GCSE Mathematics
GCSEMathematicsPaper 2 Foundation TierMark scheme8300June 2017Version: 1.0 Final
Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevantquestions, by a panel of subject teachers. This mark scheme includes any amendments made at thestandardisation events which all associates participate in and is the scheme which was used by them inthis examination. The standardisation process ensures that the mark scheme covers the students’responses to questions and that every associate understands and applies it in the same correct way.As preparation for standardisation each associate analyses a number of students’ scripts. Alternativeanswers not already covered by the mark scheme are discussed and legislated for. If, after thestandardisation process, associates encounter unusual answers which have not been raised they arerequired to refer these to the Lead Assessment Writer.It must be stressed that a mark scheme is a working document, in many cases further developed andexpanded on the basis of students’ reactions to a particular paper. Assumptions about future markschemes on the basis of one year’s document should be avoided; whilst the guiding principles ofassessment remain constant, details will change, depending on the content of a particular examinationpaper.Further copies of this mark scheme are available from aqa.org.ukCopyright 2017 AQA and its licensors. All rights reserved.AQA retains the copyright on all its publications. However, registered schools/colleges for AQA are permitted to copy material from thisbooklet for their own internal use, with the following important exception: AQA cannot give permission to schools/colleges to photocopy anymaterial that is acknowledged to a third party even for internal use within the centre.
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017Glossary for Mark SchemesGCSE examinations are marked in such a way as to award positive achievement wherever possible.Thus, for GCSE Mathematics papers, marks are awarded under various categories.If a student uses a method which is not explicitly covered by the mark scheme the same principles ofmarking should be applied. Credit should be given to any valid methods. Examiners should seek advicefrom their senior examiner if in any doubt.MMethod marks are awarded for a correct method which could leadto a correct answer.AAccuracy marks are awarded when following on from a correctmethod. It is not necessary to always see the method. This can beimplied.BMarks awarded independent of method.ftFollow through marks. Marks awarded for correct workingfollowing a mistake in an earlier step.SCSpecial case. Marks awarded for a common misinterpretationwhich has some mathematical worth.M depA method mark dependent on a previous method mark beingawarded.B depA mark that can only be awarded if a previous independent markhas been awarded.oeOr equivalent. Accept answers that are equivalent.eg accept 0.5 as well as12[a, b]Accept values between a and b inclusive.[a, b)Accept values a value b3.14 Accept answers which begin 3.14 eg 3.14, 3.142, 3.1416Use of bracketsIt is not necessary to see the bracketed work to award the marks.3
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017Examiners should consistently apply the following principlesDiagramsDiagrams that have working on them should be treated like normal responses. If a diagram has beenwritten on but the correct response is within the answer space, the work within the answer space should bemarked. Working on diagrams that contradicts work within the answer space is not to be considered aschoice but as working, and is not, therefore, penalised.Responses which appear to come from incorrect methodsWhenever there is doubt as to whether a student has used an incorrect method to obtain an answer, as ageneral principle, the benefit of doubt must be given to the student. In cases where there is no doubt thatthe answer has come from incorrect working then the student should be penalised.Questions which ask students to show workingInstructions on marking will be given but usually marks are not awarded to students who show no working.Questions which do not ask students to show workingAs a general principle, a correct response is awarded full marks.Misread or miscopyStudents often copy values from a question incorrectly. If the examiner thinks that the student has made agenuine misread, then only the accuracy marks (A or B marks), up to a maximum of 2 marks are penalised.The method marks can still be awarded.Further workOnce the correct answer has been seen, further working may be ignored unless it goes on to contradict thecorrect answer.ChoiceWhen a choice of answers and/or methods is given, mark each attempt. If both methods are valid thenM marks can be awarded but any incorrect answer or method would result in marks being lost.Work not replacedErased or crossed out work that is still legible should be marked.Work replacedErased or crossed out work that has been replaced is not awarded marks.Premature approximationRounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 markunless instructed otherwise.Continental notationAccept a comma used instead of a decimal point (for example, in measurements or currency), provided thatit is clear to the examiner that the student intended it to be a decimal point.4
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark1metresB1272B131.5B14–4 –3B126.47640( .)B1CommentsAdditional Guidance5(a)26.5B1ftCorrect or ft provided their answer to (a) isgiven to more than 1 dpAdditional Guidance5(b)8.88326612 in (a) and 8.9 in (b)B1ft8.88326612 in (a) and 26.5 in (b)B126.50B046(a)B1Additional Guidance4 must be shown on the answer line in the key5
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswer15MarkCommentsB1ftCorrect or ft 3.75 their 4 from (a) if their 4is a multiple of 4Additional Guidance6(b)(a) key blank or incorrect (b) 15B1(a) 8 (b) 30B1ft(a) 10 (b) 37.5 (or 37 or 38)B0ftIf answer line blank and 15 seen next to female row of pictogramB1The sample is too smallorthe results may be biasedB1orthe sample is not representativeAdditional Guidance6(c)6This was only/ just 1 hourB1More men might come at different timesB1It might have been a girls’ school using itB1There were only/ just 25 people in the surveyB1The results may changeB1Ignore irrelevant comments alongside a correct statement eg There isn’t anequal number of males and females. A bigger sample is neededB1BiasedB1UnfairB0Should do it for longer until there is an equal number of males and femalesB0It was for 1 hourB0The results are about people not lockersB0Not a lot of people use the family changing roomB0In that hour not many people used the changing roomsB0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkComments17 21 21 21 23 25 29 32 36Puts list into orderorAllow one omission, extra or transcriptionerror in a full list36 32 29 25 23 21 21 21 17or17 21 21 21 23M1or36 32 29 25 23oror79 12Allow one transcription error in a list of onlythe first or last fiveWorks out the position of the median in thelistor 5th value23A1Additional GuidanceAnswer 23 (from any or no list)M1A1Puts list into order then finds the meanM1A0Just circles or identifies 29 or gives answer 29States 5th and circles 29M0M1A07
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark8(a)LibraryB18(b)180 B1[5.6, 6] (cm) or [56, 60] (mm)B1their 5.8 200 or their 58 20M1[1120, 1200]A1ftCommentsMay be on mapft B0M1 if their 5.8 200 correctly evaluatedAdditional Guidance[5.6, 6] can come from measurement or Pythagoras’ TheoremAnswer in correct range with no incorrect evaluationB1M1A15.6 200, answer 1160B1M1A0(incorrect evaluation seen)8(c)6.2 200 1240B0M1A1ft3 down, 5 across, 8 200 1600B0M1A1ft3 200, 5 200, answer 1600B0M1A1ft3 and 5 seen, answer 1600B0M1A1ft7 seen, answer 14008(scale method implied)B0M1A1ftAnswer only 1400B0M0A0ftAnswer [1.12, 1.2] km with or without [1120, 1200] seenB1M1A0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkValid reasonB1CommentsIndication that the shortest distancebetween two points is a straight line, butyou can’t generally walk in a straight linebetween two places in a townAdditional Guidance8(d)You would have to walk along the streetsB1There wouldn’t be a straight road between themB1You would have to walk along and then downB1There might be buildings in the wayB1You can’t go as the crow fliesB1There may be obstacles in the wayB1It isn’t a straight path in real lifeB1Can’t go directlyB1There might be buildings in the way such as the libraryB0The monument is in the wayB0It’s not a walking routeB0There is more than one routeB0May have taken a different routeB0Walking is slowerB0You may need to go past the town hallB0You might take a detourB09
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsMust be in correct boxesBalance ( )B1 ( )84.09 or ( )940.30212.48B2( )84.09or ( )84.09p and ( )940.30porB1ft for their 84.09 856.21( )940.30Additional GuidanceDate13/12/2016DescriptionCredit ( )Debit( )Starting balanceBalance ( )212.48B2914/12/2016Council tax15/12/2016Salary128.39856.2184.09940.30340.87 and 1197.08B1ft340.87 and 1197.08pB0ft84.09 and 940.3B1Ignore any working in grey boxes1084.09p and 940.30pB1 84.09p and 940.30pB184.09p and 940.3(p)B0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark36 9 11M144A1Commentsoe 36 9 and 36 2 4Additional Guidance10Only 36 1.2M0A011 9 1.2 and 36 1.2M1A011 9 1.2 and 36 1.2 Answer 43.2 (or 43)M1A011 9 1.2 and 36 1.2 Answer 44 (even after 43.2 seen)M1A1Only11of 36911 369M0M111
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkComments4x 14 3 or 4x 17or(14 3) 4 or 17 4M1orx–3 14 444.25 or171or 444A1Additional GuidanceEmbedded answer of 4.25 with 4.25 not selected on answer line11eg 4 4.25 – 3 14 with no answer given or answer of 14 or 1714 3 and answer 4.25M1A114 3 onlyM0A0Trial and improvement with answer 4.25M1A1Trial and improvement with no answer or answer other than 4.25M0A04.25 or12M1A0171or 4 seen and then answer 4 given44M1A1Answer of 4.25M1A017 4 (and no further)M1A0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCorrect criticisms about any two ofCommentsB1 for one correct comment about point,position or lengththe incorrect plotting of (17, 80) at(17,60)B2the incorrect position of the line ofbest fitAllow reference to a better line of best fitdrawn eg The line should look like minethe incorrect length of the line of bestfit (outside the range of the data)Additional GuidanceA comment about the incorrect point must refer to the specific point12(a)One of the points is wrong and point at (17, 60) circled on graphB1Not plotted (17, 80) correctlyB1x on 60 should be on 80B1Point at 60 is wrongB1Day 3 is wrong/ there is no day 3 on the graphB117 is plotted at 60/ 17 should be plotted at 80B1One of the points is wrongB0Points on the graph don’t match the tableB0Not put all the points in the correct placeB0A comment about the line of best fit must not have any misconceptionThe line is not steep enough/ at wrong angle/ should be more verticalB1The line isn’t a line of best fit/ the line doesn’t fit the pointsB1The line of best fit goes below 17/ condone past 30 (implies outside range)B1The line of best fit is wrong/ not drawn accurately/ not drawn properlyB0It isn’t a line of best fit because it doesn’t start at 0B0The line of best fit is wrong it should go through (0, 0)B0The line of best fit doesn’t go through the pointsB0The line is wrong it only goes through one crossB0The line of best fit doesn’t go to the axis (implies it’s too short)B013
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkTicks NoCommentsAllow any unambiguous indication of No, ifboxes blank may be in the reasonandB1oeeg No, it should be the hottest – the coldestexplanation that it should be thehighest value – the lowest valueAdditional Guidance12(b)14Does not tick or say NoB0Ticks No and It should be 30 – 17B1Ticks No and It should be 13B1Ticks No and He hasn’t subtracted the lowest valueB1Ticks No and It should be 17 – 30 13B1Ticks No and Range biggest – smallestB1Ticks No and The lowest temperature is 17 not 20B1Ticks No and He hasn’t used the lowest temperatureB1Ticks No and The lowest temperature is not 20B1Ticks No and The lowest temperature is 17B1Ticks No and The numbers range from 17 to 30B1Ticks No and It should be 30 – 17 23B0Ticks No and It should be 17 – 30B0Ticks No and You should take the smallest from the largest 30 – 26B0Ticks No and You should take the smallest from the largest 180 – 17B0Ticks No and It should be the smallest – the largestB0Ticks Yes and It should be the highest value – the lowest valueB0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsAlternative method 1180 150 80 130 120 or 660their 660 0.15 or 99or their 660 0.85 or 5617 5 or 35their 660 – their 99 – their 35or their 561 – their 35526(.00)M1M1depoeM1M1depA1dep on M1M1M1SC4 509Alternative method 212(c)180 0.15 or 27oeand 150 0.15 or 22.5(0)and 80 0.15 or 12M1and 130 0.15 or 19.5(0)and 120 0.15 or 18their 27 their 22.5(0) their 12 their 19.5(0) their 18 or 997 5 or 35M1depM1180 150 80 130 120 – their 99M1dep– their 35dep on M1M1M1526(.00)SC4 509A1Alternative methods 3, 4 and Additional Guidance continue on the next three pages15
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsAlternative method 3oe180 0.15 or 27and 150 0.15 or 22.5(0)and 80 0.15 or 12M1and 130 0.15 or 19.5(0)and 120 0.15 or 18180 – their 27 or 153Working out 85% of all five sales scoresM1M1depand 150 – their 22.5(0) or 127.5(0)and 80 – their 12 or 68M1depand 130 – their 19.5(0) or 110.5(0)and 120 – their 18 or 10212(c)cont7 5 or 35ortheir 153 – 7 or 146and their 127.5(0) – 7 or 120.5(0)Subtracting five 7sM1and their 68 – 7 or 61and their 110.5(0) – 7 or 103.5(0)and their 102 – 7 or 95their 153 their 127.5(0) their 68 their 110.5(0) their 102 – their 35orM1depdep on M1M1M1their 146 their 120.5(0) their 61 their 103.5(0) their 95526(.00)A1SC4 509Alternative method 4 and Additional Guidance continue on the next two pages16
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsAlternative method 4oe180 0.15 or 27and 150 0.15 or 22.5(0)and 80 0.15 or 12M1and 130 0.15 or 19.5(0)and 120 0.15 or 18their 27 7 or 34Adding five 7sand their 22.5(0) 7 or 29.5(0)and their 12 7 or 19M1and their 19.5(0) 7 or 26.5(0)and their 18 7 or 2512(c)conttheir 34 their 29.5(0) their 19 their 26.5(0) their 25 or 134dep on M1M1or180 – their 34 or 146and 150 – their 29.5(0) or 120.5(0)M1depand 80 – their 19 or 61and 130 – their 26.5(0) or 103.5(0)and 120 – their 25 or 95180 150 80 130 120 – their134ordep on M1M1M1M1deptheir 146 their 120.5(0) their 61 their 103.5(0) their 95526(.00)A1SC4 509Additional Guidance continues on the next page17
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017Additional Guidance509 comes from using 60 from the incorrect point on the scatter graphSC4Use the scheme that awards the best mark35M199M1M1dep134M1M1M1dep660 – 35 625 0.15 625 93.75Answer 93.75M1M0M1M0A0Build up method for 15% must be correct or method shown for incorrectparts18eg 10% of 660 60, 5% 30, 15% 90M1M0depeg 10% of 660 660 10 60, 5% 30, 15% 90M1M1dep
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark360 – (21 36 160 90)or 360 – 307or 270 – (21 36 160)CommentsoeM1or 270 – 2175313A1Additional Guidance53 (may be on diagram) with no incorrect working or no working53 on diagram with different answer on answer lineM1A1A0360 – (21 36 160) or 360 – 217 or 143 (ignoring 90 )M0A0180 – (90 36) 54M0A019
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsAlternative method 170 2.2 or 154their 154 14 or 11 14 15411M1M1dep70 2.2 14 oe is M1M1depA1Alternative method 214 2.2 or 6.36 or 6.4or 2.2 14 or 0.157. or 0.16M170 their 6.36or 70 their 0.157M1depor 11.006. or 10.9375 or 10.991411A1Additional Guidance14 2.2 6.3 and 70 6.3 11.1M1M1depA0Only 70 6.3 11.1M0M0depA0Only 70 6.4 ( 10.9375)M1M1depA0eg 10.9375 answer 11M1M1dep A1Only 70 14 or 570 14 5 and 5 2.220M0M1M1dep70 2.2 154, 154 14 11, 11 70 Answer 770 (11 seen)M1M1depA070 2.2 154, 154 14 70 Answer 770M1M0depA0
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkComments13 20 27 and Add 7oe ruleorB1 one correct arithmetic progression(using numbers from the list) with no orincorrect rule ie15 27 39 and Add 12or13 20 2720 15 10 and Subtract 5ororB227 20 13 and Subtract 715 27 39oror20 15 1039 27 15 and Subtract 12or27 20 13or39 27 15Additional Guidance15Accept the expression for the nth term as the rule13 20 27 and 7n 6 or eg 7 6or 15 27 39 and 12n 3or 20 15 10 and 25 – 5nB2or 27 20 13 and 34 – 7nor 39 27 15 and 51 – 12nIgnore incorrect expression for the nth term alongside a correct ruleeg 13 20 27 and Add 7 so n 7B213 20 27 and 7 or 7 more or going up in 7sB220 15 10 and five times table (scores for the arithmetic progression)B113 20 27 and n 7 (scores for the arithmetic progression)B1Using number(s) not on the listB010 15 20 and Add 5B021
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark161:4B11711000B13 250 or 750M11470 12 or 17 640M1538 000 – 464 500 or 73 500M1their 73 500 0.28 or 20 580M1deptheir 17 640 their 20 580 their 750or 38 970M1dep38 970 and NoCommentsoedep on 3rd M1dep on 3rd and 4th M1Must be adding salary, profit share andbonusA1Additional Guidance18For the last method mark, the 3rd and 4th M must have been awarded, butallow the addition of any number of months’ salary and any number of 250bonuses (at least one month of salary and at least one month of bonus)1470 20 580 250M0M0M1M1depM1depA020 5803rdM14thM1depBuild up method for 28% must be correct or method shown for incorrectparts22eg1 1% of 73 500 730, 28% 20 440 (will also lose the 5th Mdep)4thM0depeg2 1% of 73 500 73 500 100 730, 28% 20 4404thM1depeg3 10% of 73 500 7350, 1% 73.5, 28% 2058 (and 5th Mdep0)4thM0depeg4 10% of 73 500 7350, 1% 7350 10 73.5,28% 7350 7350 588 15 2884thM1dep
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMarkCommentsAlternative method 1 (hits and misses)A counter exampleeg Katy could be 6 : 2 and Ben hit 5using both ratioseg Ben 10 hits and 2 misses andor using numbers of hits and missesfor both playersKaty 12 hits and 4 missesB2B1 for a correct number of hits and misses(not 3 and 1) or a correct equivalent ratio forKatyAlternative method 2 (hits and total throws or proportion of hits)A counter exampleeg Katy could have hit 6 out of 8, Ben hit 5using total throws and number of hitsfor both playerseg Katy could haveor using proportion of hits for bothplayers191810and Ben2412B2B1 for a correct number of total throws andhits (not 3 out of 4) or a correct proportion of3hits (not ) for Katy4Additional GuidanceMust use the given ratios(Ben) 5 : 1(Katy) 6 : 2B215 : 3 and 15 : 5 (so the same hits)B2(Katy) 6 : 2 or (Katy) 6 hits and 2 missesB1List of equivalent ratios for (Ben and) Katy with no counter example chosenB115 : 3 and 9 : 3B1Fractions of hits out of total throws oe percentages or decimals or wordseg53and64B0eg2018and2424B1eg56and68B2Ben had (two) more throws – he had 6 and she had 4B023
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017QuestionAnswerMark1or 10% or 0.110B1CommentsoeAdditional Guidance20(a)Ratio eg 1 : 10 or 1 : 9B01seen and
MARK SCHEME – GCSE MATHEMATICS – 8300/2F – JUNE 2017 3 Glossary for Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, for GCSE Mathematics papers, marks are awarded under various categories.
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