y 3 5x + 3 = 4y accept any letter used f y 28 5f( x) 3 (= x) 4 5y 3 4 (= x) 5x 3 Condone y = ( any other letter) 4 Page 20 Version 1.0

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