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.
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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.
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.
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.
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