GURNEY, RAYNER & WILLIAMS (shown here) is an excellent textbook, recommended for all first-year A-Level students regardless of exam board.

Many schoolteachers assume that if you have chosen to do A-Level Maths, then you must already be very good at basic maths and you're dead keen to learn lots more... with the result that many students find the first few months of Year 12 extremely challenging!

My approach is different. For a new Y12 student, I start by assessing their strengths and weaknesses in Pure Maths, particularly those topics overlapping GCSE and A-level (powers, quadratics, inequalities, simultaneous equations) - strong skills in these are fundamental to success in A-level - so that is absolutely our number one priority when starting out.

The PM1 syllabus widens out to include major new concepts such as Differentiation, Integration, Trigonometric Equations, and Logarithms. Provided the student has a firm foundation in the basics, each of these can be tackled and mastered in turn. 

The component parts of A-Level Maths are unequally weighted, with more of the marks for Pure Maths (2/3), and less for Statistics (1/6) and Mechanics (1/6). Furthermore, Pure Maths skills are often very important in Statistics and Mechanics, but not the other way around. Because of this, I prioritise doing all of PM1 (or at least the bulk of it) before starting S1 or M1.

M1 is generally smaller and more manageable than S1. If students become adept at using the 'SUVAT' equations, and learn to draw thorough Force Diagrams for questions on Connected Particles, M1 can usually be covered relatively quickly.

S1 usually takes longer and is best tackled in two parts. The first part is 'Handling Data' (Mean & Deviation, Median & Quartiles, Histograms, Correlation & Regression etc.) - in this section it is vital that the student learn to apply methods correctly AND understand what the calculated statistics represent. 

The second part of S1 is 'Probability and Hypothesis Testing'. At first this is easy enough, but then leads on to some sophisticated concepts considerably ahead of anything studied in GCSE - and vital for second-year Statistics (S2). Because of this, it can often be better to do this second part of S1 before the first.

Once the main parts of the syllabus have been understood, the student is ready to start practising past papers. When doing papers, it is important to mark your work carefully and to analyse where you have lost marks. The following marksheets can be useful for this.