## Mei Differential Equations Coursework Cascades

The normal method of assessment is by unit examinations, held in January and June each year, in ... and C2, together with one applied unit, either M1, S1 or D1.

Oxford Cambridge and RSA Examinations

MEI STRUCTURED MATHEMATICS A Credit Accumulation Scheme for Advanced Mathematics

OCR ADVANCED SUBSIDIARY GCE IN MATHEMATICS (MEI) (3895) OCR ADVANCED SUBSIDIARY GCE IN FURTHER MATHEMATICS (MEI) (3896/3897) OCR ADVANCED SUBSIDIARY GCE IN PURE MATHEMATICS (MEI) (3898) OCR ADVANCED GCE IN MATHEMATICS (MEI) OCR ADVANCED GCE IN FURTHER MATHEMATICS (MEI) OCR ADVANCED GCE IN PURE MATHEMATICS (MEI)

(7895) (7896/7897) (7898)

QAN (3895) 100/3417/1 QAN (3896/3897) 100/6016/9 QAN (3898) 100/6017/0 QAN (7895) 100/3418/3 QAN (7896/7897) 100/6018/2 QAN (7898) 100/6019/4

Key Features • • • • •

Unrivalled levels of support and advice. Web-based resources covering the units. Clear and appropriate progression routes from GCSE for all students. Flexibility in provision of Further Mathematics. User friendly and accessible.

This specification was devised by Mathematics in Education and Industry (MEI) and is administered by OCR.

© MEI/OCR 2003

Support and Advice The specification is accompanied by a complete support package provided by MEI and OCR. The two organisations work closely together with MEI taking responsibility for the curriculum and teaching aspects of the course, and OCR the assessment. • • • • • • • •

Advice is always available at the end of the telephone or by e-mail. One-day INSET courses provided by both MEI and OCR. The MEI annual three-day conference. MEI branch meetings. An e-mail user group run by OCR. Regular newsletters from MEI. Specimen and past examination papers, mark schemes and examiners’ reports. Coursework resource materials and exemplar marked tasks.

Web-based Support The units in this specification are supported by a very large purpose-built website designed to help students and teachers.

Routes of Progression This specification is designed to provide routes of progression through mathematics between GCSE and Higher Education and/or employment. It has the flexibility to meet the diverse needs of the wide variety of students needing mathematics at this level.

Further Mathematics A feature of this specification is the flexibility that it allows teachers in delivering Further Mathematics. It is possible to teach this concurrently with AS and Advanced GCE Mathematics, starting both at the same time, or to teach the two courses sequentially, or some combination of the two.

User friendliness This specification has been designed by teachers for students. Thus the accompanying text books, one for each unit, are accessible to students, easy to read and work from. The Students’ Handbook provides a particularly helpful source of information.

First AS assessment January 2005 First A2 assessment June 2005 First AS certification January 2005 First GCE certification June 2005

© MEI/OCR 2003

QAN (3895-8) 100/3417/1 QAN (7895-8) 100/3418/3

CONTENTS Section A: Specification Summary Section B: User Summary Section C: General Information 1

2

3

4

5

5 7 9

Introduction

9

1.1

Rationale

9

1.2

Certification Title

12

1.3

Language

13

1.4

Exclusions

13

1.5

Key Skills

14

1.6

Code of Practice Requirements

14

1.7

Spiritual, Moral, Ethical, Social and Cultural Issues

14

1.8

Environmental Education, European Dimension and Health and Safety Issues

15

1.9

Avoidance of Bias

15

1.10 Calculators and Computers

15

Specification Aims

16

2.1

Aims of MEI

16

2.2

Aims of this Specification

16

Assessment Objectives

17

3.1

Application to AS and A2

17

3.2

Specification Grid

18

Scheme of Assessment

19

4.1

Units of Assessment

19

4.2

Structure

20

4.3

Rules of Combination

22

4.4

Final Certification

25

4.5

Availability

27

4.6

Re-sits

27

4.7

Question Papers

28

4.8

Coursework

29

4.9

Special Arrangements

31

4.10 Differentiation

32

4.11 Grade Descriptions

32

Subject Content

34

5.1

Assumed Knowledge

34

5.2

Modelling

35

5.3

Competence Statements

36

© MEI/OCR 2003 Oxford, Cambridge and RSA Examinations

Contents MEI Structured Mathematics

3

6

7

Unit Specifications

37

6.1

Introduction to Advanced Mathematics, C1 (4751) AS

37

6.2

Concepts for Advanced Mathematics, C2 (4752) AS

46

6.3

Methods for Advanced Mathematics, C3 (4753) A2

54

6.4

Applications of Advanced Mathematics, C4 (4754) A2

67

6.5

Further Concepts for Advanced Mathematics, FP1 (4755) AS

73

6.6

Further Methods for Advanced Mathematics, FP2 (4756) A2

80

6.7

Further Applications of Advanced Mathematics, FP3 (4757) A2

92

6.8

Differential Equations, DE (4758) A2

104

6.9

Mechanics 1, M1 (4761) AS

115

6.10 Mechanics 2, M2 (4762) A2

123

6.11 Mechanics 3, M3 (4763) A2

129

6.12 Mechanics 4, M4 (4764) A2

137

6.13 Statistics 1, S1 (4766) AS

143

6.14 Statistics 2, S2 (4767) A2

153

6.15 Statistics 3, S3 (4768) A2

159

6.16 Statistics 4, S4 (4769) A2

165

6.17 Decision Mathematics 1, D1 (4771) AS

175

6.18 Decision Mathematics 2, D2 (4772) A2

181

6.19 Decision Mathematics Computation, DC (4773) A2

187

6.20 Numerical Methods, NM (4776) AS

193

6.21 Numerical Computation, NC (4777) A2

201

Further Information and Training for Teachers

206

Appendix A: Mathematical Formulae Appendix B: Mathematical Notation

4

Contents MEI Structured Mathematics

207 209

© MEI/OCR 2003 Oxford, Cambridge and RSA Examinations

SECTION A: SPECIFICATION SUMMARY The units in MEI Structured Mathematics form a step-by-step route of progression through the subject, from Intermediate Tier GCSE into the first year of university. For those who are insecure about their foundation, access to the scheme is provided by the Free Standing Mathematics Qualification, Foundations of Advanced Mathematics.

The subject is developed consistently and logically through the 21 AS and A2 units, following strands of Pure Mathematics, Mechanics, Statistics, Decision Mathematics and Numerical Analysis. Each unit is designed both as a worthwhile and coherent course of study in its own right, taking about 45 hours of teaching time, and as a stepping stone to further work. Suitable combinations of three and six modules give rise to AS and Advanced GCE qualifications in Mathematics, Further Mathematics and Pure Mathematics. Candidates usually take their units at different stages through their course, accumulating credit as they do so. The normal method of assessment is by unit examinations, held in January and June each year, in most cases lasting 1½ hours. Three units also have coursework requirements. Candidates are allowed to re-sit units, with the best mark counting.

© MEI/OCR 2003 Section A: Specification Summary Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

5

The Advanced Subsidiary GCE is assessed at a standard appropriate for candidates who have completed the first year of study of a two-year Advanced GCE course, i.e. between GCSE and Advanced GCE. It forms the first half of the Advanced GCE course in terms of teaching time and content. When combined with the second half of the Advanced GCE course, known as ‘A2’, the advanced Subsidiary forms 50% of the assessment of the total Advanced GCE. However the Advanced Subsidiary can be taken as a stand-alone qualification. A2 is weighted at 50% of the total assessment of the Advanced GCE.

6

Section A: Specification Summary © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

SECTION B: USER SUMMARY USING THIS SPECIFICATION This specification provides a route of progression through mathematics between GCSE and Higher Education and/or employment. •

Students start with AS Mathematics. This consists of the two AS units in Pure Mathematics, C1 and C2, together with one applied unit, either M1, S1 or D1.

•

Many students take one year over AS Mathematics but this is not a requirement; they can take a longer or a shorter time, as appropriate to their circumstances.

•

Examinations are available in January and June.

•

Unit results are notified in the form of a grade and a Uniform Mark. The total of a candidate’s Uniform Marks on relevant modules determines the grade awarded at AS GCE (or Advanced GCE).

•

A unit may be re-sat any number of times with the best result standing.

•

To obtain an AS award a ‘certification entry’ must be made to OCR. There is no requirement for candidates going on to Advanced GCE to make such an entry.

•

To complete Advanced GCE Mathematics, candidates take three more units, C3, C4 and another applied unit.

•

The applied unit may be in the same strand as that taken for AS in which case it will be an A2 unit (e.g. S2 following on from S1). Alternatively it may be in a different strand in which case it will be an AS unit (e.g. M1 following on from S1).

•

Many candidates will take these three units in the second year of their course but there is no requirement for this to be the case.

•

An Advanced GCE award will only be made to those who apply for it.

•

Candidates may also take Further Mathematics at AS and Advanced GCE. There is considerable flexibility in the way that this can be done.

•

AS Further Mathematics consists of FP1 and two other units which may be AS or A2.

•

The three units for AS Further Mathematics may be taken in the first year. The compulsory unit FP1 has been designed to be accessible for students who have completed Higher Tier GCSE and are studying C1 and C2 concurrently. The AS units, M1, S1, D1 and NM are also suitable for those taking AS Further Mathematics in the first year.

•

Many of those who take AS Further Mathematics in the first year then take another three units in their second year to obtain Advanced GCE Further Mathematics. Such candidates take 12 units, six for Mathematics and six for Further Mathematics.

•

Other AS Further Mathematics students spread their study over two years rather than completing it in the first year.

•

Another pattern of entry is for candidates to complete Advanced GCE Mathematics in their first year and then to go onto Further Mathematics in their second year.

•

Those who take Advanced GCE Mathematics and AS Further Mathematics must do at least 9 units.

© MEI/OCR 2003 Oxford, Cambridge and RSA Examinations

Section B: User Summary MEI Structured Mathematics

7

•

Those who take Advanced GCE Mathematics and Advanced GCE Further Mathematics must do at least 12 units. The Further Mathematics must include both FP1 and FP2.

•

The rules of aggregation mean that it is to candidates’ advantage to certificate Advanced GCE Mathematics and AS or Advanced GCE Further Mathematics at the same time.

•

Candidates who take 15 or 18 units are eligible for additional awards in Further Mathematics.

SUMMARY OF CHANGES FROM THE PREVIOUS MEI SPECIFICATION The revisions to the subject criteria have resulted in considerable changes to the assessment arrangements compared to those in the previous specification (those for first teaching in September 2000). These in turn have affected the provision of units in MEI Structured Mathematics and their content: •

the core material is now covered in four units, two at AS and two at A2. The two AS units are compulsory for Advanced Subsidiary Mathematics and all four core units are compulsory for Advanced GCE Mathematics;

•

consequently the first four units in the Pure Mathematics strand, C1 to C4 are all new;

•

only two applied units now contribute to Advanced GCE Mathematics;

•

the reduction in the amount of Applied Mathematics in Advanced GCE Mathematics means that it is no longer feasible to provide as many applied units for Further Mathematics, and so there are fewer Mechanics and Statistics units. However the provision in Decision Mathematics remains unaltered;

•

Mechanics 4 and Statistics 4 are new units, drawing material from a number of units in the previous specification;

•

in addition there are some changes to Statistics 1, 2 and 3; these reflect their new status within the Advanced GCE, particularly the fact that Statistics 3 is no longer the natural ending point for those Advanced GCE students whose Applied Mathematics is entirely statistics;

•

Advanced Subsidiary Further Mathematics may now be obtained on three AS units. One of these is a new Pure Mathematics unit Further Concepts for Advanced Mathematics, FP1;

•

the content of Further Concepts for Advanced Mathematics, FP1, depends only on the AS subject criteria and so is inevitably different from that of the unit which it replaces. This change has had knock-on effects to the content of the two remaining units in Pure Mathematics;

•

the number of subject titles available has been reduced in line with the new subject criteria.

In addition, there are some other changes that are not a direct consequence of the new subject criteria. In particular, those responsible for this specification were aware that, following the introduction of Curriculum 2000, mathematics was making much greater demands on students’ time than other subjects and so there is a reduction in the amount of coursework required.

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Section B: User Summary MEI Structured Mathematics

© MEI/OCR 2003 Oxford, Cambridge and RSA Examinations

SECTION C: GENERAL INFORMATION 1

Introduction

1.1

RATIONALE

1.1.1 This Specification This booklet contains the specification for MEI Structured Mathematics for first teaching in September 2004. It covers Advanced Subsidiary GCE (AS) and Advanced GCE (A Level) qualifications in Mathematics and Further Mathematics and also in Pure Mathematics. This specification was developed by Mathematics in Education and Industry (MEI) and is assessed by OCR. Support for those delivering the specification comes from both bodies and this is one of its particular strengths. This specification is designed to help more students to fulfil their potential by taking and enjoying mathematics courses that are relevant to their needs post-16. This involves four key elements: breadth, depth, being up-to-date and providing students with the ability to use their mathematics. •

Most students at this level are taking mathematics as a support subject. Their needs are almost as diverse as their main fields of study, and consequently this specification includes the breadth of several distinct strands of mathematics: Pure Mathematics, Mechanics, Statistics, Decision Mathematics and Numerical Analysis.

•

There are, however, those students who will go on to read mathematics at university and perhaps then become professional mathematicians. These students need the challenge of taking the subject to some depth and this is provided by the considerable wealth of Further Mathematics units in this specification, culminating in FP3, M4 and S4.

•

Mathematics has been transformed at this level by the impact of modern technology: the calculator, the spreadsheet and dedicated software. There are many places where this specification either requires or strongly encourages the use of such technology. The units DC and NC have computer based examinations; options in FP2 and FP3 are based on graphical calculators, and the coursework in C3 and NM is based on the use of suitable devices.

•

Many students complete mathematics courses quite well able to do routine examination questions but unable to relate what they have learnt to the world around them. This specification is designed to provide students with the necessary interpretive and modelling skills to be able to use their mathematics. Modelling and interpretation are stressed in the papers and some of the coursework and there is a comprehension question as part of the assessment of C4.

MEI is a curriculum development body and in devising this specification the long term needs of students have been its paramount concern. This specification meets the requirements of the Common Criteria (QCA, 1999), the GCE Advanced Subsidiary and Advanced Level Qualification-Specific Criteria (QCA, 1999) and the Subject Criteria for Mathematics (QCA, 2002). © MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

9

1.1.2 MEI and OCR MEI is a long established, independent curriculum development body, with a membership consisting almost entirely of working teachers. MEI provide advice and INSET relating to all the curriculum and teaching aspects of the course. It also provides teaching materials, and the accompanying series of textbooks is the product of a partnership between MEI and a major publishing house. A particular feature of this specification is the very substantial website (see Section 7), covering all the various units. Students can access this at school or college, or when working at home. Not only does this help them with their immediate mathematics course; it also develops the skills they will need for independent learning throughout their lives. OCR’s involvement is primarily centred on the assessment, awarding and issuing of results. However, members of the Qualification Team are available to give advice, receive feedback and give general support. OCR also provides INSET and materials such as Examiners’ Reports, mark schemes and past papers. It is thus a feature of this specification that an exceptional level of help is always available to teachers and students, at the end of the telephone or on-line.

1.1.3 Background The period leading up to the start of this specification has been a difficult one for post-16 mathematics with a substantial drop in the numbers taking the subject. This specification has been designed to redress that situation by ensuring that the various units can indeed be taught and learnt within the time allocated. Considerable thought has gone into its design, and from a large number of people, many of them classroom teachers or lecturers. Those responsible are confident that the specification makes full use of the new opportunities opened up by the changes to the subject criteria: mathematics will be accessible to many more students but will also provide sufficient challenge for the most able. MEI Structured Mathematics was first introduced in 1990 and was subsequently refined in 1994 and 2000 to take account of new subject cores and advice from teachers and lecturers. The philosophy underlying the 1990 specification was described in its introduction, which is reproduced verbatim later in this section. This specification represents a new interpretation of the same philosophy. It takes account not only of the requirements of the 2002 subject criteria but also of the quite different environment in which post-16 mathematics is now embedded. The major changes from the previous MEI specification (that for first teaching in September 2000) are outlined for the convenience of users on page 8 of this specification. However, it is more appropriate to see this as a specification in its own right, which, while building on past experience, is designed for present-day students working in present-day conditions.

10

Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

1.1.4 New Opportunities The new subject criteria, published by QCA in December 2002, are intended to make mathematics more accessible for students and easier for schools and colleges to deliver within existing time constraints. This specification is designed to take full advantage of the opportunities this opens up. The content of the subject core is little changed but it is now spread over four units, two at AS and two at A2, instead of the previous three. This means that the content of each individual Pure Mathematics unit is reduced so that more time can be given to teaching the topics within it. A particular feature of this specification is the first Pure Mathematics unit, C1. It is designed to give students a firm foundation in the basic skills that they will need for all their other units, thereby making advanced study of mathematics accessible to many more people. Another major new opportunity occurs with Further Mathematics. It is now, for the first time, possible to obtain AS Further Mathematics on three AS units. In this specification, the first Pure Mathematics unit, FP1, is a genuine AS unit and students who have been successful at Higher Tier GCSE should be able to start studying it at the same time as C1 and C2. It will no longer be necessary for potential Further Mathematics students to mark time while they learn enough of the single Mathematics to allow them to get started. It is however still possible for schools and colleges to deliver Further Mathematics in other ways: for example by doing three extra units over the two years for the AS qualification. That point illustrates another feature of this specification, its flexibility. It is designed to meet the needs of a wide range of students, from those who find AS Level a real challenge to others who are blessed with extraordinary talent in mathematics. The flexibility also covers the needs of schools and colleges with widely differing numbers of post-16 mathematics students.

1.1.5 A Route of Progression MEI Structured Mathematics is designed not just to be a specification for AS or Advanced GCE Mathematics but to provide a route of progression through the subject starting at Intermediate Tier GCSE and going into what is first year work in some university courses. The specification is also, by design, entirely suitable for those who are already in employment, or are intending to progress directly into it.

1.1.6 Underlying Philosophy: Introduction to the 1990 Syllabus This section contains the introduction to the first MEI Structured Mathematics specification and is included as a statement of underlying philosophy. These were the first modular A Levels in any subject and their development was accompanied by serious consideration of how the needs of industry and adult life could best be addressed through a mathematics specification. ‘Our decision to develop this structure, based on 45-hour Components, for the study of Mathematics beyond GCSE stems from our conviction, as practising teachers, that it will better meet the needs of our students. We believe its introduction will result in more people taking the subject at both A and AS, and that the use of a greater variety of assessment techniques will allow content to be taught and learnt more appropriately with due emphasis given to the processes involved. © MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

11

Mathematics is required by a wide range of students, from those intending to read the subject at university to those needing particular techniques to support other subjects or their chosen careers. Many syllabuses are compromises between these needs, but the necessity to accommodate the most able students results in the content being set at a level which is inaccessible to many, perhaps the majority of, sixth formers. The choice allowed within this scheme means that in planning courses centres will be able to select those components that are relevant to their students’ needs, confident that the work will be at an appropriate level of difficulty. While there are some areas of Mathematics which we feel to be quite adequately assessed by formal examination, there are others which will benefit from the use of alternative assessment methods, making possible, for example, the use of computers in Numerical Analysis and of substantial sets of data in Statistics. Other topics, like Modelling and Problem Solving, have until now been largely untested because by their nature the time they take is longer than can be allowed in an examination. A guiding principle of this scheme is that each Component is assessed in a manner appropriate to its content. We are concerned that students should learn an approach to Mathematics that will equip them to use it in the adult world and to be able to communicate what they are doing to those around them. We believe that this cannot be achieved solely by careful selection of syllabus content and have framed our Coursework requirements to develop skills and attitudes which we believe to be important. Students will be encouraged to undertake certain Coursework tasks in teams and to give presentations of their work. To further a cross-curricular view of Mathematics we have made provision for suitable Coursework from other subjects to be admissible. We believe that this scheme will do much to improve both the quantity and the quality of Mathematics being learnt in our schools and colleges.’

1.2

CERTIFICATION TITLE

This specification will be shown on a certificate as one or more of the following: •

OCR Advanced Subsidiary GCE in Mathematics (MEI)

•

OCR Advanced Subsidiary GCE in Further Mathematics (MEI)

•

OCR Advanced Subsidiary GCE in Pure Mathematics (MEI)

•

OCR Advanced GCE in Mathematics (MEI)

•

OCR Advanced GCE in Further Mathematics (MEI)

•

OCR Advanced GCE in Pure Mathematics (MEI)

Candidates who complete 15 or 18 units respectively will have achieved at least the equivalent of the standard of Advanced Subsidiary GCE Further Mathematics and Advanced GCE Further Mathematics in their additional units. The achievements of such candidates will be recognised by additional awards in Further Mathematics (Additional) with the code numbers 3897 (AS) and 7897 (Advanced GCE).

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

1.3

LANGUAGE

This specification, and all associated assessment materials, are available only in English. The language used in all question papers will be plain, clear, free from bias and appropriate to the qualification.

1.4

EXCLUSIONS

1.4.1 Exclusions within this Specification Qualifications in Further Mathematics are not free-standing. Thus: •

candidates for Advanced Subsidiary GCE in Further Mathematics are required either to have obtained, or to be currently obtaining, either an Advanced Subsidiary GCE in Mathematics or an Advanced GCE in Mathematics;

•

candidates for Advanced GCE in Further Mathematics are required either to have obtained, or to be currently obtaining, an Advanced GCE in Mathematics.

Advanced Subsidiary GCE in Pure Mathematics may not be taken with any other Advanced Subsidiary GCE qualification within this specification. Advanced GCE in Pure Mathematics may not be taken with any other Advanced GCE qualification within this specification.

1.4.2 Exclusions Relating to other Specifications No Advanced Subsidiary GCE qualification within this specification may be taken at the same time as any other Advanced Subsidiary GCE having the same title nor with OCR Free Standing Mathematics Qualification (Advanced): Additional Mathematics. No Advanced GCE qualification within this specification may be taken with any other Advanced GCE having the same title. Candidates may not obtain certification (under any title) from this specification, based on units from other mathematics specifications, without prior permission from OCR. Candidates may not enter a unit from this specification and a unit with the same title from other mathematics specifications. Every specification is assigned to a national classification code indicating the subject area to which it belongs. Centres should be aware that candidates who enter for more than one GCE qualification with the same classification code will have only one grade (the highest) counted for the purpose of School and College Performance Tables.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

13

The national classification codes for the subjects covered by this specification are as follows: Mathematics Pure Mathematics Further Mathematics

1.5

2210 2230 2330

KEY SKILLS

In accordance with the aims of MEI, this scheme has been designed to meet the request of industry (e.g. the CBI) that students be provided with opportunities to use and develop Key Skills. The table below indicates which modules are particularly likely to provide opportunities for the various Key Skills at Level 3.

Module

Communication

C3

4753

9

C4

4754

9

DE

4758

9

DC

4773

NM 4776 NC

1.6

4777

Application of

Information

Working with

Number

Technology

Others

9

9

Learning and Performance

Problem Solving

9 9

9

9

9

9 9

Improving Own

9

9 9

9

9

9 9

9

9

9

CODE OF PRACTICE REQUIREMENTS

All qualifications covered by this specification will comply in all aspects with the GCE Code of Practice for courses starting in September 2004.

1.7

SPIRITUAL, MORAL, ETHICAL, SOCIAL AND CULTURAL ISSUES

Students are required to examine arguments critically and so to distinguish between truth and falsehood. They are also expected to interpret the results of modelling exercises and there are times when this inevitably raises moral and cultural issues. Such issues will not be assessed in the examination questions; nor do they feature, per se, in the assessment criteria for any coursework tasks.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

1.8

ENVIRONMENTAL EDUCATION, EUROPEAN DIMENSION AND HEALTH AND SAFETY ISSUES

While the work developed in teaching this specification may use examples, particularly involving modelling and statistics, that raise environmental issues, these issues do not in themselves form part of the specification. The work developed in teaching this specification may at times involve examples that raise health and safety issues. These issues do not in themselves form part of this specification. OCR has taken account of the 1988 Resolution of the Council of the European Community and the Report Environmental Responsibility: An Agenda for Further and Higher Education, 1993 in preparing this specification and associated specimen assessment materials. Teachers should be aware that students may be exposed to risks when doing coursework. They should apply usual laboratory precautions when experimental work is involved. Students should not be expected to collect data on their own when outside their Centre. Teachers should be aware of the dangers of repetitive strain injury for any student who spends a long time working on a computer.

1.9

AVOIDANCE OF BIAS

MEI and OCR have taken great care in the preparation of this specification and assessment materials to avoid bias of any kind.

1.10

CALCULATORS AND COMPUTERS

Students are expected to make appropriate use of graphical calculators and computers.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

15

2

Specification Aims

2.1

AIMS OF MEI

‘To promote the links between education and industry at Secondary School level, and to produce relevant examination and teaching specifications and support material.’

2.2

AIMS OF THIS SPECIFICATION

This course should encourage students to:

16

•

develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment;

•

develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs;

•

extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems;

•

develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected;

•

recognise how a situation may be represented mathematically and understand the relationship between ‘real world’ problems and standard and other mathematical models and how these can be refined and improved;

•

use mathematics as an effective means of communication;

•

read and comprehend mathematical arguments and articles concerning applications of mathematics;

•

acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations;

•

develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general;

•

take increasing responsibility for their own learning and the evaluation of their own mathematical development.

Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

3

Assessment Objectives

3.1

APPLICATION TO AS AND A2

This specification requires students to demonstrate the following assessment objectives in the context of the knowledge, understanding and skills prescribed. The assessment objectives for Advanced Subsidiary GCE and for Advanced GCE are the same. Students should be able to demonstrate that they can:

AO1

•

recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of contexts.

AO2

•

construct rigorous mathematical arguments and proofs through use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions, including the construction of extended arguments for handling substantial problems presented in unstructured form.

AO3

•

recall, select and use their knowledge of standard mathematical models to represent situations in the real world;

•

recognise and understand given representations involving standard models;

•

present and interpret results from such models in terms of the original situation, including discussion of assumptions made and refinement of such models.

AO4

•

comprehend translations of common realistic contexts into mathematics;

•

use the results of calculations to make predictions, or comment on the context;

•

where appropriate, read critically and comprehend longer mathematical arguments or examples of applications.

AO5

•

use contemporary calculator technology and other permitted resources (such as formulae booklets or statistical tables) accurately and efficiently;

•

understand when not to use such technology, and its limitations;

•

give answers to appropriate accuracy.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

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3.2

SPECIFICATION GRID

The table below gives the permitted allocation of marks to assessment objectives for the various units. The figures given are percentages. These allocations ensure that any allowable combination of units for AS Mathematics or Advanced GCE Mathematics satisfies the weightings given in Subject Criteria for Mathematics.

18

Weighting of Assessment Objective (%)

Entry Code

Unit Code

4751

C1

Introduction to Advanced Mathematics

4752

C2

4753

Unit Name

Level AO1

AO2

AO3

AO4

AO5

AS

40-50 40-50

0-10

0-10

0-5

Concepts for Advanced Mathematics

AS

30-40 30-40

5-15

5-15 10-20

C3

Methods for Advanced Mathematics

A2

40-45 40-45

0-10

0-10 10-20

4754

C4

Applications of Advanced Mathematics

A2

30-35 30-35 10-20 15-25

5-15

4755

FP1

Further Concepts for Advanced Mathematics

AS

35-45 35-45

0-10

0-10

0-10

4756

FP2

Further Methods for Advanced Mathematics

A2

35-45 35-45

0-10

0-10

0-10

4757

FP3

Further Applications of Advanced Mathematics

A2

35-45 35-45

0-10

0-10

0-10

4758

DE

Differential Equations

A2

20-30 20-30 25-35 10-20

5-15

4761

M1

Mechanics 1

AS

20-30 20-30 25-35 10-20

5-15

4762

M2

Mechanics 2

A2

20-30 20-30 25-35 10-20

5-15

4763

M3

Mechanics 3

A2

20-30 20-30 25-35 10-20

5-15

4764

M4

Mechanics 4

A2

20-30 20-30 25-35 10-20

5-15

4766

S1

Statistics 1

AS

20-30 20-30 25-35 10-20

5-15

4767

S2

Statistics 2

A2

20-30 20-30 25-35 10-20

5-15

4768

S3

Statistics 3

A2

20-30 20-30 25-35 10-20

5-15

4769

S4

Statistics 4

A2

20-30 20-30 25-35 10-20

5-15

4771

D1

Decision Mathematics 1

AS

20-30 20-30 25-35 10-20

5-15

4772

D2

Decision Mathematics 2

A2

20-30 20-30 25-35 10-20

5-15

4773

DC

Decision Mathematics Computation

A2

20-30 20-30 25-35

5-15

10-30

4776

NM

Numerical Methods

AS

30-40 30-40

0-10

0-10

20-30

4777

NC

Numerical Computation

A2

25-35 25-35

0-10

10-20 20-30

Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4

Scheme of Assessment

4.1

UNITS OF ASSESSMENT

4.1.1 Summary Table Entry Code

Unit Code

Level

4751

C1

AS

4752

C2

4753

C3

4754

C4

Examination Questions* (approximate mark allocation)

Time (hours)

Introduction to Advanced Mathematics

A: 8-10 × ≤ 5 = 36; B: 3 × 12 = 36

1½

AS

Concepts for Advanced Mathematics

A: 8-10 × ≤ 5 = 36; B: 3 × 12 = 36

1½

A2

Methods for Advanced Mathematics

A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36 Coursework: 18

1½

Applications of Advanced Mathematics Paper A

A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36

1½

Applications of Advanced Mathematics Paper B

Comprehension: 18

A2

Unit Name

1

4755

FP1

AS

Further Concepts for Advanced Mathematics

A: 5-7 × ≤ 8 = 36; B: 3 × 12 = 36

1½

4756

FP2

A2

Further Methods for Advanced Mathematics

A: 3 × 18 = 54; B: 1 (from 2) × 18 = 18

1½

4757

FP3

A2

Further Applications of Advanced Mathematics

3 (from 5) × 24 = 72

1½

4758

DE

A2

Differential Equations

3 (from 4) × 24 = 72; Coursework: 18

1½

4761

M1

AS

Mechanics 1

A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36

1½

4762

M2

A2

Mechanics 2

4 × 18 = 72

1½

4763

M3

A2

Mechanics 3

4 × 18 = 72

1½

4764

M4

A2

Mechanics 4

A: 2 × 12 = 24; B: 2 × 24 = 48

1½

4766

S1

AS

Statistics 1

A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36

1½

4767

S2

A2

Statistics 2

4 × 18 = 72

1½

4768

S3

A2

Statistics 3

4 × 18 = 72

1½

4769

S4

A2

Statistics 4

3 (from 4) × 24 = 72

1½

4771

D1

AS

Decision Mathematics 1

A: 3 × 8 = 24; B: 3 × 16 = 48

1½

4772

D2

A2

Decision Mathematics 2

A: 2 × 16 = 32; B: 2 × 20 = 40

1½

4773

DC

A2

Decision Mathematics Computation

4 × 18 = 72

2½

4776

NM

AS

Numerical Methods

A: 5-7 × ≤ 8 = 36; B: 2 × 18 = 36 Coursework: 18

1½

4777

NC

A2

Numerical Computation

3 (from 4) × 24 = 72

2½

* number of questions x number of marks for each = total mark For Units 4753, 4758 and 4776, Centres have the option of submitting new coursework (entry code Option A) or carrying forward a coursework mark from a previous session (Option B).

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4.1.2 Weighting For all certifications, the contribution of each unit is the same. Thus each unit carries 331/3% of the total marks for an Advanced Subsidiary certification and 162/3% of the total marks for an Advanced GCE certification.

4.2

STRUCTURE

4.2.1 Recommended Order The assumed knowledge required to start any unit is stated on the title page of its specification. In general, students are recommended to take the units in any strand in numerical order. Students will also find it helpful to refer to the diagram on the cover of this specification and also on page 5. The lines connecting the various units indicate the recommended order and the positions (left to right) of the units indicate their level of sophistication. The assessment of a unit may require work from an earlier unit in the same strand. However such earlier work will not form the focus of a question. This specification has been designed so that in general the applied modules are supported by the techniques in the pure modules at the same level. Where this is not the case, it is highlighted on the unit’s title page. There are, however, no formal restrictions on the order in which units may be taken.

4.2.2 Constraints A student’s choice of units for these awards is subject to the following restrictions (a) to (d).

(a)

Mathematics and Further Mathematics Subject Criteria: Compulsory Units

Combinations of units leading to certifications entitled Mathematics and Further Mathematics required to cover the mathematics subject criteria. The content of this is covered by the following compulsory units. Mathematics

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Advanced Subsidiary GCE:

C1, Introduction to Advanced Mathematics C2, Concepts for Advanced Mathematics

Advanced GCE:

C1, Introduction to Advanced Mathematics C2, Concepts for Advanced Mathematics C3, Methods for Advanced Mathematics C4, Applications of Advanced Mathematics

Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

Further Mathematics Advanced Subsidiary GCE:

FP1, Further Concepts for Advanced Mathematics

Advanced GCE:

FP1, Further Concepts for Advanced Mathematics FP2, Further Methods for Advanced Mathematics

(b)

Balance between Pure and Applied Units

There must be a balance between pure and applied mathematics. There must be one applied unit in AS Mathematics and two applied units in Advanced GCE Mathematics. Pure Units

Applied Units

C1, Introduction to Advanced Mathematics

DE, Differential Equations

C2, Concepts for Advanced Mathematics

M1, Mechanics 1

C3, Methods for Advanced Mathematics

M2, Mechanics 2

C4, Applications of Advanced Mathematics

M3, Mechanics 3

FP1, Further Concepts for Advanced Mathematics

M4, Mechanics 4

FP2, Further Methods for Advanced Mathematics

S1, Statistics 1

FP3, Further Applications of Advanced Mathematics

S2, Statistics 2

NM, Numerical Methods NC, Numerical Computation

S3, Statistics 3 S4, Statistics 4 D1, Decision Mathematics 1 D2, Decision Mathematics 2 DC, Decision Mathematics Computation

(c)

AS and A2 Units

AS GCE Mathematics consists of three AS units. Advanced GCE Mathematics consists of either three AS units and three A2 units or four AS units and two A2 units.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

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(d)

Mathematics Units not allowed in Further Mathematics

The following units cover the Subject Criteria for Advanced GCE Mathematics and so may not contribute to Further Mathematics awards. C1, Introduction to Advanced Mathematics C2, Concepts for Advanced Mathematics C3, Methods for Advanced Mathematics C4, Applications of Advanced Mathematics These units may, however, contribute towards awards in Pure Mathematics, but only as described in Sections 4.3.7 and 4.3.8.

4.2.3 Synoptic Assessment The subject criteria for mathematics require that any combination of units valid for the certification of Advanced GCE Mathematics (7895) or Advanced GCE Pure Mathematics (7898) must include a minimum of 20% synoptic assessment. Synoptic assessment in mathematics addresses candidates’ understanding of the connections between different elements of the subject. It involves the explicit drawing together of knowledge, understanding and skills learned in different parts of the Advanced GCE course through using and applying methods developed at earlier stages of study in solving problems. Making and understanding connections in this way is intrinsic to mathematics. In this specification the Units C1 to C4 contribute over 30% synoptic assessment and so all valid combinations of units meet the synoptic requirement. There is also a further contribution from the two applied units in Advanced GCE Mathematics and from the two further pure units in Advanced GCE Pure Mathematics. There are no requirements concerning synoptic assessment relating to the certification of Advanced Subsidiary GCE or to Advanced GCE Further Mathematics.

4.3

RULES OF COMBINATION

4.3.1 Advanced Subsidiary GCE Mathematics (3895) Candidates take one of the following combinations of units: either or or

C1, C2 and M1 C1, C2 and S1 C1, C2 and D1

No other combination of units may be used to claim AS GCE Mathematics.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4.3.2 Advanced GCE Mathematics (7895) All Advanced GCE Mathematics combinations include: C1, C2, C3 and C4. The other two units must be one of the following combinations: M1, M2; S1, S2; D1, D2; D1, DC; M1, S1; M1, D1; S1, D1 No other combination of units may be used to claim Advanced GCE Mathematics. The entry codes for these units are repeated here for the convenience of users. C1

4751

M1

4761

S1

4766

D1

4771

C2

4752

M2

4762

S2

4767

D2

4772

C3

4753

DC

4773

C4

4754

4.3.3 Advanced Subsidiary GCE Further Mathematics (3896) The three units for Advanced Subsidiary GCE Further Mathematics must include: FP1 The remaining two units may be any two other units subject to the conditions that: •

a total of six different units are required for certification in Advanced Subsidiary GCE Mathematics and Advanced Subsidiary GCE Further Mathematics;

•

a total of nine different units are required for certification in Advanced GCE Mathematics and Advanced Subsidiary GCE Further Mathematics.

Candidates would generally be advised not to certificate for Advanced Subsidiary GCE Futher Mathematics before certificating for Advanced GCE Mathematics.

4.3.4 Advanced GCE Further Mathematics (7896) The six units for Advanced GCE Further Mathematics must include both: FP1; FP2 The remaining four units may be any four other units subject to the conditions that: •

a total of 12 different units are required for certification in Advanced GCE Mathematics and Advanced GCE Further Mathematics;

•

at least two of the four units are A2 units.

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4.3.5 Additional Qualification in Advanced Subsidiary GCE Further Mathematics (3897) Candidates who offer 15 units are eligible for an additional award in Advanced Subsidiary GCE Further Mathematics. Such candidates must have fulfilled the requirements for Advanced GCE Mathematics and Advanced GCE Further Mathematics.

4.3.6 Additional Qualification in Advanced GCE Further Mathematics (7897) Candidates who offer 18 units are eligible for an additional award in Advanced GCE Further Mathematics. Such candidates must have fulfilled the requirements for Advanced GCE Mathematics and Advanced GCE Further Mathematics.

4.3.7 Advanced Subsidiary GCE Pure Mathematics (3898) Candidates take one of the following combinations of units: either or or or

C1, C2 and FP1 C1, C2 and NM C1, C2 and C3 C1, C2 and C4

No other combination of units may be used to claim AS GCE Pure Mathematics. A qualification in AS Pure Mathematics may not be obtained in combination with any qualification in Mathematics or Further Mathematics.

4.3.8 Advanced GCE Pure Mathematics (7898) All Advanced GCE Pure Mathematics combinations include: C1, C2, C3 and C4. The other two units must be one of the following combinations: FP1, FP2; FP1, FP3; FP1, NC; NM, FP2; NM, FP3; NM, NC No other combination of units may be used to claim Advanced GCE Pure Mathematics. A qualification in Advanced GCE Pure Mathematics may not be obtained in combination with any qualification in Mathematics or Further Mathematics.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4.4

FINAL CERTIFICATION

Each unit is given a grade and a Uniform Mark, using procedures laid down by QCA in the document ‘GCE A and AS Code of Practice’. The relationship between total Uniform Mark and subject grade follows the national scheme.

4.4.1 Certification of Mathematics Candidates enter for three units of assessment at Advanced Subsidiary, followed by three A2 units to complete the Advanced GCE. To claim an award at the end of the course, candidates’ unit results must be aggregated. This does not happen automatically and Centres must make separate ‘certification entries’. Candidates may request certification entries for: either or or

Advanced Subsidiary GCE aggregation Advanced Subsidiary GCE aggregation, bank the result, and complete the A2 assessment at a later date Advanced GCE aggregation.

Candidates must enter the appropriate AS and A2 units to qualify for the full Advanced GCE award.

4.4.2 Certification of Mathematics and Further Mathematics: Order of Aggregation Units that contribute to an award in Advanced GCE Mathematics may not also be used for an award in Advanced GCE Further Mathematics. Candidates who are awarded certificates in both Advanced GCE Mathematics and Advanced GCE Further Mathematics must use unit results from 12 different teaching modules. Candidates who are awarded certificates in both Advanced GCE Mathematics and Advanced Subsidiary GCE Further Mathematics must use unit results from nine different teaching modules. When a candidate has requested awards in both Mathematics and Further Mathematics, OCR will adopt the following procedures. In the majority of cases, certification for Advanced GCE Mathematics is made at the same time as the request for Further Mathematics certification. In this situation: •

the best Mathematics grade available to the candidate will be determined;

•

the combination of units which allows the least total Uniform Mark to be used in achieving that grade legally is selected;

•

the remaining units are then used to grade the Further Mathematics.

Note: In the aggregation process, in order to achieve the best set of grades for a candidate as described above, it is possible that AS GCE Further Mathematics may include some A2 units.

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In a small number of cases a candidate, who originally embarked on a nine-unit or twelve-unit course, may decide not to go beyond the six units obtained in the first year. Since separate grading procedures will apply to these candidates, Centres will need to write to the OCR Subject Officer outlining the case for the candidate. Provided the candidate has a valid combination for AS Mathematics + AS Further Mathematics (as opposed to Advanced GCE Mathematics), then, as described above: •

the best AS Mathematics grade available to the candidate will be determined;

•

the combination of units which allows the least total Uniform Mark to be used in achieving that grade legally is selected;

•

the remaining units are then used to grade the AS Further Mathematics.

4.4.3 Awarding of Grades The Advanced Subsidiary has a weighting of 50% when used in an Advanced GCE award. Advanced GCE awards are based on the aggregation of the weighted Advanced Subsidiary (50%) and A2 (50%) Uniform Marks Both Advanced Subsidiary GCE and Advanced GCE qualifications are awarded on the scale A to E or U (unclassified).

4.4.4 Extra Units A candidate may submit more than the required number of units for a subject award (for example, seven instead of six for an Advanced GCE). In that case the legal combination for that award which is most favourable to the candidate will normally be chosen.

4.4.5 Enquiries on Results Candidates will receive their final unit results at the same time as their subject results. In common with other Advanced GCE results, the subject results are at that stage provisional to allow enquiries on results. Enquiries concerning marking are made at the unit level and so only those units taken at the last sitting may be the subject of such appeals. Enquiries are subject to OCR’s general regulations.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4.5

AVAILABILITY

4.5.1 Unit Availability There are two examination sessions each year, in January and June. In June all units are assessed. In January all units are assessed, with the following exceptions: FP3, M4, S4, D2, DC and NC. However during the phasing-in period, i.e. in January and June 2005, the availability of assessment is yet to be determined.

4.5.2 Certification Availability Certification is available following the January and June examinations.

4.5.3 Shelf-life of Units Individual unit results, prior to certification of the qualification, have a shelf-life limited only by that of the specifications.

4.6

RE-SITS

4.6.1 Re-sits of Units There is no limit to the number of times a candidate may re-sit a unit. The best result will count.

4.6.2 Re-sits of Advanced Subsidiary GCE and Advanced GCE Candidates may take the whole qualification more than once.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

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4.7

QUESTION PAPERS

4.7.1 Style of Question Papers The assessment requirements of the various units are summarised in the table in Section 4.1.1. Most units are assessed by a single question paper lasting 1½ hours. The exceptions are as follows: •

there is also a coursework requirement in C3, DE and NM;

•

the examinations for DC and NC last 2½ hours;

•

there are two parts to the examination for C4. As well as the 1½ hour Paper A (with two sections) there is a comprehension question lasting 1 hour (Paper B).

Many of the question papers have two sections, A and B. The questions in Section A are short and test techniques. The questions in Section B are longer and also test candidates’ ability to follow a more extended piece of mathematics. In most papers there is no choice of questions but there are options in the papers for the following units: FP2, FP3, DE, S4 and NC.

4.7.2 Use of Language Candidates are expected to use clear, precise and appropriate mathematical language, as described in Assessment Objective 2.

4.7.3 Standard Candidates and Centres must note that each A2 unit is assessed at Advanced GCE standard and that no concessions are made to any candidate on the grounds that the examination has been taken early in the course. Centres may disadvantage their candidates by entering them for a unit examination before they are ready.

4.7.4 Thresholds At the time of setting, each examination paper will be designed so that 50% of the marks are available to grade E candidates , 75% to grade C and 100% to grade A. Typically candidates are expected to achieve about four fifths of the marks available to achieve a grade, giving design grades of : A 80%, B 70%, C 60%, D 50% and E 40%. The actual grading is carried out by the Awarding Committee. They make allowance for examination performance and for any features of a particular paper that only become apparent after it has been taken. Thus some variation from the design grades can be expected in the award.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4.7.5 Calculators No calculating aids may be used in the examination for Unit C1. For all other units, a graphical calculator is allowed. Computers, and calculators with computer algebra functions, are not permitted in answering any of the units with the exceptions of DC and NC.

4.7.6 Mathematical Formulae and Statistical Tables A booklet (MF2) containing Mathematical Formulae and Statistical Tables is available for the use of candidates in all unit examinations. Details of formulae which candidates are expected to know and the mathematical notation that will be used in question papers are contained in Appendices A and B. A fuller booklet, entitled Students’ Handbook, is also available for students’ use during the course. This includes all relevant formulae for each unit; those that students are expected to know are identified. The Students’ Handbook also includes a list of the notation to be used and the statistical tables. Schools and colleges needing copies for their students’ use may obtain them from the MEI Office (see Section 7 for the address).

4.8

COURSEWORK

4.8.1 Rationale The requirements of the following units include a single piece of coursework, which will count for 20% of the assessment of the unit: C3, Methods for Advanced Mathematics DE, Differential Equations NM, Numerical Methods. In each case the coursework covers particular skills or topics that are, by their nature, unsuitable for assessment within a timed examination but are nonetheless important aspects of their modules. The work undertaken in coursework is thus of a different kind from that experienced in examinations. As a result of the coursework, students should gain better understanding of how mathematics is applied in real-life situations.

4.8.2 Use of Language Candidates are expected to use clear, precise and appropriate mathematical language, as described in Assessment Objective 2.

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4.8.3 Guidance Teachers should give students such guidance and instruction as is necessary to ensure that they understand the task they have been given, and know how to set about it. They should explain the basis on which it will be assessed. Teachers should feel free to answer reasonable questions and to discuss students’ work with them, until the point where they are working on their final write-up. A student who takes up and develops advice offered by the teacher should not be penalised for doing so. Teachers should not leave students to muddle along without any understanding of what they are doing. If, however, a student needs to be led all the way through the work, this should be taken into account in the marking, and a note of explanation written on the assessment sheet. Teachers should appreciate that a moderator can usually detect when a student has been given substantial help and that it is to the student’s disadvantage if no mention is made of this on the assessment sheet. Students may discuss a task freely among themselves and may work in small groups. The final write-up must, however, be a student’s own work. It is not expected that students will work in larger groups than are necessary. Coursework may be based on work for another subject (e.g. Geography or Economics), where this is appropriate, but the final write-up must be submitted in a form appropriate for Mathematics. In order to obtain marks for the assessment domain Oral Communication, students must either give a presentation to the rest of the class, have an interview with the assessor or be engaged in on-going discussion.

4.8.4 Coursework Tasks Centres are free to develop their own coursework tasks and in that case they may seek advice from OCR about the suitability of a proposed task in relation both to its subject content and its assessment. However, Centres that are new to the scheme are strongly advised to start with tasks in the MEI folder entitled Coursework Resource Material. This is available from the MEI Office (see Section 7 for address).

4.8.5 Moderation Coursework is assessed by the teacher responsible for the module or by someone else approved by the Centre. It should be completed and submitted within a time interval appropriate to the task. Consequently the teacher has two roles. While the student is working on coursework, the teacher may give assistance as described earlier. However, once the student has handed in the final write-up, the teacher becomes the assessor and no further help may be given. Only one assessment of a piece of coursework is permitted; it may not be handed back for improvement or alteration. The coursework is assessed over a number of domains according to the criteria laid down in the unit specification. The method of assessment of Oral Communication should be stated and a brief report on the outcome written in the space provided on the assessment sheet.

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Section C: General Information © MEI/OCR 2003 MEI Structured Mathematics Oxford, Cambridge and RSA Examinations

4.8.6 Internal Standardisation Centres that have more than one teaching group for a particular module must carry out internal standardisation of the coursework produced to ensure that a consistent standard is being maintained across the different groups. This must be carried out in accordance with guidelines from OCR. An important outcome of the internal standardisation process will be the production of a rank order of all candidates.

4.8.7 External Moderation After coursework is marked by the teacher and internally standardised by the Centre, the marks are then submitted to OCR by the specified date, after which postal moderation takes place in accordance with OCR procedures. Centres must ensure that the work of all the candidates is available for moderation. As a result of external moderation, the coursework marks of a Centre may be changed, in order to ensure consistent standards between Centres.

4.8.8 Re-Sits If a unit is re-taken, candidates are offered the option of submitting new coursework (Entry Code Option A) or carrying over the coursework mark from a previous session (Option B).

4.8.9 Minimum Coursework Requirements If a candidate submits no work for the coursework component, then the candidate should be indicated as being absent from that component on the coursework Mark Sheet submitted to OCR. If a candidate completes any work at all for the coursework component then the work should be assessed according to the criteria and marking instructions and the appropriate mark awarded, which may be 0 (zero).

4.8.10 Authentication As with all coursework, Centres must be able to verify that the work submitted for assessment is the candidate’s own work.

4.9

SPECIAL ARRANGEMENTS

For candidates who are unable to complete the full assessment or whose performance may be unduly affected through no fault of their own, teachers should consult the Inter-Board Regulations and Guidance Booklet for Special Arrangements and Special Consideration. In such cases advice should be sought from OCR as early as possible during the course.

© MEI/OCR 2003 Section C: General Information Oxford, Cambridge and RSA Examinations MEI Structured Mathematics

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4.10

DIFFERENTIATION

In the question papers differentiation is achieved by setting questions which are designed to assess candidates at their appropriate levels of ability and which are intended to allow candidates to demonstrate what they know, understand and can do. In coursework, differentiation is by task and by outcome. Students undertake assignments which enable them to display positive achievement.

4.11

GRADE DESCRIPTIONS

The following grade descriptions indicate the level of attainment characteristic of the given grade at Advanced GCE. They give a general indication of the required learning outcomes at each specified grade. The descriptions should be interpreted in relation to the content outlined in the specification; they are not designed to define that content. The grade awarded will depend in practice upon the extent to which the candidate has met the assessment objectives overall. Shortcomings in some aspects of the examination may be balanced by better performances in others.

Grade A

Candidates recall or recognise almost all the mathematical facts, concepts and techniques that are needed, and select appropriate ones to use in a wide variety of contexts. Candidates manipulate mathematical expressions and use graphs, sketches and diagrams, all with high accuracy and skill. They use mathematical language correctly and proceed logically and rigorously through extended arguments or proofs. When confronted with unstructured problems they can often devise and implement an effective solution strategy. If errors are made in their calculations or logic, these are sometimes noticed and corrected. Candidates recall or recognise almost all the standard models that are needed, and select appropriate ones to represent a wide variety of situations in the real world. They correctly refer results from calculations using the model to the original situation; they give sensible interpretations of their results in the context of the original realistic situation. They make intelligent comments on the modelling assumptions and possible refinements to the model. Candidates comprehend or understand the meaning of almost all translations into mathematics of common realistic contexts. They correctly refer the results of calculations back to the given context and usually make sensible comments or predictions. They can distil the essential mathematical information from extended pieces of prose having mathematical content. They can comment meaningfully on the mathematical information. Candidates make appropriate and efficient use of contemporary calculator technology and other permitted resources, and are aware of any limitations to their use. They present results to an appropriate degree of accuracy.

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Grade C

One of the modules for Further Maths (MEI) is Differential Equations (DE), within which there is an element of coursework. The task of my class is to model the landing of an aircraft. However, I am finding this most challenging, mostly due to the fact that we have no guide or template to follow!

Is there anybody in the same position as me, or currently undertaking Differential Equations Coursework?

Thank you very much.- (Original post by
**hello calum**)

I'm not doing this myself, but I think you can write a differential equation taking friction and air resistance into account.

so if R=mg

and

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