GCSE Mathematics (9-1)
Welcome. This is a complete, interactive GCSE Mathematics book for England, covering both Foundation and Higher tier. Everything here is free to read online, and there is nothing to install.
How to use this book
Each section has three pages:
| Page | What it is for |
|---|---|
| Learn | The teaching: ideas, worked examples, and something to try |
| Practise with help | Questions with hints you reveal only if you need them |
| Practise | Independent questions, with answers at the end |
Each chapter opens with a problem you will be able to solve by the end, and ends with a Review that mixes the chapter's methods together.
Higher only. Some sections are for Higher tier only. They are marked in the chapter lists. If you are taking Foundation, you can skip them.
The formulae booklet
A Formulae button sits at the bottom right of every page. It opens a searchable booklet of the formulae and tables you are given in the exam. Choose your exam board and tier, and it shows only what that board allows.
Computer-checked answers
Every answer in this book is checked by a computer algebra system when the book is built. If a worked step were wrong, the build would fail. The questions and the answers are printed from the same checked source, so they cannot disagree.
Chapters
- Number skills
- Factors, multiples and primes Higher only sections
- Powers, roots and indices Higher only sections
- Fractions, decimals and percentages Higher only sections
- Ratio and proportion Higher only sections
- Percentages and financial mathematics
- Measures, accuracy, standard form and surds Higher only sections
- Algebraic expressions and manipulation Higher only sections
- Equations and inequalities Higher only sections
- Sequences Higher only sections
- Straight-line graphs and rates of change Higher only sections
- Quadratic expressions, equations and graphs Higher only sections
- Other functions and graphs Higher only sections
- Simultaneous equations and iteration Higher only sections
- Functions, algebraic fractions and proof Higher only sections
- Angles, polygons and geometrical reasoning Higher only sections
- Properties, constructions, loci and bearings
- Transformations, congruence and similarity Higher only sections
- Perimeter, area, surface area and volume
- Pythagoras' theorem and trigonometry Higher only sections
- Circle geometry and circle theorems Higher only sections
- Vectors Higher only sections
- Probability Higher only sections
- Statistics: representing and analysing data
- Statistics: spread, grouped data and correlation Higher only sections
Learn more
- Glossary — the key words, by topic
- Number · Algebra · Geometry · Probability and statistics