Mark Scheme (Results) Summer International GCSE Mathematics (4MB0) Paper 02R

Transcription

1 Mark Scheme (Results) Summer 01 International GCSE Mathematics (4MB0) Paper 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 10 years, and by working across 70 countries, in 100 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 01 Publications Code UG068 All the material in this publication is copyright Pearson Education Ltd 01

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. When examiners are in doubt regarding the application of the mark scheme to a candidate s response, the team leader must be consulted. 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 awrt answers which round to... 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 International GCSE Maths B Summer 01 Mark Scheme 1 Rearranging so that the coefficient of x or y is the same in both eqns OR isolating x or y Subtracting or adding equations OR substituting expression for x or y to obtain y or x NB: Allow 1 slip total for both M marks. x = 4 y = 1 dep eg y = () then y = 1 () then x (1) = 10 (dep) then x = 4 () OR x = 0 () then x = 4 () the (4) y = 10 (dep) then y = 4 () 4 4 (a) CAB 70 o reason: isosceles triangle and DAF 0 o reason: alternate segment theorem OR ECD 60 o reason: angles on straight line OR CDA 70 o reason: alternate segment theorem leading to CAD 60 o reason: angles on straight line or angles of triangle OR Taking O to be the centre of circle COA 140 o (angles of a quadrilateral) BAO BCO 90 (angles between tangent and radius) then CDA 70 o angle at centre

6 leading to CAD 60 o angles of a triangle NB: At least TWO reasons required for full marks ( marks) plus all angles correct. Special Case 1: (1 mark) only if no reasons given but all angles correct. (b) Special Case : ( marks) for one reason given and all angles correct. AD 6 sin0 sin" CAD" AD 6 sin 0 sin" CAD" dep AD =.1 cm 6 (a) dy dx 1 x = 0 ( 1 term correct in a linear exp in x) x 1 Substituting x in y y dep 4 (b)(i) (b)(ii) dy (x = -1) = +1, dx dy (x = 0) = -1 dx Since gradients are +1, 0 and -1 at x = -1, -1/ and 0 respecitively 1 1, 6 is a maximum (correct conclusion) 4 NB: All values of d y must be used for a dx correct conclusion

7 OR d y dx 1 1, 6 4 is a maximum (correct conclusion) 6 4(a) n ( F M V ) or 4(b) n F M V or of people not buying F, M or V or number of people not buying anything 1 B - 1eeoo 4(c) F V M or ( F V ) ( M V ) (o.e) 1 4(d) 90 + (60--x-x) + (0--x-x) + (0-x-x-) + + x + x + x = 17 (an attempt to add all of the values from their Venn diagram. allowing 1 slip fully correct (NB: there must be at least TWO entries in the Venn diagram in (b otherwise award no marks x = 6 dep 7

8 (a) x x x (x + ) = x (x +) (Removing the denominators.) ) x - x - 1 = 0 (correct conclusion) (b) ( ) 4()( 1) x (Fully correct substitution into formula) dep x = awrt.6 (or better.89) ".89" (substituting their x into (x+) 1.8 km ft 4 7 6(a) M = 1 0 B -1eeoo 6(b) Special Case: Award (1 mark) for a (1x) matrix Marks for value of a (1, 1): = a a = 10 Marks for b (1, ): a + 4b = 1 b = Marks for c (, 1): c + d = c c = 4 Marks for d (, ): 4 + = d d = 8 10

9 7(a) Yellow 7(b)(i) Blue 1/6 or B -1eeoo ft 7(b)(ii) 7(c)(i) 10/6 or 0.78 Probabilities are ft from their table P(score=) x P(score=) = or ft 7(c)(ii) P(total = 9) = {P(4 then ) + P( then 4)} + {P( then 6) + P(6 then )} + {P( then 7) + P(7 then )} = 4 4 " " " " " " " " {Grand Total probs} correct All {Grand Total probs} correct NB: B marks are ft from their table All correct Grand Totals added = or 1 17 or or ft ft 6 10 Special Case: " " " " B0 M0 scores

10 8(a) Penalise labelling ONCE only in this QUESTION (parts a-d) ABC drawn and labelled. 1 8(b) 1 B DEF drawn DEF -1eeoo 1 1 8(c) B PQR -1eeoo If triangle not plotted then you may still award the available B marks for their coordinates of the vertices PQR drawn NB: fts are from their matrix multiplication 8(d) 70 o (rotation) OR -90 o (rotation) OR 90 o clockwise (Enlargement) scale factor, ft About origin (o.e) 9 9(a)(i) 9(a)(ii) OC = a + b CB = - ( a + b ) + 4b CG = (b a) dep (b a) (oe) 9(b)(i) FG = ( a + b) + (b a) 4 FC CG FG = 1 b ft ft NB: Only apply ft if their vectors correctly arrive at FG = " " b

11 OR FCG FC CG FG s are similar, OCB OC CB OB 9(c) FG 4 b 1 (cao) From given ratios and (b)(i), as: ft 4 FCG FC CG FG s are similar, OCB OC CB OB OR ft FG : OB = 1 : 4 = 1 : 0 = : leading to OCB : FCG = : (o.e) dep (so the M marks can be fts ) : 9 1 b FG NB: Sight of vector division, eg OB 4b scores M0 M0 A0 9(d) OCB = " " FCG = " " 18 (=0) 9 9 OCB = 0 (cao) 1 10(a) 10(b) Height of hemispherical top = 0 r = h + r correct conclusion 1 4 V = hr + r (one volume correct) 1 (both volumes correct) V = V 1 4 (0 - r)r + r (eliminating h) = y = r 0 r (correct conclusion 7 dep dep 4

12 10(c) or (d) Note: Penalise ncc ONCE correct curve drawn -1 mark for each of the following: incorrect/non-uniform scale straight line segments each point missed ( ½ small square) each missed segment each point not plotted each point incorrectly plotted ( ½ small square) tramlines very poor curve eg line too thick 10(e) V max 18( 1) B -1eeoo 10(f) (condone missing ) ft 1 Indication of looking for range.1( 0.1) r 6.( 0.1) OR.1 (to) 6. ft Note: If there is no indication on their diagram (eg a horizontal line or vertical lines) and they have an incorrect inequality eg.7 r and r 6., then award M0 A0. A correct inequality eg.1( 0.1) r 6.( 0.1) by itself scores 14

13 11(a) Penalise incorrect rounding ONCE. sin BE 11(b) BE = cm -> 11.8 cm X is a pointt on DC so that EX is perpendicular to DC so DX = cm ED = (1 "" ) (= 1) ED = > 1.4 cm 11(c) 8 sin 0 (BD= 16) BD 1.69 = "11.81" "16" cos EBD EBD 1 "11.81" "16" "1.69" cos "11.81" "16" EBD = >0.1 o, 0. o NB: Watch for an answer of EBD = 19 or 10 which usually means a score of M0 A0. dep dep 11(d) ACDE: ACDE 1 (8 ) 1 (=78) 4 ACDE = 78 cm BED: BED 1 "11.81" "16" sin"0.07" [OR (Heron s formula) "1.69" "11.81" "16" s ( = 0.1) BED 0.1 (0.1 "1.69") (0.1 "11.81") (0.1 "16") OR Sine Rule for EDB BED o DEB "1.69" "11.81" sin"8.744" o ] BED = awrt 7, 7 (eg 7.4, 7.84 cm )

14 Required Surface Area = 10, 11 cm 14

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