40 practice paper_3_h_-_set_c_mark_scheme


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40 practice paper_3_h_-_set_c_mark_scheme

  1. 1. Specification B – Practice Paper CHigher Unit 3Mark SchemeGCSEGCSE Mathematics (Modular)Paper: 5MB3H_01Edexcel Limited. Registered in England and Wales No. 4496750Registered Office: One90 High Holborn, London WC1V 7BH
  2. 2. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEMENOTES ON MARKING PRINCIPLES1 Types of markM marks: method marksA marks: accuracy marksB marks: unconditional accuracy marks (independent of M marks)2 Abbreviationscao – correct answer only ft – follow throughisw – ignore subsequent working SC: special caseoe – or equivalent (and appropriate) dep – dependentindep - independent3 No workingIf no working is shown then correct answers normally score full marksIf no working is shown then incorrect (even though nearly correct) answers score no marks.4 With workingIf there is a wrong answer indicated on the answer line always check the working in the body of the script (and on anydiagrams), and award any marks appropriate from the mark scheme.If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not beenreplaced by alternative work.If it is clear from the working that the “correct” answer has been obtained from incorrect working, award 0 marks. Sendthe response to review, and discuss each of these situations with your Team Leader.If there is no answer on the answer line then check the working for an obvious answer.Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of thesesituations with your Team Leader.If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makesclear the method that has been used.Paper: 5MB3H_01 2Session: Practice Paper C
  3. 3. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEME5 Follow through marksFollow through marks which involve a single stage calculation can be awarded without working since you can check theanswer yourself, but if ambiguous do not award.Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevantworking, even if it appears obvious that there is only one way you could get the answer given.6 Ignoring subsequent workIt is appropriate to ignore subsequent work when the additional work does not change the answer in a way that isinappropriate for the question: e.g. incorrect canceling of a fraction that would otherwise be correctIt is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect e.g.algebra.Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answerline; mark the correct answer.7 ProbabilityProbability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to aprobability, this should be written to at least 2 decimal places (unless tenths).Incorrect notation should lose the accuracy marks, but be awarded any implied method marks.If a probability answer is given on the answer line using both incorrect and correct notation, award the marks.If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer.8 Linear equationsFull marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated inworking (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified asthe solution, the accuracy mark is lost but any method marks can be awarded.9 Parts of questionsUnless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another.10 Use of ranges for answersIf an answer is within a range this is inclusive, unless otherwise stated.Paper: 5MB3H_01 3Session: Practice Paper C
  4. 4. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEME5MB3H Practice paper CQuestion Working Answer Mark Notes1(a)C = πDΠ× 16 =50.26(54…) 2M1 for 16 × πA1 for answer in range 50.24 to 50.29(b)A = π × r2Π × 8 × 8 =201.06 2M1 for 8 × 8 × πA1 for answer in range 200.96 to 201.142(a) 32 2M1 for establishing 16 km in 30 minutes or 16 ÷ 0.5A1 for 32 cao(b)Graphcompleted1 B1 for joining (40, 16) to (65, 0)3(a)Rectangle 4 cm long 2 cm highwith horizontal line at 1 cmCorrect frontelevation2M1 for rectangle with length 4 or width 2A1 for fully correct front elevation(b)Rectangle with length 4cm andwidth 3 cmCorrect plan 2M1 for rectangle with length 4cm or width 3 cmA1 for fully correct plan4(a) 3, –3, 3 2B2 for all 3 missing values correct(B1 for 1 missing value correct)(b)Correct curve2B2 for plotting all points correctly joined by a curve(B1 for plotting their points correctly)(c) 1.3, –2.3 2B1 for 1.3 ± 0.2 ft from their lineB1 for –2.3 ± 0.2 ft from their line514² + 6² = 196 + 36 = 232√(14² + 6²) = √(196 + 36) = √23215.23 3M1 for 14² + 6² or 196 + 36 or 232M1 for √(14² + 6²) or √(196 + 36) or √232A1 for 15.23(154621)645° angleconstructed3M1 for drawing an arc centre A and for stepping out two morearcs from the intersection of the arc and the given straightline and bisecting the two arcs to give an angle of 90°M1 for arcs showing the bisection of an angle of 90°A1 for angle of 45° drawn ± 2°7Correct regionmarked3M1 for attempt to bisect angle A showing construction linesM1 for drawing an arc with radius 5 cm tolerance ± 2mm thattouches AB and ACA1 for shading correct region84028 50100.× = £11.40£28.50 – £11.40 =£17.10 3M1 for attempt to find 40% of 28.50M1 for £28.50 – “£11.40”C1 for communicating correct method and answerPaper: 5MB3H_01 4Session: Practice Paper C
  5. 5. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEMEQuestion Working Answer Mark Notes9(i) 360 –138 222° 2M1 for 360 – 138A1 for 222 cao(ii) 180 + 63Alternative360 – (180 – 63)243° 2 M1 for 180 + 63 or drawing in North line andmarking in 63° correctly as an alternate angle or117° correctly as an allied angleA1 for 243° cao10(a)3x – 5 = 7x + 30–5 – 30 = 7x – 3x4x = –35x = – 8.75–8.75 2M1 for attempt to move variables to one side or theconstant terms to the other sideA1 for – 8 .75(b) 20 – 2x = 5(2x + 3)20 – 2x = 10x + 155 = 12xx = 5 ÷ 125123M1 for attempt to multiply RHS by 5 or sight of 10x + 15M1 for attempt to move variables to one side or theconstant terms to the other sideA1 for512oe11(a) –1, 0, 1 2B2 for –1, 0, 1(B1 for –2, –1, 0, 1 or 2 numbers correct out of –1, 0, 1)(b)Crosses at(–1, –1), (0, –1),(1, –1), (0, 0),(1, 0), (1, 1)3B3 for all 6 points only marked correctly(B2 for 3 points correctly ignoring any extras orincorrect points)(B1 for 1 point correctly marked ignoring any extras orincorrect points)12(a) 6 × 102× 8 × 1044.8 × 1073M1 for 6 × 102× 8 × 104A1 for 48 000 000 oeA1 for(b)2.4 × 105+ 3.7 × 104240 000 + 37 000 277 000 2M1 for writing one number correctly as an ordinalynumber of sight of 240 000 or 37 000A1 for 277 000 caoPaper: 5MB3H_01 5Session: Practice Paper C
  6. 6. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEMEQuestion Working Answer Mark Notes13 (1.04)52M1 for 1.04 raised to a power or a number raised to thepower 5A1 cao*14180 – 90 – 35(Angle in a semicircle is 90°)55°2B1 for 55°C1 for angle (subtended by a diameter at thecircumference) in a semicircle is 90°180 – (35 + 35)110°2B1 for 110C1 radii are equal so base angles of an isosceles triangleare equal and angles in a triangle add to 180°1585% = £5515% = 55 ÷ 85 × 159.71 3M1 for realising £55 is 85% or sight of 85 ÷ 0.85or 55 ÷ 85M1 for “55 ÷ 0.85” × 0.15 or “55 ÷ 85” × 15A1 for 9.71 cao1610x + 4y =162x – 4y = 8 +12x = 24x = 25 × 2 + 2y = 8 y = –1x = 2y = –13M1 for attempt to eliminate y by multiplying firstequation by 2 and attempt to addA1 for y = 2A1 for x = –1NB for trial and improvement no marks awarded unlessboth values are correct172120360A xπ= × × =23xπArc length =1202360xπ× × =23xπRadius of cone(r) =23xπ÷ π =23xV = ⅓πr²h =2427x hπ × ×V = 3A2427x hπ × ×= 3 ×23xπh =2745M1 for attempt to find an expression in terms of x for AM1 for attempt to find an expression in terms of x forthe arc length of the sectorM1 for attempt to use the arc length of the sector tofind the radius of the circular base of the coneM1 for attempt to substitute their values for V and Ainto V = 3AA1 for274oePaper: 5MB3H_01 6Session: Practice Paper C
  7. 7. GCSE MATHEMATICS HIGHERUNIT 3 PRACTICE PAPER C MARKSCHEMEQuestion Working Answer Mark Notes1854sin58.4258.4216sin28sin2528sin25sin×==×==DCDBDBDBADB34.4 5M1 forDBADB 28sin25sin=M1 for16sin28sin25×=DBA1 for 42.58M1 for 54sin58.42 ×=DCA1 for 34.4 or better (34.448)19(3x – 1)(x + 1) = 0Alternativex = (–2 + 4) ÷ 6 or (–2–4) ÷ 6X = ⅓ or –1 3M1 for correctly substituting into quadratic formula orattempt to factorise or complete the squareA1 for x = ⅓A1 for x = –120(a) (i)(a) (ii)6b – 6a6a2B1 caoB1 cao(b)EX= EF + FA + AB + AX= 6a + 6b + 6b – 6a – 3a12b – 3a 2M1 for attempt write EX in terms of a and bA1 cao*(c) AB : BY = 3 : 2AY = 10b – 10aEY = 6a + 6b + 10b – 10a= 16b – 4aE is on EX and EY and areparallel so they must be on thesame straight line sinceEX = 3(4b – a)EY = 4(4b – a)Proof given 3M1 for establishing vector AY or vector BYM1 for establishing vector EYC1 for explanation of why E, X and y lie on a straightline.Paper: 5MB3H_01 7Session: Practice Paper C