A level textbooks
The books on this page are the ones I recommend to students who want something a bit more rigorous and thorough than the exam boards’ official textbooks. They don’t necessarily tie up exactly with any particular exam board though, but they’re excellent for a thorough understanding and I used them in my teaching as much as possible. As such they can also be great books for teachers teaching from the core textbooks but wanting extra exercises or to find some more thorough explanations to add into their teaching.
All the books below link to Amazon, so please use those links if this page has been useful to you!
Introducing Pure Mathematics
Robert Smedley and Garry Wiseman
Further Pure Mathematics
Brian Gaulter
Pure/Core
These textbooks contain through explanations and justifications of the results of A-level maths. Each section has loads of exercises (and answers in the back) including a lot of repetition of variations on easier questions, but also some really tough starred questions. Don’t do all the exercises then, but they’re great for a wide range of abilities at A-level.
Mechanics
Covers all the A-level single maths content and quite a few further maths topics. Rigorous explanations, also including a lot of exercises, including some more STEP style ‘no numbers’ questions throughout so good for a range of students or to top up the main A-level textbooks.
Understanding Mechanics
A. J. Sadler and D. W. S. Thorning
Understanding Statistics
Graham Upton and Ian Cook
Statistics
Statistics is notoriously badly explained at A-level. I used this book a lot when teaching A-level for the first time, to find great rigorous explanations and a range of exercise and examples of the techniques. A good reference for people who just need to use a bit of stats in other subjects too.
Mechanics and Statistics
An excellent alternative to the Mechanics and Statistics books mentioned above, from the same series as the books I’ve recommended for Pure/Core maths.
Introducing Statistics
Ian Cook and others
Introducing Mechanics
Brian Jefferson and Tony Beadsworth
A First Course in Calculus
Serge Lang
Problem-Solving Strategies
Arthur Engel
More pure and problem solving
If you’re looking to push things a bit further these are great books. Problem Solving Strategies contains some really tough problems, but great for pushing further maths students, and A First Course in Calculus has a lot of rigorous proof and more detail of extra cases that aren’t always necessarily included at A-level
Know a good maths book that is missing? Submit it here and we will consider adding it to the lists.