Mark Scheme (Results) November 2010

Transcription

1 Mark Scheme (Results) November 00 GCSE GCSE Mathematics (Modular) 5MBH Unit - Higher

2 GCSE MATHEMATICS MB0 Edecel is one of the leading eamining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. Through a network of UK and overseas offices, Edecel s centres receive the support they need to help them deliver their education and training programmes to learners. For further information, please call our GCE line on , our GCSE team on , or visit our website at If you have any subject specific questions about the content of this Mark Scheme that require the help of a subject specialist, you may find our Ask The Epert service helpful. Ask The Epert can be accessed online at the following link: November 00 Publications Code UG05868 All the material in this publication is copyright Edecel Ltd 00 5MBH_0 0

3 GCSE MATHEMATICS MB0 NOTES ON MARKING PRINCIPLES All candidates must receive the same treatment. Eaminers must mark the first candidate in eactly 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. All the marks on the mark scheme are designed to be awarded. Eaminers should always award full marks if deserved, i.e if the answer matches the mark scheme. Eaminers should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. 4 Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and eemplification may be limited. 5 Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. 6 Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows: i) ensure that tet is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labeling conventions. ii) select and use a form and style of writing appropriate to purpose and to comple subject matter Reasoning, eplanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used. 5MBH_0 0

4 GCSE MATHEMATICS MB0 7 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 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 it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. Send the 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 these situations 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 makes clear the method that has been used. 8 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. 9 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: e.g. incorrect canceling 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 e.g. algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. 0 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. 5MBH_0 4 0

5 GCSE MATHEMATICS MB0 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. Range of answers Unless otherwise stated, when an answer is given as a range (e.g.5 4.) then this is inclusive of the end points (e.g.5, 4.) and includes all numbers within the range (e.g 4, 4.) Guidance on the use of codes within this mark scheme M method mark A accuracy mark B Working mark C communication mark QWC quality of written communication oe or equivalent cao correct answer only ft follow through sc special case dep dependent (on a previous mark or conclusion) indep independent isw ignore subsequent working 5MBH_0 5 0

6 GCSE MATHEMATICS MB0 5MBH_0 6 0

7 GCSE MATHEMATICS MB0 5MBH_0 40 ( + 4)( = 0) 80 4 M for 40 ( + 4) or 0 or 40 7 " 0" 4 A cao (a) 8 bc B cao (b) 6w 5t M for w 5t or 6w or -5t A cao (c) M for all 4 terms correct with or without signs or out of no more than four terms correct with signs or ( ) + 7( ) or ( + 7 ) ( + 7) A cao M for or 8 and 4 seen or correct method to find 0% and 5% of 80 eg and oe A cao 5MBH_0 7 0

8 GCSE MATHEMATICS MB0 5MBH_0 4 BFD = 4 HFB = 0 o M for EDC = 4 or DHF = 80 0 M for A cao or M for BFD = 4 or HFB = 0 M for 0 4 A cao or M for AFH = 80 0 = 70 M for = 68 A cao 5 4 M for list of at least multiples of 8 and multiples of or correct method to write either 8 or as product of prime factors A cao ( = 40) 60 "40" 9 M for 80 40( = 40) M (dep) for 60 "40" A cao 5MBH_0 8 0

9 GCSE MATHEMATICS MB0 5MBH_0 7 (a) 68 9 M for A cao (b) Table of values or Use y = m + c With m = 5 9, c = Single line from (0, ) to (50, ) B for correct single straight line from (0, ) to (50, ) [B for at least points correctly plotted (ft from (a)) and joined with line segments or correct points plotted two of which must be the etremes with no joining or a single line of gradient 5 9 passing through (0,) B for correctly plotted points ft from (a) or a single line of gradient 5 9 or a single line with positive gradient passing through (0,) or correct pairs of values, may include (0,68) from (a) if correct] (c) 7.8 B for answer in range 6-9 or ft from line drawn (± mm) NB : Whole question needs to be clipped together 5MBH_0 9 0

10 GCSE MATHEMATICS MB0 5MBH_0 8 7 = 84 4 M for 7 ( = 84) 84 ( 6) M for " 84" ( 6) ( = 75) 75 M for area or (, 64,) 96 seen with area calculated. A cao (dep on all M marks) or M for 4 ( = 48) M for " 48" + ( + 6) M for area or (, 64,) 96 seen with area calculated. A cao (dep on all M marks) M for 6 + ( 6) ( = 7) M for " 7" + 4 M for area or (, 64,) 96 seen with area calculated. A cao (dep on all M marks) 5MBH_0 0 0

11 GCSE MATHEMATICS MB0 5MBH_ = M ( = 4400) = 40% B for = 40% or = M for or 95 or 5 = 5 4 M for complete method to find 5% of = 95% A cao Saved 5% or M for ( = 4400) 0% of 4400 = 440 B for 0 % = oe 5% 0f 4400 = M + + or or M for complete method to find of A cao or M ( = 4400) M for oe (= 40) M for 4400 oe (= 5760 ) 5 M A cao SC if no other marks awarded M for ( = 080) M for 600 ( = 4400) 5 5MBH_0 0

12 GCSE MATHEMATICS MB0 5MBH_0 0 (a) ( 4wy 5w+ 6y ) M for a correct factor taken outside the brackets Or 4wy(a term epression in w and y, with just one error) A cao (b) (m + 8)(m 5) M for (m ± 8)(m ± 5) A cao minutes 6 M for 0 0 0( = 7000) (a) B cao M for " 7000" 0 A for 600 cm min oe M for (0 + 80) 40 0 ( = 0000) M for " 0000 "600" A for 00 minutes or hours 0 mins oe SC B for 4 hours (b) 8 8 y 6 M for 8 k y or 8 y (k 0) Or 8 k y 8 (k 0) or k y (k 0, k ) or 6 y - 6 y - 6 y - A cao 5MBH_0 0

13 GCSE MATHEMATICS MB0 5MBH_ M for or or or Or A cao 6 4* ( )( + ) + ( )(( + 5) ( + )) = Or ( )( + 5) ( )(( + 5) ( + )) = = Show 4 M for correct epression for a single rectangle area ( )( + ) or ( )( + 5) M for correct epression for triangle area ( )(( + 5) ( + )) M for all 4 terms correct with or without signs or out of no more than four terms correct with signs in epansion of any two linear epressions. C for and all steps clearly shown in a logical progression QWC: All steps need to be clearly laid out showing a logical progression 5MBH_0 0

14 GCSE MATHEMATICS MB0 5MBH_ MBH_0 5 7 ( ) 7 + = = 5 + = ( )( ) ( )( ) + = + = + 4 B for ( )( ) + = M for correct process to obtain any common denominator M for correct epansion and simplification of numerator A cao

15 GCSE MATHEMATICS MB0 5MBH_0 5 Alternative method 4 Alternative Method 7 + M for correct process to obtain any common denominator ( ) (7 )( ) = ( )( ) ( )( ) = ( ) (7+ )( ) ( )( ) B for M (dep on first M) for correct epansion and simplification of numerator A cao = ( )( ) = ( )( ) = ( )( ) ( + )( ) = + 5MBH_0 5 0

16 GCSE MATHEMATICS MB0 5MBH_0 6* AOT = 90 5 B for AOT = 90 (Angle between tangent and radius is or OAT = 90 or OBT= 90 (may be shown on diagram) 90 o ) B for AOC = 90 + AOC = 90 + B for completing the proof (Tangents from an eternal point are equal) C for reasons: Angle between tangent and radius is 90 and ACB = (80 (90 + )) = 90 Tangents from an eternal point are equal. QWC: proof should be clearly laid out with technical Or language correct [C for of: Angle between tangent and radius is 90 or Obtuse angle BOA = 80 Tangents from an eternal point are equal, (Angle between tangent and radius is QWC: proof should be clearly laid out with technical 90 o ) language correct] Refle angle BOA = 80 + (Tangents from an eternal point are equal) ACB = ( 60 (80 + )) 90 OR B for obtuse angle BOA = 80 or OAT = 90 or OBT= 90 (may be shown on diagram) B for refle angle BOA = 80 + B for completing the proof C for reasons: Angle between tangent and radius is 90 and Tangents from an eternal point are equal. QWC: proof should be clearly laid out with technical language correct [C for of: Angle between tangent and radius is 90 or Tangents from an eternal point are equal, QWC: proof should be clearly laid out with technical language correct] 5MBH_0 6 0

17 GCSE MATHEMATICS MB0 5MBH_0 6* Alternative method Alternative method AOB = = 80 (Angle between tangent and radius is 90 o ) ACB = ( 80 ) / (Angle at the circumference is half angle at the centre) B for AOB = B for ACB = (80 )/ B for completing the proof C for reasons: Angle between tangent and radius is 90 and Angle at the circumference is half angle at the centre QWC: proof should be clearly laid out with technical language correct [C for of: Angle between tangent and radius is 90 or Angle at the circumference is half angle at the centre QWC: proof should be clearly laid out with technical language correct] B maybe awarded for a fully correct alternative method. 5MBH_0 7 0

18 GCSE MATHEMATICS MB0 5MBH_0 8 0

19 GCSE MATHEMATICS MB0 Further copies of this publication are available from Edecel Publications, Adamsway, Mansfield, Notts, NG8 4FN Telephone Fa Order Code UG05868 November 00 For more information on Edecel qualifications, please visit Edecel Limited. Registered in England and Wales no Registered Office: One90 High Holborn, London, WCV 7BH 5MBH_0 9 0