# 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. Note that all the pdfs are "editable pdfs" - they can be opened by Adobe Reader and used as they are, but if you want to edit them, you can open them with LibreOffice or Apache OpenOffice (both of which are free) and they can be edited as normal documents. For more detail, see here

If you have any comments or queries, you can contact me at a.lewis@mathsanswers.org.uk though I don't guarantee to reply promptly!

WHAT'S NEW:

### Polyominoes

Fill a variety of shapes with pieces made from squares, like a jigsaw. If you get stuck, you can check whether the pieces you have placed so far are correct, or get some pieces placed for you. There are puzzles in three different sizes:

Tetrominoes: Use 10 shapes each made of 4 squares. There are 10 different puzzles available.

Pentominoes: Use 12 shapes each made of 5 squares. There are 20 different puzzles available.

Hexominoes: Use up to 35 shapes each made of 6 squares. There are 10 different puzzles available.

## 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

## Problem Solving

A couple of sheets of extension questions, aimed at encouraging brighter students to think through a problem, are available here.

## 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

### Polyominoes

Fill a variety of shapes with pieces made from squares, like a jigsaw. If you get stuck, you can check whether the pieces you have placed so far are correct, or get some pieces placed for you. There are puzzles in three different sizes:

Tetrominoes: Use 10 shapes each made of 4 squares. There are 10 different puzzles available.

Pentominoes: Use 12 shapes each made of 5 squares. There are 20 different puzzles available.

Hexominoes: Use up to 35 shapes each made of 6 squares. There are 10 different puzzles available.

### Squares

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.

### Dominate

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.

### Tangrams

Choose a shape, and then fill it with the seven "Tans".

This is an ancient puzzle which originated in China and spread to the Western world in the early 19th century.

### Flipit

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.

## Investigations

### Tessellations

A page introducing tessellations, with a worksheet for an investigation into semi-regular tessellations, and examples created using each of the tools below

NEW:

### Tessellate!

An online tool for designing tessellations out of regular polygons.

• Click on the polygons on the left to add them to the canvas.
• Then drag them and rotate them to start forming your tessellation.
• Form groups of tiles which can be added with a single click to speed up the creation process.
• Full instructions for use are available by clicking the help button in the program.
• Or watch a Youtube video showing how to use it.

### TessMaker

An online tool to help with the design of tessellations, for example in the style of Maurits Escher.

• Start by choosing a type of tile (parallelogram, kite, etc) and how the tiles will fit together (by rotating, reflecting, etc).
• Then add extra points and drag them around to make an interesting shape.
• Decorate the shape using the drawing tools.
• Then click the tessellation tab to see the completed tessellation
• Full instructions for use are available by clicking the help button in the program.
• Or watch a Youtube video showing how to use it.

### 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.