Please note that this website is under development.
Study material is currently available for the first 22 weeks of year 1 of the course.
Study sessions are being regularly added, and you are very welcome to return to view the new material.

A-level Mathematics


This course is intended for independent students who wish to study A-level mathematics as a self-taught subject. Examinations can then be taken to gain the A-level mathematics qualification. This may be needed to improve employment opportunities or as an entrance requirement for a higher education course.

It is hoped that the course will also be of use to A-level mathematics students at school or college who wish to undertake additional self-study in preparation for the examinations.

Structure of the course

The course is arranged as a series of weekly study blocks which allow the subject material to be studied in a logical order, followed by a period of examination revision. The study schedule can be selected by clicking the
'Weekly sessions' option on the main menu above.

Each topic page is divided into a number of study activities. Further details are given alongside:

Topic study activities

Study notes

The session begins with background information, illustrated by worked examples of the mathematical techniques involved.

Multiple choice questions

A series of multiple choice questions are provided which allow you to test your understanding of the mathematical methods.

Longer questions

Longer examination-type questions are then provided. You may check your results by displaying worked answers.

Practical applications

Where appropriate, a case study will demonstrate the use of the current topic in a real-world mathematical application.


Where appropriate, Excel spreadsheet files can be downloaded from the topic web pages which will carry out mathematial processing related to the current topics.

Large data set

The A-level examination boards each provide a spreadsheet file containing a large set of data. This is to allow students an opportunity to carry out realistic practical statistical analysis as part of the course. One or more questions in the examination will be based on the large data set, and may involve analysing a summary or graph produced from the data set.

For the purpose of the current course, you are asked to download the large data set 'Quarterly provisional motor vehicle traffic by vehicle type and road class, Great Britain' from the UK Government web site. This is a spreadsheet in Open Document format which can be loaded into Microsoft Excel or other spreadsheets. The data set will be used during this course to demonstrate a number of the statistical methods introduced during the teaching sessions.


All information, questions and soutions for the session may be downloaded as a PDF document.

Examination boards

The subject content for AS-level and A-level Mathematics has been specified nationally by the Department for Education, and is common across all exam boards. The course is normally studied over two years, with AS-level examinations at the end of year 1, followed by A-level examinations at the end of year 2.

The objectives of the course are:

  • To gain an understanding of mathematical argument, language and proof.
  • To gain skills in mathematical problem solving.
  • To undertake mathematical modelling.
  • To gain experience of using technology in mathematics.

Links are given alongside to the AS-level and A-level mathematics syllabuses of different exam boards.

This course is based on the examination structure of WJEC, but the series of topics covered will be found in the syllabuses of each of the other exam boards.

Examination syllabuses

Assumed previous knowledge

To undertake this course, it is assumed that students have a good knowledge of GCSE mathematics, or have studied mathematics to an equivalent level.

If you are uncertain about the level of previous knowledge required, please view the sample GCSE examination papers by clicking the links opposite.

A number of excellent textbooks are available, covering the GCSE mathematics specifications offered by different examination boards.


This website has been compiled by Graham Hall.

He has taught computer science and mathematics at Coleg Meirion-Dwyfor in North Wales, and as a tutor for Open University computing and mathematics courses.

He is joint author of the book 'Developing Numeracy in Further Education'.


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