Mark Scheme (Higher) : Paper 2 Calculator - June 2018

GCSEMathematics8300/2 – Paper 2 Higher TierMark schemeJune 2018Version/Stage: 1.0 Final

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018Mark 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 2018 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.2

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018Glossary 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 – 8300/2H – JUNE 2018Examiners 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 – 8300/2H – JUNE 2018QuestionAnswersegment1CommentsB1Additional Guidance6 1072B1Additional Guidance3:23B1Additional Guidance400%4MarkB1Additional Guidance5

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkAll 5 correctCommentsB3 for 4 correctB4B2 for 3 correctB1 for 1 or 2 correctAdditional Guidance.Arithmetic progression.5.eometric progressionibonacci se uenceB4.Triangular numbersube numbersuare numbersTwo connections from a LH box is choice so is incorrect for that boxConnections do not have to be straight lines6

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAlternative method 1Any one ofoe oror .( )% or eg 60 000 : 420 000 or 1 : 7or17480 000 : 420 000 or 8 : 7or oror .( )% or 87or420 000 60 000 or 7M1or420 000 480 000 or 0.875or 87.5% or78or 6or .( )% or or19or540 000 60 000 or 9Any one ofmust be a matching pair (could bedifferent forms) to award M2(see A1 for list of matching pairs)60 000 480 000 or 0.125or 12.5% or18oeeg 60 000 : 480 000 or 1 : 8oror540 000 480 000 or 1.125or 112.5% or540 000 : 480 000 or 9 : 898M1or480 000 60 000 or 8or or 0.89 oror .( )% or % or89Mark scheme continues on the next page7

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsoe11andand No78eg 1 : 7 and 1 : 8 and Noor89andand No78or. and .and Noor.( )% and. % and Noor. and .and Noor.( )% and 12.5% and Noor7 and 8 and No6contA1or78andand No89or11andand No98or9 and 8 and Noor. and .and Noor.( )% and. % and Noor.and . or .and Noor. % and.( )% or% and NoMark scheme continues on the next page8

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAlternative method 2No and any one ofoe60 000 480 000 and420 000B2 any one of the calculations[67200, 68640]B1 any one of the fractions oeorfor equivalent fractions, decimals andpercentages see Alternative method 160 000 540 000 and 67 500480 000or60 000 420 000 and 52 500480 000or60 000 480 000 and540 0006cont[52 800, 53 334]orB3420 000 540 000 and 472 500480 000or480 000 480 000 and420 000[547 200, 548 640]or480 000 480 000 and540 000[422 400, 427 200]or540 000 420 000 and 472 500480 000Additional guidance continues on the next page9

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAdditional GuidanceIn Alt 1, for M2 the matching pair do not have to be in comparable formeg 14.3% and1and No8M1M1A0For comparable fractions, they must be in their lowest terms or have thesame numerators or the same denominators for the A16conteg Alt 160 00060 000andand No420 000480 000M1M1A1For comparable ratios, they must be in their lowest terms or have thesame LH sides or the same RH sides for the A1eg Alt 1 60 000 : 420 000 and 60 000 : 480 000 and NoM1M1A1If working with percentages, condone absence of % symbol10eg Alt 1 14 and 12.5 and NoM1M1A1Both are increases of 60 000 and it is then over different amounts socannot be the same percentageM0M0A0

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsTwo different probabilities fromoe15or 0.75 or 75%20B1 for one correct probabilityor22or .30 or.( )%or17or 0.425 or 0.4340or 42.5% or 43%or7(a)B254or 0.6 or 60%90or37or 0.74 or 74%50or32or .60 or.( )%or39or .70or or 0.56. % or%Additional guidance continues on the next page11

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAdditional GuidanceAccept108as one of the probabilities180Mark the answer line if it has two answers ignoring any incorrectprobabilities in the working linesIgnore any incorrect cancelling or change of form (fraction, decimal orpercentage)If the answer line only has one answer, check the working lines for asecond answer for B2. Ignore any extra probabilities, unless incorrect,in which case award B1 max7(a)conteg Working lines1554Answer line2090B2eg Working lines15 554,Answer line20 1590B1If the answer line is blank, check the working lines for answers for B1 orB2. Ignore any extra probabilities, unless incorrect, in which case awardB1 maxeg Working lines15 22 54,,Answer line blank20 30 90B2eg Working lines15 5 54,,Answer line blank20 15 90B1Probabilities must not be given as ratiosDo not accept the average of the given probabilities as answer12

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAlternative method 1 (ft their part (a))Their probability with the greaternumber of trialsft their two different probabilities frompart (a)B1ftandvalid reason eg More throwsboth probabilities must have adenominator based on throwsAlternative method 2 (independent of part (a))oe5490B1andvalid reason eg Total throwsAdditional GuidanceAccept any unambiguous indication of their probability eg the day7(b)Using ratiosB0Ignore any non-contradictory statements60% and It’s for all three daysB154and It takes into account more throws90B11722(withalso in (a)) and Because he threw it more on Wednesday4030B1ft54and Shows the overall probability90B154and Probability over total throws90B154(with Wednesday probability in (a)) and It’s the average total days,90not just WednesdaysB1ftAdditional guidance continues on the next page13

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerCorrect ft probability orMarkComments54and It’s more reliable90B054and There’s a lot of data907(b)contCorrect ft probability orB054and He may get better with more throws9054and He throws 90 times90Correct ft probability orB054and More hits90B0Alternative method 122.5(0) and 4or27 and 8or31.5(0) and 12or36 and 16or8M140.5(0) and 20or45 and 24or30 : 16or45 : 2445 and 24 chosenA16A1eg 45 : 24 is the final ratio seenMark scheme and additional guidance continues on the next page14B0

MARK SCHEME – GCSE MATHEMATICS – 8300/2H – JUNE 2018QuestionAnswerMarkCommentsAlternative method 2any letter18 4.5x and 4x seenor18 4.5x4x 158M1sets up correct equationeliminates denominators8(18 4.5x) 60xor 144 36x 60xoeM1depoeor 24x 1448cont6A1Additional GuidanceAnswer 6 that is not from incorrect methodM1A1A145 and 24 followed by eg 49.5(0) and 28 (answer not 6)M1A0A0Equivalent ratio to 15 : 8 that is not 30 : 16 or 45 : 24eg 60 : 32M0A0A0(answer not 6)Final calculation15 24 45 (answer not 6)8M1A1A015