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Mark Scheme (Results)Summer 2015Pearson Edexcel International GCSEMathematics A (4MA0)Paper 4HR

Edexcel and BTEC QualificationsEdexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awardingbody. We provide a wide range of qualifications including academic, vocational,occupational and specific programmes for employers. For further information visitour qualifications websites at www.edexcel.com or www.btec.co.uk. Alternatively,you can get in touch with us using the details on our contact us page atwww.edexcel.com/contactus.Pearson: helping people progress, everywherePearson aspires to be the world’s leading learning company. Our aim is to helpeveryone progress in their lives through education. We believe in every kind oflearning, for all kinds of people, wherever they are in the world. We’ve beeninvolved in education for over 150 years, and by working across 70 countries, in 100languages, we have built an international reputation for our commitment to highstandards and raising achievement through innovation in education. Find out moreabout how we can help you and your students at: www.pearson.com/ukSummer 2015Publications Code UG042087All the material in this publication is copyright Pearson Education Ltd 2015

General Marking Guidance All candidates must receive the same treatment. Examiners mustmark the first candidate in exactly the same way as they mark thelast.Mark schemes should be applied positively. Candidates must berewarded for what they have shown they can do rather thanpenalised for omissions.Examiners should mark according to the mark scheme notaccording to their perception of where the grade boundaries maylie.There is no ceiling on achievement. All marks on the mark schemeshould be used appropriately.All the marks on the mark scheme are designed to be awarded.Examiners should always award full marks if deserved, i.e. if theanswer matches the mark scheme.Examiners should also be prepared to award zero marks if thecandidate’s response is not worthy of credit according to the markscheme.Where some judgement is required, mark schemes will provide theprinciples by which marks will be awarded and exemplification maybe limited.When examiners are in doubt regarding the application of the markscheme to a candidate’s response, the team leader must beconsulted.Crossed out work should be marked UNLESS the candidate hasreplaced it with an alternative response.Types of marko M marks: method markso A marks: accuracy markso B marks: unconditional accuracy marks (independent of Mmarks)Abbreviationso cao – correct answer onlyo ft – follow througho isw – ignore subsequent workingo SC - special caseo oe – or equivalent (and appropriate)o dep – dependento indep – independento eeoo – each error or omissiono awrt –answer which rounds to

No workingIf no working is shown then correct answers normally score fullmarksIf no working is shown then incorrect (even though nearly correct)answers score no marks.With workingIf there is a wrong answer indicated on the answer line always checkthe working in the body of the script (and on any diagrams), andaward any marks appropriate from the mark scheme.If it is clear from the working that the “correct” answer has beenobtained from incorrect working, award 0 marks.Any case of suspected misread loses A (and B) marks on that part,but can gain the M marks.If working is crossed out and still legible, then it should be given anyappropriate marks, as long as it has not been replaced by alternativework.If there is a choice of methods shown, then no marks should beawarded, unless the answer on the answer line makes clear themethod that has been used.If there is no answer on the answer line then check the working foran obvious answer.Ignoring subsequent workIt is appropriate to ignore subsequent work when the additional workdoes not change the answer in a way that is inappropriate for thequestion: eg. Incorrect cancelling of a fraction that would otherwisebe correct.It is not appropriate to ignore subsequent work when the additionalwork essentially makes the answer incorrect eg algebra.Transcription errors occur when candidates present a correct answerin working, and write it incorrectly on the answer line; mark thecorrect answer.Parts of questionsUnless allowed by the mark scheme, the marks allocated to one partof the question CANNOT be awarded in another.

Apart from Questions and 15d and 19b, where the mark scheme states otherwise, the correct answer, unless clearly obtained by anincorrect method, should be taken to imply a correct method.Question(i)1(ii)WorkingAnswer{i, a}{c, h, i, n, a, t, l, y}Mark2B1B1NotesBrackets and commas not needed.Do not allow repetitions.Total 2 marksM22oror 4 orM1 for 638 2.45 or260(.408.) rounded or truncated to3 or more significant figures or638 165 or3.86(6666.) rounded or truncated to3 or more significant figures. 60 oe2323A1caoTotal 3 marks

3(a)M17 12 15000 or 0.075 15000 oe or 1125 or1000.075 15000 15000 or 15000 1.075 oeEg161252(b)Eg 108 or 1.08 or 22500 1.08 orA1M2For finding 7.5% of 15000 orfor a complete method to increase15000 by 7.5% (eg 1.075 15000)caoFor a complete method 1800 or 100 1800 or 225 100 1800 or 22500 1800M1 for 8% 1800 or 0.08x 1800 oror 225 oror 22500 or243003A1 oeTotal 5 marks

4(a)( 2, 4), ( 1, 1), (0, 2), (1,5), (2,8), (3,11)correct line drawnfrom between x – 2and x 3B3For a correct line between x – 2 andx 3.B2If not B3, then B2 for: at least 2 correct pointsplotted or for a line passing through atleast 2 correct points or for a line drawn with positivegradient through (0,2) andclear intention to use agradient of 3 (eg. a linethrough and (0 , 2) and(0.5 , 5))B1If not B2 then B1for: at least 2 correct points stated(may be in a table) or for a line drawn with apositive gradient through #(0 , 2) or for a line with gradient 3.ft for a point marked above theiry 3x 2 if at least B1 scored in (a)orfor a point to the right of x 23(b)M1

correct pointA12Point marked above y 3x 2 andto the right of x 2 (not on lines).Label P may be omitted ifunambiguous.SCB1 for the correct region identifiedby either shading in or shading out.Total 5 marks5(a)4 9 7 1 6 3(4 9 7 1 6 3) 1oror2230311oror 15 or 15222M122(b)A1M24 9 7 1 6 3(4 9 7 1 6 3) 1oror443031oe ( 7.5) oroe ( 7.75) or 8 or443 oe ( 22.5) or 3 Condone 1 omissionEgAccept a clear intention to list thenumbers in order and find the centreof the list.For Lower quartile 1 AND Upperquartile 4Accept a correct ordered list of the 30numbers with both quartiles clearlyidentified in the correct position.M1 for Lower quartile 1 orUpper quartile 4 orAccept a correct ordered list of the 30numbers with the position of one ofthe quartiles clearly identified in thecorrect position.oe ( 23.25) or 2333A1Total 5 marks

6(a)1 0.44 0.42 0.04 or 1 – 0.9(b)(c)0.1 oe2M1A10.86 oe1B11200 0.04M1A14827.180 43 or 360 (180 43) or 360 – 137M12232AcceptAcceptoe or 10 %oroe or 86 %Accept 48 out of 1200Note: M1A0 for 48/1200Total 5 marksFor a complete method.A1Total 2 marks

8(a)(b)(c)EgM1175 97 27 oe oror2252A1M12162A1M1or 8143714Or Flaky: (flour x), fat x and Sweet: (flour x), fatx927where x may also be any positive value( 9 : 7 ) 27 : 21 or 9 :For a complete methodForandwhere x may alsobe any positive valueEg andEg 270 and oeFor3 : 2 oeA12Eg 270 (x 270) or:or 21 : 14 or 189 : 126 or1 : or 1.5 : 1ISW only if answer is incorrectlysimplifiedSCB1 for answer of 2:3 oeTotal 6 marks

9.(a)(b)10 p 1519 3 2x orB1M1Accept 10 p – 15Allow equals sign (Eg 6 2x) orcondone incorrect inequality sign(eg 6 2x)A1Allow 3 xNB: Final answer must be aninequalitySCB1 for x 3 or x 3 or x 3 or 3as an answerFor correct substitutionAllow omission of brackets.For correctly isolating 2k or –2k or kor – in a correct equation.6 2x or 2 x 3 9 or 2 x 6x32(c)6 ( 2) k ( 2) 5 or 6 –8 2k 5M1Eg 6 8 5 2k or 2k 8 5 6 or 9 2k orM13–9 –2k or k –––or –k – –––or –k –4.54.5A13(d)1 3( f 2) or 1 3 f 6 or1 92 2Accept 4 ,M11 f 23 1 23 oeA12Accept –1.66(666.) correctlyrounded or truncated to at least 3significant figures.Total 8 marks

10.cos 56 sin(90 – 56) (x )M17.4or 7.4 xcos56 orxorCorrect equation for x²eg x 2 7.42 (7.4 tan 56)2Correct statement of Sine ruleeg –or 7.4 xsin(90 – 56)M1–Correct expression for xegx 7.42 (7.4 tan 56 )213.23A1Correct expression for xeg (x) sin(90)–awrt 13.2Total 3 marks11.2 3.5 8.2 2 3.52 or 57.4 24.5 or81.9 or 180(.327.) 76.9(690.) orM2Allow 76.9(690.), 180(.327.),38.4(845.) and 218(.81.) if roundedor truncated to at least 3 significantfigures.2 3.5 8.2 3.52or 180(.327.) 38.4(845.) or 218(.81.)M1 for 2 3.5 8.2 or57.4 or 180(.3274 ) or2 3.52 or24.5 or 77 or 76.9(690 )2573A1awrt 257Total 3 marks

12.M1(Gradient ) – or (m ) –M1A13y x 3 oe5Allow (gradient or m) or( y ) – x c (c may be a number)Indep( y ) mx 3(m may be a number except 0)Allow y intercept or c 3 statedoeEg Accept 5y 3x 15 ory – 3 – (x – 0) ory – 0 – (x – 5)33535SC B2 for x 3 or L x 3Total 3 marks

13.(a)Eg.or or 0.6 ororM1or 1.66(66.) orMN12oe or (MN ) 13.5 12 8 13.5 oe8.1(b)Eg PQ 9 or oe or or PQ 9 2oe orA1M1oe or PQ 15oe or (LQ ) 9 for correct scale factor or correctequation involving MN or correctexpression for MNoeAllow use of 1.66(66.) in place ofif rounded or truncated to at least 3significant figuresoeCorrect expression for PQ or LQ(eg 9 oe or 9 oe )Correct equation involving PQ or LQ( eg oe or oe )Allow use of 1.66(66.) in place ofor 0.666(66.) in place of if roundedor truncated to at least 3 significantfigures6(c)225oe9A1B1Accept 279Accept 2.77(777.) rounded ortruncated to at least 3 significantfigures21 20 5 Also accept or 12 3 2

(d)Eg– A 105.6 or AA 105.6 or– 105.6 orM1For a correct equation involving Aft from part (c )M1For correct expression for A.ft from part (c)Decimal values should be rounded ortruncated correct to at least 3SFoeTotal 8 marks 105.6 A or A(A )–or (A )or (A )59.43A1

14.(a)V M1Allow Vt² k or t² Do not allow V 28 koe or2.52M1For correct substitution in a correctequationImplies first M1Award M2 if k 175 statedunambiguously in (a) or (b)A1Only award if V is the subject.Award M2A1 if V on answer lineand k evaluated as 175 in part (a) orpart (b)ft for k if k 1k 28 2.5² ork 175V 3(b)V M1"175"6.2524.482A1Total 5 marks

15.(a)(b)1, 5, 21correct curve11B1B1(c)(d) 1.11B1M2y 1 – 2x drawnCorrect curve through (1,3), (2, 1),(3, 5), and (4, 21).Accept –1.15 x –1.05Line must be long enough to crosscurve and verify accuracy.M1 for x3 3x2 5 2 x 1 ory 2 x 1 oe 0.8A13dep on M2Accept –0.9 x –Total 6 marks16.3223M24 1 5 1 5 1 5 1 4 6 4 or 6 6 6 6 6 6 6 Accept use of 0.16(666.) in place of and 0.83(3333.) in place of roundedor truncated to at least 2 decimalplaces.or1–M1 for oror ororP(no sixes) 67112963A1Accept awrt 0.518Total 3 marks

17.(a)(b)(c)216211 KJL 37o or PJM 60o or LKM 60oor LMP 37o or MPJ 58o or MPL 122B1B1M2If not M2 then M1 for: GJL 81o or GMJ 81o orJKL 81 orJML 99or JPK 122Angles may be marked on the diagramor labelled in the working.583A1Total 5 marks18.or 150 oror 300 oror 190 oror 30Frequency density 150, 300, 190, 30heights 3, 6, 3.8, 0.6 cmcorrect bars3M1For one correct bar drawn orone correct frequency density, notincluding 0 w 1 or1 small square 1 or1 large (cm) square 25M1For three correct bars drawn orthree frequency densities, notincluding 0 w 1A1All bars correct.Total 3 marks

19. 3(a) (i)(a) (ii)(a)(iii)(b)032Eg or11B1B1B11or1.5, 112M1For simplifyingorfor rationalising the denominator.A1For simplifyingandfor rationalising the denominator.NB: The solution must be fullycorrect (cso)or ororNote:To rationaliseacceptTo rationalise (c)oror or2 55, etc, only acceptetc.2e2 2e 3 2e 3 (2 3)2 ore² – 4eNB: Do not accept assufficient method for rationalising thedenominator.M1e 5A1Expand brackets with 3 correct termswith correct signsEg e² – 4e or e² – 2e – 2e ore² – 2e 12, etc orall 4 correct terms with signs missingeg e², 4e , 12 or e², 2e , 2e , 12caof 37A1cao 123Total 8 marks