Mark Scheme (Results) January 2015 - Maths Resource Website

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

Edexcel and BTEC QualificationsEdexcel and BTEC qualifications come from Pearson, the world’sleading learning company. We provide a wide range of ionalandspecificprogrammes for employers. For further information, please visit ourwebsite at www.edexcel.com.Our website subject pages hold useful resources, support materialand live feeds from our subject advisors giving you access to aportal of information. If you have any subject specific questionsabout this specification that require the help of a subject specialist,you may find our Ask The Expert email service helpful.www.edexcel.com/contactusPearson: helping people progress, everywhereOur aim is to help everyone progress in their lives through education. Webelieve in every kind of learning, for all kinds of people, wherever they arein the world. We’ve been involved in education for over 150 years, and byworking across 70 countries, in 100 languages, we have built aninternational reputation for our commitment to high standards and raisingachievement through innovation in education. Find out more about howwe can help you and your students at: www.pearson.com/ukJanuary 2015Publications Code UG040601All the material in this publication is copyright Pearson Education Ltd 2015

General Marking Guidance All candidates must receive the same treatment. Examinersmust mark the first candidate in exactly the same way as theymark the last.Mark schemes should be applied positively. Candidates mustbe rewarded for what they have shown they can do ratherthan penalised for omissions.Examiners should mark according to the mark scheme notaccording to their perception of where the grade boundariesmay lie.There is no ceiling on achievement. All marks on the markscheme should be used appropriately.All the marks on the mark scheme are designed to beawarded. Examiners should always award full marks ifdeserved, i.e. if the answer matches the mark scheme.Examiners should also be prepared to award zero marks if thecandidate’s response is not worthy of credit according to themark scheme.Where some judgement is required, mark schemes willprovide the principles by which marks will be awarded andexemplification may be limited.When examiners are in doubt regarding the application of themark scheme to a candidate’s response, the team leader mustbe consulted.Crossed out work should be marked UNLESS the candidatehas replaced it with an alternative response.Types of marko M marks: method markso A marks: accuracy markso B marks: unconditional accuracy marks (independent ofM marks)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 byalternative work.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 additionalwork does not change the answer in a way that is inappropriate forthe question: eg. Incorrect cancelling of a fraction that wouldotherwise be 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

IGCSE Maths Jan 2015 - Paper 4HR Mark schemeApart from Questions 4, 8, 15, 17 and 20b where the mark scheme states otherwise, the correct answer, unless clearly obtained byan incorrect method, should be taken to imply a correct method.QuesWorkingAnswerMarkNotes600 67.1 ( 40260) or3M1167.1 82.5 ( 0.813 )“40260” 82.5 or“0.813.” 600M1 dep488A1SC: B2 for 712Total 3 marksQues2a 150 oeWorkingAnswerMark2471b30 60 ( 1800) or“471” 30 ( 15.7)“471” ”1800” or“15.7” 603M1A1 awrt 471M1M1 depA1 for 0.26 – 0.262 or ft from (a)0.262cNotesRadius x h orD x h oe22h x Doe2M1A1 or h 2x D2Total 7 marks

Ques3WorkingAngle DAB 110Angle BAX 110 2 ( 55) orAngle DAX 110 2 ( 55) orAngle AXD 55Angle AXD 55 orAngle CBA 180 – 110 ( 70) orAngle ADC 180 – 110 ( 70)AnswerMark4NotesB1 can be implied by angle DAX angle BAX 55oM1M1125A1Total 4 marksQues4Working2y y 3 6orx 2x 3 12AnswerMark3NotesM1 for a complete method to eliminate one variable(condone one arithmetic error)A1 x 5x 5, y 1Ques5abiiiWorkingAnswer25n(n 2) 1(n 1) 2A1 y 1NB: Candidates showing no working score 0 marksTotal 3 marksMark12NotesB1 caoB1 for n(n 2) 1 on answer line or in tableB1 for (n 1)2 on answer line or in tableSC : If no marks scored in (i) or (ii) award B1 for n2 2n 1 in (b)Total 3 marks

Ques6abWorkingAnswer16 to 203 8 8 10 13 18 18 20 23 10 28 4 or24 80 234 360 230 112or1040Mark14NotesB1 Accept any unambiguous notation e.g. 16-20M1 finds products f x consistently withinintervals (inc end points) allow 1 errorNB. products do not have to be evaluatedM1 (dep on first M1) –uses midpointsM1 (dep on first M1) Σfx Σf3 8 8 10 13 18 18 20 23 10 28 48 10 18 20 10 4or“1040” (8 10 18 20 10 4)14.967Accept 15 if full working shownA1 14.8 14.9 or 14Total 5 marksQues7aWorkingAnswer1 14 20 8 or218 14 6 82Mark2136b420 14 ( 6)'6'2 82 or 36 64 or 100NotesM1 for a complete methodA1M1M1 dep on previous M1M1 dep on previous M1('6' 2 8 2 )10A1Total 6 marks

Ques8aWorking224 2 112 2 2 56 2 2 2 28 2 2 2 2 142 2 2 2 2 7AnswerMark32 75b56 32 1656 32 1456 28 162eg. 56, 32, 16or 56, 32, 14or 56, 28, 16NotesM1 for at least 2 correct steps in repeated factorisation(may be seen in a tree diagram)A1 2, 2, 2, 2, 2, 7 ( condone inclusion of 1)A1 2 5 7NB: Candidates showing no working score 0 marksM1 for any 3 correct distinct factors(excluding 1 and 224)A1 correct and have a sum between 99 and 110Total 5 marksQues9abcdWorkingAnswer3, 6, 9{2,3,4,6,8,9,10}{6}3, 9Mark1112NotesB1 condone {3, 6, 9}B1 condone omission of bracketsB1 condone omission of bracketsB2 cao(B1 for one of 3, 9 with no incorrect numbers)Total 5 marks

Ques10aWorkingAnswerCE 22.5oe or 22.5 9 ( 2.5) 179or 9 22.5 ( 0.4)Mark242.5b15c22.5 36 ( 225)3“225” 3618912M1 for a complete methodA1 for 42.5 or 422AE 22.5DE 10 2.5 – 10 10913.5or 10 or 10 1.5oe9NotesM1 for correct scale factorA1caoM1 or for a fully correct method to find area of triangleACE(height of triangle ABD 4.2(3 )height of triangle ACE 10.5(8 ))M1 (dep)A1 caoTotal 7 marks

Ques11abcWorkingAnswer 32y33x 2 2 yx 6 xy 4 y 2Mark1223x 2 4 xy 4 y 2d2(4 x 1)(x 2)NotesB1 caoB2 cao(B1 for one correct simplification)M1 for 4 correct terms, ignoring signs or for 3out of 4 correct terms with correct signs or . 4xy – 4y2 or3x2 4xy A1 caoM1 for (4x 1)(x 2)A1 caoTotal 7 marksQues12aWorking 85.67 10 5800Answer4Mark26.42 10 7bT4 2IkT 4IoekNotesM1 for digits 641(6 ) or 642A1 for 6.4 10 7 6.42 10 7IM1 T 4 kA1 Allow Total 4 marks

Ques13abcWorkingp (1 p) oe orp “(1 – p)” or0.2 0.8 ( 0.16)p (1 p) (1 p) p orp “(1 – p)” “(1 – p)” p or0.8 0.2 0.2 0.8 or2 “0.16”Answerp and 1 p onthe branchesMark2p213NotesB1 1 p on LH branchB1 for p and 1 – p in correct places on RHbranchesB1 accept p pM1 ft from tree diagramM1 ft from tree diagram0.32 oeA1 caoTotal 6 marks

Ques14aWorkingx 4 ( 4) 4 1 ( 1)2x 4 202Answer2Mark34.24, 0.236A1 4.235 to 4.24 and 0.236 to 0.24dep on M1Alternative scheme( x 2) 2 4 1( 0)M1x 2 5M14.24, 0.236bNotesM1 for correct substitution – condone one signerror in substitution; condone missing brackets ;allow 42;NB. Terms may be simplifiedM1 (indep) for 20 or 2 5 or 16 41.24, 3.241A1 4.235 to 4.24 and 0.236 to 0.24dep on M1B1 ft (accept more than 3 sig figs)Total 4 marks

Ques15aWorking1 2 or22Answer5Mark22.24b 1 5 6 AC 2 3 5 or B (4 5, 3 2) or (9, 5)3 6 4 10 OC " " 5 2 7 or C (4 5 1, 3 2 2)1 6 3 AE " " or2 5 2.5 1 AE AC or2 4 "10" 2 "7" E , 22 4 1 6 OE " " or 2 2 5 A1 cao3 A1 awrt 2.24M1M1 dep(10, 7)cNotesM1SC: B1 for (10, y) or (x, 7)M1M1 OE OA AE orE (“7”, “4.5”) 7 4 .5 A1 caoTotal 8 marks

Ques16aWorking ADB 90b180 – 90 70Position of T shown on diagramAnswero TDC ( DBC) 50o180 – 70 – 50 or180 – 50 – (180 – 110)Mark2M13A1M120NotesM160A1Total 5 marksQues17aWorking12 3 2 8 2 2 2 2 or12 3 2 8 2 2 2 or12 3 2 8 2 4AnswerMark28 5 2b10 3 22 2102 3 2or2102 2NotesM1 for any 3 terms correct of a 4 termexpansionA1 dep on M1 with all necessary steps shownM1 for a correct method to rationalisedenominator 325 2 3A1 dep on M1 with all necessary steps shownTotal 4 marks

Ques18Working360 9 40 (per cm sq) or360 (9 25) 1.6"40" 19 oe or7 "40" 6 "40" 6 "40" or280 240 240 or19 25 “1.6”AnswerMark3NotesM1M1 dep760A1Alternative method2a 12 6a 8 360M1360 5 and7214 '5' 4 12 '5' 4 4 '5' 12M1 depa 760A1Total 3 marks

Ques19abWorkingNNoe or kp oekx xpAnswerMark3NotesM1NNor p kkp NoekA1 p q Nk oeA1 q Nk or q Nk oe eg. q k2N 2 Nk orkq k 2q or1p kp212NkM1 ft from (a)A1 k 1, 0.52Total 5 marks

Ques20aWorkingAnswerMark2(2 x 1)(2 x 1)b4(2 x 1)1 2 3 or(2 x 1)(2 x 1) 4 x 14NotesM1 (2 x 1)(2 x 1)A1 caoM1 multiply all terms by (4x2 – 1) orcorrect equation with fractions with a commondenominator4(4 x 2 1)(2 x 1) 3 or2(2 x 1)(4 x 1) (2 x 1)(4 x 2 1)NB (4x2 – 1) may be factorised throughout4(4 x 2 1) 1(4 x 2 1) 3(4 x 2 1) or22x 14x 14(4 x2 1) (2 x 1) 3(2 x 1)(4 x2 1)4(2 x 1) 1 3(4 x2 1) oe orM1 correct equation with no fractions4(4x2 – 1) 2x 1 3(2x 1)(4x2 – 1) oe12x2 – 8x 0 or 8x – 12x2 0 orM1 correct simplified equation with all terms onone side24x3 4x2 – 8x 0 or 8x 4x2 24x3 00,23A1 dep on M2Total 6 marks

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IGCSE Maths Jan 2015 - Paper 4HR Mark scheme Apart from Questions 4, 8, 15, 17 and 20b where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method. Ques Working Answer Mark Notes 1 600 67.1 ( 40260) or 67.1 82.5 ( 0.813 ) 3 M1 “40260” 82.5 or “0.813.” 600 M1 dep 488 A1 SC: B2 for .