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

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1 GCSE MATHEMATICS NEW PRACTICE PAPER SET 2 Foundation Tier Paper Mark Scheme (Published November 2015) 800/F 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..1 Allow answers which begin.1 eg.1,.12,.116 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 FOUNDATION 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

4 Q Answer Mark Comments 1(a) 78% B1 1(b) 1 B1 2 2 is greater than 6 B1 could be odd even B B eg 6.70 overdrawn B2 crect values with increct money notation B2ft crect values with crect money notation B1ft crect values with increct money notation 2 crect values with crect money notation ft their values SC2 9.0 in final cell with rest blank SC1 9. in final cell with rest blank SC , 19.0, 58.80, Follow through their , their and their 6.7(0) + 6 crectly evaluated Igne any units given and any extra values in credit/ debit column 21.25, , 9.0 (four crect but some increct notation) B , 27.66, 17.10, (last three crect ft and all crect notation) B2ft , 27.66, 17.1, (last three crect ft but increct notation) B1ft , 19.0, 29.28, (last two crect ft and crect notation) B1ft Page Version 1.0

5 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments 8.9 B1 5(a) 12. B1ft ft their chosen card (+)8. (+).8 (+)8.9 (+) must follow 8.9 a blank card B1B1 B0B1 (+)8.9 B1 5(b) 12. B1ft ft their chosen card (+) (+)5. 8. (+) must follow (+)8.9 a blank card B1B1 B0B1 Version 1.0 Page 5

6 Q Answer Mark Comments 6(a) B1 B1 fraction, decimal percentage SC1 both fractions crect but given in wds 2 out of and 1 out of SC1 Accept decimals percentages rounded truncated to 2 sf better 6(b) All conditions met eg,,, 5, 6 Allow fractions decimals eg,,.5,.5, 6 B2 B1 five numbers with two conditions met eg,, 6, 6, 6,,,, 7,,, 6, 6 B2,,, 5, 6 is the only crect answer using only integers B their 2.9 their dep 11.6 A1 8(a) (9, 6) plotted B1 Need not be labelled 8(b) isosceles and right-angled B2 B1 both crect and 1 increct 1 crect (and 1 increct) 8(c) 1 : B1 Page 6 Version 1.0

7 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments 9(a) 5 B1 fraction their : 5 and 16 : 20 9(b) 16 A1 SC1 25 If their 5 20 gives a non-integer number of boys, then either the crect method full value must be seen f 5 The method mark may be implied by the crect ft integer value eg (a) 20 (b) 5 B0A0 Alternative method their their 1.5 cannot be.625 (their ) A1 SC 0. Alternative method 2 10 n 5 =.625 (n =) (n =) 9.5 (their ) A1 SC 0. Special case is f ((.625 5) + ) 5 SC 9.5 implies the first two marks Version 1.0 Page 7

8 Q Answer Mark Comments cm = 1 m and 1000 m = 1 km 1 km = cm cm = 2 km 5 A1 12(a) 5 and B1 B1ft ft provided at least one negative answer in (a) 12(b) 1 next then all positive B1ft ft provided at least one negative answer in (a) If both terms are negative in (a) then must circle me than in (b) must follow 5 and be crect f their answers in (a) 1 different mistakes identified B B1 f each different mistake identified from It should be a straight line Point (0, 1) plotted increctly Two s on x-axis Axes not labelled Line not labelled (y = x + 1) Accept equivalent statements Page 8 Version 1.0

9 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments π Accept [12.6, 12.75] π dep 1 [.16,.19].2 B1ft Accept 169 π 16 with no increct wking A (%) = 6(%) A1 Answer of 88 with without 8 seen in wking Condone an answer of 9, 8.96, , f the first mark A0 M0A0 Version 1.0 Page 9

10 Q Answer Mark Comments Alternative method their dep sces their 5. their dep 15.8 A1 SC Alternative method their dep sces their 5. + their their dep 15.8 A1 SC2 50. Special case is f the perimeter which implies 1.8 used SC2 17(a) (x y)(x + y) B1 Page 10 Version 1.0

11 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments 2x 2x = 1 1 = x + 5 = 65 (1 1) 5 sces 17(b) 2x = their x = their 65 their 5 2x = 60 0 A1 (1 1) 5 2 sces Embedded answer eg = 1 5 eg = 1 A0 M0A0 18(a) ( PCD BAD =) ( CDA =) 10 ( APB =) 5 ( PDA DPC =) ( PCD =) and ( DPC =) ( CDA =) 10 and ( PDA =) May be on diagram May be on diagram 85 A1 The angle being calculated must be clear from the diagram wking 18(b) 15 B1 Version 1.0 Page 11

12 Q Answer Mark Comments t < 71.5 B2 B1 1 crect bound 19 Accept f (a) B1 Alternative method (b).5 A1 Alternative method 2 y = their 6.5 A1ft ft their tan x from (a) Page 12 Version 1.0

13 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments 20(b) Alternative method tan -1 (their ) [6.8, 6.9] This could be on the diagram seen in part (a).5 A1ft ft their tan x from (a) F, accept 2 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 =, in (b), = 6 y, answer.5 M0A0 A1 in (a), tan x =, in (b), tan x = y 6 (increct), = y 6, answer.5 M0A0 in (a), tan x =, in (b), tan x = 6 y, = 6 y, answer 8 A1ft If the answer line is blank, but.5 is seen crectly embedded as the crect length on the diagram, award only the method mark A0 In alt 2 and alt their tan x must be a value f tan x and not a value f x 21(a) B1 21(b) 5 B their 150 their 12 dep dependent on M2 26 A1 Version 1.0 Page 1

14 Q Answer Mark Comments 2(a) 0 B (and 12) and 16 May be implied from a diagram as the denominat of a fractional answer May be shown by exactly two-digit outcomes in a list, grid table as the numerat of a fractional answer 2(b) fraction, decimal percentage % A1 16 F, their (sample space) diagram table may be blank A grid with crect values f at least the two-digit numbers seen implied Alternative method 1 π [117.7, 118] their [ , 118] ( 100) dep [0.785, 0.787] 0.79 [78.5, 78.7] 79 A1 Alternative method 2 2 π [117.7, 118] their [ , 118] dep [21., 21.6] 21 [78.5, 78.7] 79 A1 [0.78, 0.785) [78., 78.5) implies M2 the value may be outside the limits f A1 due to premature rounding Page 1 Version 1.0

15 MARK SCHEME GCSE MATHEMATICS NEW PRACTICE PAPER - SET 2 PAPER FOUNDATION Q Answer Mark Comments Alternative method 1 a (+) c (=) 2 and a (+) 15c (=) 5 15a (+) 20c (=) 115 and a (+) 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 A1 (a =) 5 and (c =) 2 A1 Alternative method c a = a = 15 5c c = c = 2 a 15 a 5 Makes a c the subject 2 c = 15 5c 2 a 15 a 5 = Crectly substitutes their expression to eliminate one variable (a =) 5 (c =) 2 A1 (a =) 5 and (c =) 2 A1 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 a + c = 2 and a + 15c = 15 but not a + c = 2 and a + 5c = 5 Version 1.0 Page 15

16 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 A1 eg 0.08 and and : 00 and 2 : their Two crect comparable values and The doct is crect A1 eg 12.5 and and : 8 and 00 : 2 Alternative method their 00 dep 8 from crect method and 2 and The doct is crect A1 In alt 2, 12.5% and 6.25% instead of 12.5 and 6.25 cannot get the accuracy mark A0 Page 16 Version 1.0

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