Mathematics Mei Ocr-Books Pdf

Mathematics MEI OCR
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OCR Oxford Cambridge and RSA Examinations is a unitary awarding body established by the. University of Cambridge Local Examinations Syndicate and the RSA Examinations Board in. January 1998 OCR provides a full range of GCSE A level GNVQ Key Skills and other. qualifications for schools and colleges in the United Kingdom including those previously. provided by MEG and OCEAC It is also responsible for developing new syllabuses to meet. national requirements and the needs of students and teachers. This report on the Examination provides information on the performance of candidates which it is. hoped will be useful to teachers in their preparation of candidates for future examinations It is. intended to be constructive and informative and to promote better understanding of the syllabus. content of the operation of the scheme of assessment and of the application of assessment. Reports should be read in conjunction with the published question papers and mark schemes for. the Examination, OCR will not enter into any discussion or correspondence in connection with this Report. Any enquiries about publications should be addressed to. OCR Publications, PO Box 5050, NOTTINGHAM, Telephone 0870 770 6622. Facsimile 01223 552610, E mail publications ocr org uk. Advanced GCE Further Mathematics MEI 7896, Advanced GCE Further Mathematics Additional MEI 7897. Advanced GCE Mathematics MEI 7895, Advanced GCE Pure Mathematics MEI 7898.
Advanced Subsidiary GCE Further Mathematics MEI 3896. Advanced Subsidiary GCE Further Mathematics Additional MEI 3897. Advanced Subsidiary GCE Mathematics MEI 3895, Advanced Subsidiary GCE Pure Mathematics MEI 3898. REPORT ON THE UNITS, Unit Content Page, 4751 Introduction to Advanced Mathematics C1 1. 4752 Concepts for Advanced Mathematics C2 5, 4753 Methods for Advanced Mathematics C3 Written Examination 8. 4754 Applications of Advanced Mathematics C4 11, 4755 Further Concepts for Advanced Mathematics FP1 14. 4756 Further Methods for Advanced Mathematics FP2 17. 4757 Further Applications of Advanced Mathematics FP3 20. 4758 Differential Equations Written Examination 22. 4761 Mechanics 1 24, 4762 Mechanics 2 28, 4763 Mechanics 3 30.
4764 Mechanics 4 32, 4766 Statistics 1 34, 4767 Statistics 2 37. 4768 Statistics 3 40, 4769 Statistics 4 43, 4771 Decision Mathematics 1 45. 4772 Discrete Mathematics 2 46, 4773 Decision Mathematics Computation 48. 4776 Numerical Methods Written Examination 50, 4777 Numerical Computation 52. Coursework 53, Grade Thresholds 57, GCE Mathematics And Further Mathematics Certification.
From the January 2008 Examination session there are important changes to the certification. rules for GCE Mathematics and Further Mathematics, 1 In previous sessions GCE Mathematics and Further Mathematics have been. aggregated using least best i e the candidate was awarded the highest possible. grade in their GCE Mathematics using the lowest possible number of uniform marks. The intention of this was to allow the greatest number of uniform marks to be. available to grade Further Mathematics, From January 2008 QCA have decided that this will no longer be the case. Candidates certificating for AS and or GCE Mathematics will be awarded the highest. grade with the highest uniform mark For candidates entering for Further. Mathematics both Mathematics and Further Mathematics will be initially graded. using least best to obtain the best pair of grades available Allowable combinations. of units will then be considered in order to give the candidate the highest uniform. mark possible for the GCE Mathematics that allows this pre determined pair of. grades See the next page for an example, As before the maximisation process will award a grade combination of AU above. say BE Where a candidate s grade combination includes a U grade a request from. centres to change to an aggregation will be granted No other requests to change. grading combinations will be accepted e g A candidate who has been awarded a. grade combination of AD cannot request a grading change that would result in BC. 2 In common with other subjects candidates are no longer permitted to decline AS and GCE. grades Once a grade has been issued for a certification title the units used in that. certification are locked into that qualification Candidates wishing to improve their. grades by retaking units or who have aggregated GCE Mathematics or AS Further. Mathematics in a previous session should re enter the certification codes in order to. ensure that all units are unlocked and so available for use For example a candidate. who has certificated AS Mathematics and AS Further Mathematics at the end of Year 12. and who is certificating for GCE Mathematics at the end of Year 13 should put in. certification entries for AS Mathematics and AS Further Mathematics in addition to the GCE. Mathematics, Grading Example, A candidate is entered for Mathematics and Further Mathematics with the following units. and uniform marks, Unit Uniform marks Unit Uniform marks.
C1 90 M1 80, C2 90 M2 100, C3 90 M3 90, C4 80 S1 70. FP1 100 S2 70, FP2 80 D1 60, Grading this candidate using least best gives the following unit combinations. Mathematics Further Mathematics, Unit Uniform marks Unit Uniform marks. C1 90 FP1 100, C2 90 FP2 80, C3 90 M1 80, C4 80 M2 100. S1 70 M3 90, D1 60 S2 70, Total 480 Grade A Total 520 Grade A.
Under the new system having fixed the best pair of grades as two As the mark for the. Mathematics would be increased by combining the units in a more advantageous manner. The table below shows the allowable combination of units. Option Applied units Total uniform Applied units Total uniform. used for marks for used for marks for Further, Maths Mathematics Mathematics Mathematics. 1 M1 S1 500 M2 M3 S2 D1 500, 2 M1 D1 490 M2 M3 S1 S2 510. 3 S1 D1 480 M1 M2 M3 S2 520, 4 M1 M2 530 M3 S1 S2 D1 470. 5 S1 S2 490 M1 M2 M3 D1 510, Option 4 gives the highest uniform mark for Mathematics However this would only give a. grade B in the Further Mathematics and so is discarded Option 1 is the next highest. uniform mark for Mathematics and gives an A in Further Mathematics and so this is the. combination of units that would be used, Report on the Units taken in June 2008.
4751 Introduction to Advanced Mathematics C1, General Comments. The usual spread of candidates from very good to extremely weak was seen Time did not. appear to be a problem even for weak candidates with most parts of the last question usually. being attempted, Compared to some recent past papers there were perhaps fewer parts in this paper that. hindered good candidates from obtaining high marks so that more candidates gained over 60. marks for instance than compared with last June Some topics such as using the discriminant. to determine when the roots of a quadratic equation are real remain poorly done by many. candidates, Some centres continue to issue graph paper to their candidates in the examination This is to. their disadvantage when some with graph paper then spend time attempting plotted graphs. often with inappropriate scales when all that is required is a sketch graph. The examiners are also concerned that some candidates may not be sufficiently practised in. non calculator work There were fewer fractions used in this paper than in last January s but. nonetheless poor arithmetic can lower the mark considerably for some candidates. Comments on Individual Questions, 1 This ought to have been an easy starter Many picked up both marks but some did not. reach 4x 6 and some who did then gave x 32, 2 Most knew what to do and many gained full marks To find the intercepts those who.
rearranged to y 32 x 4 before substituting y 0 often gave themselves too hard a. task in finding x Some gave just the y intercept The usual errors were seen in the. gradient with 32 and 32 x being seen more than occasionally Thankfully the gradient. was rarely inverted, 3 Although many were able quickly to factorise and solve 2x2 3x 0 weaker candidates. often found this difficult with the formula being frequently used and an error often made. such as 4 2 0 8 or in not knowing what to do with 04 Some rearranged the. equation then divided by x and found only one root. In the second part many did not know the condition for real roots A common error was. to substitute k instead of k for c often then making errors with the resulting negative. coefficient in the inequality, 4 This was reasonably well answered with parts i and iii usually correct part ii. presented the most problems to candidates with false instead of either being a. common response Many candidates showed no working, Report on the Units taken in June 2008. 5 Many candidates made a good start on rearranging the equation by correctly multiplying. by x 2 with relatively few omitting the brackets Those who knew the strategy to use. often proceeded to gain the rest of the marks but some floundered from here Some. weaker candidates started by multiplying the right hand side by then multiplying. out and often cancelling the x2 terms Some candidates used spare time at the end of. the examination to have another attempt at this question after failing to manage it first. time round some of these later attempts were successful. 6 In this question on indices the correct answer of 5 in the first part was common. sometimes given with no working shown Of those who did not gain 2 marks many. knew that a square root was involved often reaching 51 or 51 but not managing to. cope correctly with the reciprocal A few thought the index was also inverted and. calculated 252, In the second part those who did not gain full marks often had partially correct answers. with the most common error being to think that x 2 x 7 and so on as expected. 7 Most of the candidates made an attempt at the first part and realised that they needed. to multiply the numerator and denominator by 5 3 A few used 5 3 However. many of the candidates made an error in determining the new denominator with. expressions such as 25 3 or 25 9 being used, In the second part most candidates obtained a mark for getting 9 6 7 6 7.
However the final term was often wrong such as 28 14 or 4 7 Some errors were. made in combining the terms involving 7, 8 Although most candidates had some idea about what was required here many of them. were unable to cope with the 2 3 element It often appeared with the x included and in. the form 2x3 even if it was written as 2x 3 it was frequently evaluated as 2x3 The. negative sign was also often dropped There were also a number of candidates who. only included two of the required elements such as 10 x 25 or 10 x 23 A few. candidates tried to take a factor of 5 outside the brackets but they commonly then made. errors Very few candidates tried to multiply out 5 2x 5 but of those who did most. failed to do so correctly, 9 Most candidates were able to factorise or use the formula and of these most went on. to arrive at the values of y Only a minority realised that there was a connection. between this equation and the next As a consequence few candidates gained full. marks on this question as they were unable to determine four roots from the quartic. equation Of those who did realise that x2 was equal to 3 or 4 many only gave the two. positive roots 2 was sometimes left in the form 4, Report on the Units taken in June 2008. 10 i Completing the square was done better than expected aided by the fact that no. fractions were involved this time Many candidates had clearly learned a. formula for this Some got as far as x 3 2 but did not know how to proceed. from there, ii Although some realised the relevance to part i and just wrote down the answer. as expected a surprising number started again and used calculus to obtain the. result sometimes making errors in the process, iii In sketching the graph most knew the general shape of a parabola but many.
omitted the fact that it went though 0 2 often having a graph with a negative. y intercept from estimating the general direction of the curve Some did not use. their turning point from part ii but instead had the minimum at 0 2 or 3 0. iv Most candidates equated the two expressions for y and many then rearranged. successfully and went on to obtain x 4 as the only root Forgetting to then go. on to obtain the y value was a frequent error Many did not realise or failed to. state that the equal roots implied that the line was a tangent Instead some. successfully used calculus to show that the gradients of the curve and the line. were the same at 4 6 Weaker candidates who had got this far sometimes. thought that showing that 4 6 satisfied both equations was sufficient to imply. the line was a tangent Candidates who started this part by substituting. for x rarely made progress, 11 In general this was the section B question which caused most difficulty to. candidates particularly part iv, i Many gained both marks with calculating f 4 being the most common. method Working out 7 16 proved beyond some whilst the other main error. was in 7 4 becoming 28 More able candidates often divided by x 4 and. positioned themselves well for part ii, ii Many coped correctly with the division and achieved 2x2 x 3 with fewer sign. errors being seen than in some past papers Some obtained this by inspection. Mathematics MEI Advanced GCE A2 7895 8 Advanced Subsidiary GCE AS 3895 8 June 2008 3895 8 7895 8 MS R 08 OCR Oxford Cambridge and RSA Examinations is a unitary awarding body established by the University of Cambridge Local Examinations Syndicate and the RSA Examinations Board in January 1998 OCR provides a full range of GCSE A level GNVQ Key Skills and other qualifications for

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