Mark Scheme (Results) January International GCSE Mathematics (4MB0) Paper 01

Transcription

1 Mark Scheme (Results) January 01 International GCSE Mathematics (4MB0) Paper 01

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 call our GCE line on , our GCSE team on , or visit our qualifications website at For information about our BTEC qualifications, please call , or visit our website at 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. Ask The Expert can be accessed online at the following link: 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 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for raising achievement through innovation in education. Find out more about how we can help you and your students at: January 01 Publications Code UG0075 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 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 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.

4 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. Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer 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 relevant working, even if it appears obvious that there is only one way you could get the answer given. 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. Probability Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least 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. Linear equations Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded. Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another.

5 1(a) 1(b) January 01 International GCSE Mathematics (4MB0) Paper 01 Mark Scheme (o.e.) % or 88% 1 ft 60 π 9 8. cm (awrt) 0 4 Attempt at factorising quadratic 4 SC: allow for ( x )( x+ 11) (x 4) (x + 11) 5 x = y = 6 1 term correctly differentiated 7(a) 7(b) 6 x + (o.e.) x Attempt at arranging numbers in sequential order International GCSE Mathematics (4MB0) Paper 01 January 01

6 8 (cos θ =) tan 40 - sin 0 (cos θ = ) 0.4 (or better) dep θ = 70. (awrt) (=.8) 100 OR (0.7) 4 ".8" % decrease = x100 4 OR 100 (1 "0.4") DEP 65.7% (awrt) 10 ( xx ) ( x )( x+ ) 11(a) 11(b) factorising numerator 1 factorising denominator (applying usual rule for factorisation) x x + 5, 6, 7, 8, 9, 10 B (-1 eeoo) or or :5 or 5 : 5 or 0.16 or 4.6 or better seen (Vol of B =) 8 "5" "" 176 cm (awrt) International GCSE Mathematics (4MB0) Paper 01 January 01

7 m = k 10 = k = 80 x = "80" (DEP) 1.5 x = (a) B (-1 eeoo) 15(b) B (-1 eeoo) 16 ACB = 58 o or BAC = 58 o AOD = 9 o or AOB = 88 CAD = 44 o o ft ("58 o BAD = " + "44 ") 10 4 ft 17(a) (o.e.) km 17(b) (o.e.) cm International GCSE Mathematics (4MB0) Paper 01 January 01

8 18(a) 4x 4x (b) (x + 18) = 4x + 18 SC: allow for ("4x+ 18") = ( x+ 18) x = 9 19(a) 8 15x 1 19(b) 15x = 8 y (fg) -1 : 8 x x (o.e.) 15 19(c) 1 1 ft (=96 cm ) Either 1 π (1.5) or 4 π (1.5) 1 "96" π (1.5) + 4 π (1.5) (DEP) 10 m (awrt) 4 International GCSE Mathematics (4MB0) Paper 01 January 01

9 1(a) 4 7 red blue, yellow , yellow red, yellow, (b) 14 1 (o.e.) or or better Either: Correctly balancing both equations (to eliminate either x/y) (no slips) Or Making x or y the subject of one of the equations (one sign slip) Correctly deciding whether to add or subtract (one sign slip) Or Substitution their equation in x (or y) into second equation. (DEP) (a) 5 7 x = (oe) 8 5 y = (oe) International GCSE Mathematics (4MB0) Paper 01 January 01

10 (b) Bus 144 o Cycle 60 o Train 6 o Walk 10 o one correct sector (± 1 ) one correct sector (± 1 ) + all labels all correct (± 1 ) (with/without labels) 4(a) Attempt at bisector of ACB drawn ± 1 mm on AB 4(b) Complete arc drawn inside triangle, centre A, any radius radius 5 cm (± 1 mm) 4(c) Correct region shaded 1 ft 5(a) tanθ = o (awrt) International GCSE Mathematics (4MB0) Paper 01 January 01

11 5(b) OB = ( + ) = ( 18) OA = 4 + (= 0) 1 OAB = " 18" " 0 " sin(45 "6.6") (DEP) Or: Area of any rectangle/triangle/trapezium which would lead to a solution A second rectangle/triangle/trapezium which leads further towards a solution. Complete method involving simple areas (DEP) 6(a).99/.00/ 4 One line correct All lines correct 6(b)(i) 5m/s 1 6(b)(ii) ( ).5m/s 1 6(c) 1 5 ("0" "5") m ft International GCSE Mathematics (4MB0) Paper 01 January 01

12 7(a) ( AC = ) cos 68 (=.76) AC = 4 0 cos 68 or better (DEP) 4.77 cm (cc) 7(b) sin BCA sin 68 = "4.77" sin68 sin BCA = "4.77" (DEP) 7(c) 5.6/5.7 CD cos"5.7" = cm /4.07 cm ft International GCSE Mathematics (4MB0) Paper 01 January 01

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