A-level Mathematics/MEI/DE

Examination
Candidates answer three questions from four, each worth 24 marks. The total time allowed is 1 hour 30 minutes. The total number of marks for the paper is 72.

Structure
The total marks available for coursework is 18. One modelling assignment involving the use of differential equations at an appropriate level of sophistication. There are no restrictions on the context chosen.

How Differential Equations are used to Solve Real-World Problems
Rationale The aims of the coursework are that students should learn how differential equations are used to solve real-world problems and that they should appreciate how the theory they have learnt for the examination helps them to do this. The objectives are that they should be able to undertake the various steps in the problem solving procedure shown in the flow chart in Section 5.2. The assessment criteria are closely related to these steps.

Description There are two aspects to the work. (i) The modelling cycle consists of pen and paper development of the consequences of the basic assumptions made, leading to a predicted outcome which must then be tested against reality. (ii) In the experimental cycle, results are collected in order to give insight into the situation under investigation, so that a realistic model can be developed.

Level of Work The task represents 20% of the assessment and the work involved should be consistent with that figure, both in quantity and level of sophistication. Tasks which allow only superficial or trivial treatment should be avoided.

Assessment Each task must be assessed on one of the coursework assessment sheets, A or B. The assessor decides on the appropriate sheet according to the way the candidate has approached the particular task. (A) In this case the modelling cycle is investigated in some depth, whilst the check against reality may use the data from published sources, from experiments which the candidate has not actually performed or from experience; there must however be a quantitative element in such data. (B) The work presented is approximately evenly divided between developing the model, and one or more experiments conducted by the candidate to verify the quality of predictions from it and/or to inform its development. No other mark sheet may be used, nor may these be amended in any way. One mark is available for each criterion statement. Half marks may be awarded, but the overall total must be rounded (up or down) to an integer. Note that in the case of Mark Scheme A, the marks for ‘Manipulating the Model’ may be awarded for the quality of the work either on the first or the second modelling cycles.

Task Selection Centres are encouraged to develop their own coursework tasks. If they have any doubt about the suitability of a proposed task, they are recommended to submit details of it to the Principal Coursework Moderator, via OCR. However, Centres which are new to the scheme are strongly recommended to use the tasks published by MEI while they are familiarising themselves with the nature of coursework. They should ensure that the material they have is that published for this specification and not that for an earlier specification. Centres are advised that the choice of suitable tasks is crucial to the success of their candidates’ coursework.

A Mark Scheme is available at the OCR website (Specification B: MEI).

Assumed Knowledge
Candidates are expected to know the content of C1, C2, C3 and C4. In addition candidates are expected to know basic kinematics and Newton’s Second Law. Relevant knowledge of complex numbers will also be required. Unless otherwise specified the value of the acceleration due to gravity should be taken to be exactly 9.8 ms-2.

Topics Covered

 * /Introduction to Differential Equations/
 * /Numerical Methods/
 * /Linear Equations/
 * /Systems of Differential Equations/