Mark Scheme (Results) Summer Pearson Edexcel International GCSE in Mathematics B Paper 2R (4MB0/02R)
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1 Mark Scheme (Results) Summer 04 Pearson Edexcel International GCSE in Mathematics B Paper R (4MB0/0R)
2 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information, please visit our website at Our website subject pages hold useful resources, support material and live feeds from our subject advisors giving you access to a portal of information. If you have any subject specific questions about this specification that require the help of a subject specialist, you may find our Ask The Expert service helpful. Pearson: helping people progress, everywhere Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 50 years, and by working across 70 countries, in 00 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: Summer 04 Publications Code UG0949 All the material in this publication is copyright Pearson Education Ltd 04
3 General Marking Guidance All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie. There is no ceiling on achievement. All marks on the mark scheme should 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 the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. Types of mark o M marks: method marks o A marks: accuracy marks o B marks: unconditional accuracy marks (independent of M marks) Abbreviations o cao correct answer only o ft follow through o isw ignore subsequent working o SC - special case o oe or equivalent (and appropriate) o dep dependent o indep independent o eeoo each error or omission
4 No working If no working is shown then correct answers normally score full marks If no working is shown then incorrect (even though nearly correct) answers score no marks. With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If it is clear from the working that the correct answer has been obtained 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 any appropriate marks, as long as it has not been replaced by alternative work. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. If there is no answer on the answer line then check the working for an obvious answer. Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg. Incorrect cancelling of a fraction that would otherwise be correct. It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect eg algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another.
5 Question Number Answer Notes Marks Total (a) (5 ( )) + ( 8 7) (oe) 7 (cao) (b) ( ) (oe) 5 5,, (oe) (awrt.88) A = One term correct All correct 4 " " (DEP ) B = (cao) 4 6 B = 7 NB: ft on their B B ft a b 4 + = " " 4 c d eq n s for a, b, c and d from above equation, Max. slips allowed in their eq n s (cao)
6 a = 8 a = 4 b= b= 6 c= 6 c= d = 4 d = 7 B ft 5 5 B = ( ) 0.55 ( ) 774 (cao) "774" ( = 0.9 ) and 0 ( ) + 40 ( ) + 40 ( ) (can be embedded within working) 44 (cao) % (cao) (a) 9 x 5 x (b) (i) "(9 x)" + "(5 x)" + x+ 6 = 6 (c) (ii) x = 8 (cwo) "8" 9 B B Bft 8 9, 0.4 (or better), 4.% (cao) B 6
7 Question Number 5 Answer Notes Marks Total (a) (b) 0 6, (o.e) 9 9 7, " " or " " " " B B B (o.e.) " " or " " " " (o.e) , 4 0, 7 5 (awrt 0.467, 46.7%) 6 6 (a) (i) 7, awrt. (ii) 9 B, B (b) y+ x= x= y y = - x x = y (No slips) x, x, x (cao) (c) ( x) 5 (4x -4x+)-5 8x 8x (cwo) NB: Answer given (ag) (d) "8x 8x " 45 = (oe) Attempt to solve a trinomial quadratic B ft (INDEP)
8 x = x = - (cwo) (cwo) 4 0 Question Number 7 Answer Notes Marks Total (a) 400 x (o.e.) B (b) 400 x 60 (o.e) B (c) (oe) B (d) " " " " = " " x 60 x (o.e) B ft (e) " x ( x 60) = xx ( 60) " (removal of denominator(s), but denominators must involve x, slip allowed when expanding brackets) x 60x 7000 = 0 (cwo) Attempt to factorise a trinomial quadratic (INDEP) x = 00 (cao) 4 (f) (oe) $06 (to their correct nearest dollar) B ft
9 Question Number Answer Notes Marks Total 8 (a) (i) 4b (ii) a b B, B (iii) BE = BA + AE = "( a b) " + ("4 b" a) BE = BC EC = b+ ( a "4 b" ) a + b (cao, oe) (iv) CD = CB + BD = b + (" a b") (b) CD = CA + AD = ( "4 b" a) + "( b a) " 7 a b (cao, oe) a µ (" + b") (c) BX = BC + CX = 7 b + λ(" a b") 7 λa + ( λ) b 7 λa + b λb 7 (d) µ = λ or µ = λ (from equating their components of a AND equating their components of b of vector versions of their BX ) B ft 6 λ = µ = (cwo)
10 Question Answer Notes Marks Total Number 9 Penalise LABELLING ONCE only (a) Triangle P drawn and labelled B (b) y = drawn and labelled (ie y = - Or line of reflection ) B (c) Triangle Q drawn and labelled (coords: ( 5,),( 5,4),(,) ) B (d) c s coords in (c) (seen or implied) Triangle R drawn and labelled (coords: (,),(,7),(0, 4) ) A ft (- ee) (e) Triangle S drawn and labelled (coords: (7, ),(5, 5),(4, 8) ) B ft (- ee) (f) c s coords in (e) (seen or implied) Triangle T drawn and labelled (coords: ( 5, ),( 5,0),(, ) ) (cao) A (- ee) (g) Reflection y = B B
11 Question Answer Notes Marks Total Number 0 NB: Penalise not corrected ONCE only in the question. (a) AC = cos 65 ( cos 65) AC = + ( ) AC = 8 sin 65 + (4 8 cos 65) ( ) AC = 8 sin 65 + (4 8 cos 65) AC =. m (b) 8 "." sin sin 65 ACD = 8 sin 65 ACD = sin "." 8 sin 65 tan ACD = 4 8 cos 65 8 sin 65 ACD = tan 4 8 cos 65 NB: Other right-angled trig. solutions possible. 8 = 4 + "." 4 "." cos ACD 4 + "." 8 ACD = cos 4 "." ACD = 44.9 NB: Watch for the incorrect assumption that AC bisects BCD so that ACD = 45 o. This scores M0 M0 A0 (c) BCA = 90 "44.9" B ft
12 ABC = 0 "." sin(90 "44.9") 64 m NB: Assumption that ABCD is a cyclic quadrilateral scores B0 M0 A0 (d) ADB = ADC + ABC BCD route: Area of ADC = 8 4 sin 65 awrt 96 m Area of ADB = "96" + "64" 4 0 ADB = AD AB sin DAB route: AB = 0 + "." 0 "." cos"45." ( 0 "." 0 "." cos"45." ) AB = + (AB=6.80) AB = awrt 6.8 then DAC = 80 (65 + "44.86") = "6.80" sin CAB = sin"45." CAB = ( ) DAB = "70.9" + "57.56" = 7.68 ( ) BD = =.4, 4 6 "6.80" + 8 ".4" "6.80" 8 = 7.67 DAB = cos
13 Finally ( ADB = AD AB sin DAB route: ) Area of ADB = 8 "6.80" sin"7.68" (DEP on correct method for DAB and AB) ADB = AD BD sin ADB route: ( ) BD = =.4 BD = awrt., BDC = tan ( = ) 4 BDA = 65 "9.8056" = 5.9 ( ) Finally ( ADB = AD BD sin ADB route: ) Area of ADB = 8 ".4" sin"5.9" (DEP on method for ADB and BD) ADB = 0 m 4
14 Question Number Answer Notes Marks Total (a) 4 y+ x B (b) x("4 y+ x") 40 (c) y = x B ft 40 = + (cwo) (ag) S x 4x x (d) One term correctly differentiated 60 x x 60 " x " = 0 x 4. (cao) 4 (e) (f) graph penalties (-) straight line segment(s) each point missed (± ½ small sq.) each missed segment each point not plotted each point incorrectly plotted (± ½ small sq.) tramlines very poor curve i.e. line too thick (g) line drawn at S = 75 accept any x [.,.4] NB: Drawing S =75 may be implied by answer x [.,.4] B B B B ft (- eeoo) 6
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