Maths Answers

Here you will find notes, practice questions and solutions for GCSE, detailed notes for A-Level, and you can test your maths skills online.

The material on this site has been accumulated over many years of maths teaching. It is made available here in the hope that it may be of some use to teachers or students. For more detail, see here

If you have any comments or queries, you can contact me at though I don't guarantee to reply promptly!



TessMaker is a tool to help with the design of tessellations, for example in the style of Maurits Escher.

Year 7-11 (GCSE) Notes and Worksheets

These are available topic by topic here.

There is also a page with various Revision Sheets and Answers

Maths Olympics

Anyone is welcome to enter the Maths Olympics here. This is a collection of "events" (topics). If you enter an event, you will be given ten questions to answer. Get them all right, and you get a gold medal. One wrong, silver, two wrong, bronze. You also get a time for the event.

You will need to make up a user name for yourself so that you can keep track of what medals you have won. Why not try for a complete set? (If you aren't sure what (English) school year you are in, just choose "not at school".)

A Level Core Maths Notes and Worksheets

These are available here.

A Level Statistics Notes and Worksheets

These are available here.

A Level Further Pure Maths Notes and Worksheets

These are available here.

Online Demonstration Software

These are tools for demonstrating various mathematical concepts. So far there is just one:

Graphs of Probability Distributions
Use this tool to see how good an approximation a Poisson or Normal distribution is to a Binomial distribution, etc.

Mathematical Puzzles

Here you will find Number Puzzles, Algebra Puzzles, Shapes Puzzles and Miscellaneous Puzzles for various age groups.

A collection of Christmas puzzles of various kinds.

Online Games and Investigations


Place four counters at the corner of a square before your opponent!

This is a game I invented over 30 years ago. Originally it was played with counters on a paper board. Then around 1985 I wrote a version which ran on a Research Machines Nimbus (in text mode!), a few years later I converted it to Windows, and now finally we have the online version.

There is also the Squares Challenge, which looks at the number of possible winning squares on different size game boards.


Drag dominos onto a board so that the dots add up to the correct totals.

I didn't invent this game, but I haven't been able to find any trace of it for many years. It's a really nice puzzle game, so I decided it was due for a revival. For more of a challenge, choose a harder level.


Can you turn all the counters blue?

I didn't invent this game. But my version gives the option to set up a particular starting position, and return to it at any point. It also keeps a record of the moves made, which helps with working out the strategy to use in solving the game.




TessMaker is a tool to help with the design of tessellations, for example in the style of Maurits Escher.

Recurring and non-recurring decimals

An investigation into the decimal expansion of 1/n for different values of n ,with hints and some answers. There are also a couple of tools to help with working out long recurring decimals, and prime factorisation of large integers.

To use the documents on this site, you need Adobe Reader. This is installed on most computers, but if necessary you can download it (free of charge) from here