# A Level Mathematics Coursework

### A-level Mathematics (6360) and A-level Statistics (6380)

For use with the specifications from September 2004.

The following tasks are recommended by AQA for centres choosing to undertake coursework for the AQA A-level Mathematics and Statistics specifications.

(Coursework is **optional **– for each unit with coursework and a written paper, there is an equivalent unit with the same subject content but assessed by written paper only. See the specifications for full details.)

These coursework tasks have been chosen because they relate to the subject content of the unit and they give students the opportunity to meet all the assessment criteria. Teachers and students may choose their own tasks, but AQA strongly advises that, if they do, they consult their coursework adviser before using the task with students so that the adviser can reassure them that the proposed task is suitable.

#### Statistics Unit 1 (MS1A/SS1A)

##### Task A: Is There a Link?

Collect appropriate data to test whether there is a link between two variables. You should calculate and interpret relevant correlation coefficient(s), as well as calculating appropriate regression line(s). You could then make predictions and discuss them. You could refer to outliers and their effects on your results. Some possible choices are:

- Length of a paperback book vs cost of the book.
- Reaction time vs hand-eye coordination in a game.
- GCSE scores vs 'AS' / 'A2' results.
- Goals scored vs goals conceded (or points achieved) in different leagues in sports.

##### Task B: Measurements

Collect the data from a population with a view to estimating population parameters (for example, and ) by using the estimation techniques in this module. Your work should involve taking a random sample as well as calculating and comparing confidence intervals.

Possible choices are heights, weights, pulse rates or reaction times of males and females and/or different age groups. Measurements of trees, shells, etc, of different types and locations could also be compared.

##### Task C: Estimation

Collect data from a population with a view to estimating population parameters (for example, and ) by using the estimation techniques in this module. Your work should involve taking a random sample as well as calculating and comparing confidence intervals.

How good are people at estimating lengths, weights, times, angles, sizes, etc?

Using sub-groups of equal numbers of males/females, non-scientists/scientists, etc, would provide further data for comparison.

##### Task D: Authorship

Collect data from a population with a view to estimating population parameters (eg and ) by using the estimation techniques in this module. Your work should involve taking a random sample as well as calculating and comparing confidence intervals.

Investigate whether it is possible to gain information about authorship of a text using statistical measures.

Some possible choices are:

- modern text vs historical text
- adult text vs child's text
- books by the same authors.

TSR Wiki > Study Help > Exams and Qualifications > A Levels > Mathematics A Level

Maths is a popular subject at A Level and covers a large area of knowledge and skills.

## Why Study Maths?

There are many reasons why people choose to study A Level Mathematics. It might be a requirement for what you want to study at university (physics, psychology, economics, computing, and business studies prefer students to have A Level maths if possible). Since maths is one of the most traditional subjects a good grade in maths can boost an application for pretty much every course!

Studies have also shown that people with Maths A Level also tend to earn more on average than people without it. Though this itself may or may not be a good enough reason to study maths, the skills it allows you to develop include problem solving, logic and analysing situations. Add in the improvements to your basic numeracy skills and that bit of creativity needed to solve maths problems and you've got yourself a set of skills which would make you more desirable for almost any job!

Or perhaps you're looking for an easy 'A' grade. Over 45% of people achieve this grade in Maths, with a third achieving it at AS. This definitely makes it worth considering.

Finally, you might also really like maths - this is as good a reason as any to continue studying it. If you study something you enjoy you are likely to do better at it. With maths there is the excitement of new discoveries you will make. You will see more of the beauty of it and realise just how much everything around in the universe is connected to mathematics.

The bottom line is, maths is an amazing subject to have at A Level and provided you have a solid understanding of the GCSE concepts before you start, alongside some perseverance and effort, you should be able to do well.

## Course Structure

**Mathematics A Level** is almost always now taken as a modular course. Each module is specific to particular of areas of work, and the work slightly varies from exam board to exam board. Generally all the information below relates to Edexcel's specification. In the links to specific modules below you will find textbook answers, textbook mistakes, and links to TSR where you can see how the community finds the module.

### A Level Maths modules

### Unit Combinations

*{A / B / C} - indicates that you can chose one of the options A, B or C*

**Mathematics:**

AS Level: C1, C2, {M1 / S1 / D1}

A2 Level: C1, C2, C3, C4, {M1,M2 / S1,S2 / D1,D2 / M1,S1 / S1,D1 / M1,D1}

**Pure Mathematics:**

AS Level: C1, C2, C3

A2 Level: C1, C2, C3, C4, FP1, {FP2 / FP3}

**Further Mathematics:**

AS Level: FP1, {Applied Module A}, {Applied Module B}

A2 Level: FP1, {FP2 / FP3}, {Applied Module A}, {Applied Module B}, {Applied Module C}, {Applied Module D}

**Applied Modules:**

A-D can be any applied modules you haven't already used in AS/A2 Mathematics, although you will have to have done M1, M2, M3 before doing M4 (for example). One of these 'Applied Modules A-D' could be FP2/FP3 as well (if you decide to do both of them)

**Further Mathematics (Additional):**

AS Level: {Three more applied modules not used for any other award} - if you've done 15-17 maths units altogether

A2 Level: {Six more applied modules not used for any other award} - if you've done all 18 maths units

Additional further maths is not currently available if you study with AQA exam board or with the main OCR (A) specification. As well as Edexcel, OCRMEI also offers Further Maths Additional, from 15 or 18 units (but since OCR MEI has many more units available than Edexcel, not all the units will be used up).

**Statistics:** AS Level:S1,S2,S3 A2 Level:S4,S5,S6

### Other Boards' Course Structures

All boards have the central 'core' units of C1-4. They also have the 'further pure' FP1-3. They may also contain a selection of mechanics (most have M1-4), statistics (most have S1-4) and decision maths/discrete units D1-2. Each one of these usually rests on the one before it, as do all the pure core units. But the relationships between these areas can be different, and especially over the further pure units: each one has the relationship between its pure core and further pure units structured differently.

**AQA** has C1-4, FP1-**4**, M1-**5**, S1-6, D1-2. Note that it has FP4 as well as FP1-3. FP2, FP3, FP4 are all options independent of each other that can be used in Further Maths (one of which must be used in the A-level). It is an A-level with FP1 as an AS module (rather than A2 as Edexcel and WJEC), though not available for use in A-level Mathematics, only Further Maths. In terms of its material, it is quite different from the other A-levels: there are no sequences and series in C1 for example, but both the factor theorem and the remainder theorem are compulsory for C1. There is some unique material (e.g. Simpson's rule for integration as well as the trapezium and mid-ordinate rules). And significantly, AQA has a coursework-and-exam option for M1 and S1 (and before 2007, M2 and S2 as well) as well as an all-exam option where most boards do not.

**CCEA** has C1-4, FP1-3, M1-4, S1-*2*. It lacks Decision Maths modules, as does WJEC. Along with WJEC it has the most restricted range of units, lacking S3 and S4. It is a FP1-as-AS module, like AQA, OCR and OCR MEI. Unlike Edexcel, AQA, and OCR, but like MEI and WJEC, FP3 is dependent on FP2. It is the only specification to make both FP2 and FP3 compulsory for A-level Further Maths. It lacks coverage of certain statistical tests and the binomial and Poisson distributions.

**OCR** (A) has the bare core of modules: C1-4, FP1-3, M1-4, S1-4, D1-2. There is no M5. It is a FP1-as-AS specification. Its structure is very much like AQA's - units FP2 and FP3 are independent of each other, and at least one of them must be taken at A2.

**OCR MEI** has probably the most diverse range of modules: C1-4, FP1-3, M1-4, S1-4, D1-2, **DC**, **NM**, **NC**, **DE**. The pure modules, both core and further, have names more than "Pure Core 1" or "Further Pure 1" - C1 is "Introduction to Advanced Mathematics", C2 is "Concepts for Advanced Mathematics", C3 is "Methods for Advanced Mathematics", C4 is "Applications for Advanced Mathematics"; FP1 is "Further Concepts for Advanced Mathematics", FP2 "Further Methods for Advanced Mathematics", FP3 "Further Applications for Advanced Mathematics". C3 has a compulsory coursework component to do with numerical methods such as the Newton-Raphson method, making MEI the only board with compulsory coursework in Maths or Further Maths. C4 has two papers, one of which is a comprehension with an article as an example of mathematical modelling. OCR MEI has a structure like CCEA's, with FP1-as-AS, FP3 dependent on FP2; but FP3 is not compulsory unlike in CCEA.

The extra modules are as follows: NM is "Numerical Methods", a pure maths AS unit only available to Further Maths, dependent on C2 only, with a coursework component; NC is "Numerical Computation", a pure maths A2 unit requiring a computer with a spreadsheet program and printer (unique to MEI), only available to Further Maths which dependent on NM only; DC is "Decision Mathematics Computation", an applied A2 unit requiring a computer with a spreadsheet program and printer, available to Maths and F. Maths and dependent on D1 only; DE is "Differential Equations", an applied A2 unit available only to Further Maths, dependent on C4, and with a coursework component. The units FP2, FP3, DE, S4, DC and NC all have options in their question papers, also a unique feature of MEI.

**WJEC** has C1-4, FP1-3, M1-*3*, S1-*3*; it lacks Decision modules, and M4, S4, making it as limited as CCEA. It is a FP1-as-A2 specification, and FP2 is a compulsory unit for Further Maths A-level, like Edexcel; but FP3 is dependent on FP2, not independent options, unlike Edexcel.

### Cashing-In

When you cash-in for one of the above awards, your individual modules marks from the required units (as shown above) will be combined and you will be given a mark out of 300 for AS Level and 600 for A2 Level.

In combining units for an awards, they will be selected in such a way (where possible), so that you are awarded the highest grades possible using the most UMS marks (for example: if you can get an A for A2 Mathematics using the units you have already sat, the units will be selected in such a way that your mark will be as high as possible).

Before January 2008, grades were awarded for getting the highest grade with the *lowest* amount of UMS marks in Maths. This enabled units in which you got higher UMS marks to be used for a future qualification (eg: Further Maths). AD in Maths and Further Maths would always be selected over BC; this remains for the new certification system. However, if a U results in Further Maths and can be re-arranged, a request can be made to lower the Maths grade to bring up the Further Maths grade: for example AU may be requested to change to BE.

### Changes to the A-level for 2008

The A-level reforms for first teaching in September 2008 do not affect A-level Mathematics, Further Mathematics, Further Mathematics Additional, Statistics, and AS Use of Mathematics, except for the introduction of the A* grade. It is important to note that for the Mathematics A-level alone, the "90%+ in the A2 units" condition is modified to "90% in the aggregate of C3 and C4 units"; for Further Mathematics (and presumably Further Mathematics Additional too) the best 3 A2 units will be taken as A2. Note that the A* grade is available from summer 2010 (with cash-in for the relevant A-level, due to the grade's nature as an overall grade), and so if the A-level is retaken in 2010 then it is possible to gain an A* grade, even though you may have started the A-level before 2008.

For further information on the A* in mathematics, see here.

#### Edexcel's post-2008 specification

Edexcel *is* modifying its specification slightly for the 2008 reform, and it will be available to students taking the A-level from January and summer 2009 onwards. There has been a lot of rearrangement between FP1, FP2 and FP3, making FP1 an AS unit and reliant on C2 only (unlike in the post-2004 reform FP1, which was still A2 and reliant on C4); this enables the Further Maths A-level to be taught concurrently with the Maths A-level, as well as being able to teach the whole of Maths A-level before the Further Maths A-level (which was virtually compulsory prior to this reform). FP2 and FP3 have had major changes amongst themselves too. The dependency chart for the pure units in the new Edexcel specification now resembles a cross between the current AQA and OCR (A) specifications (see above) - FP1-as-AS, either FP2 or FP3 compulsory for A2 Further Maths, no FP4. As for the Decision units, some D1 material has moved to D2 for balance - specifically flows in networks and the Simplex algorithm for linear programming.

Thus, students who do A-level Further Maths in 2009 will have the option of doing the old, post-2004 specification (FP1 = 6674, FP2 = 6675, FP3 = 6676), and the new, post-2008 specification (FP1 = 6667, FP2 = 6668, FP3 = 6669). This means that these changes not only hit the year group for all other new A-level subjects (who started the new AS in September 2008, and take Further Maths either all in the academic year 2009-2010 or over the two academic years 2008-2010) but they *may* also affect the year group above (those who started AS in September 2007 and take Further Maths in the year 2008-2009). With decision maths, D1 and D2 will completely switch over from January 2009. Thus there is no change in unit code for D1 and D2.

See here for further information on the Edexcel 2008 changes.

### Other Qualifications

It is also possible to study for other qualifications in maths while doing your A Levels. Like with many subjects an AEA is available in maths. Also, the STEP exams are still available in maths and often form a part of the offers people receive for studying maths at Cambridge or Warwick Universities.

## Study help

Why not read our A Level mathematics revision notes? Get help with areas you struggle with, read up around the subject or maybe add your own revision notes for others to use.

Also, this list of maths websites might also be of use to you, either for study help or for finding out about more maths and the applications of maths. Besides,you can also find the latest past papers here: Updated: Lastest Past Papers

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