The transition from GCSE to A-Level Maths can be a challenging one. You will probably feel that Maths has suddenly gotten a lot harder, and you’ll be going from topic to topic very quickly. There will be more of an emphasis on Algebra and Proofs. Statistics and Mechanics will also now appear on the syllabus as separate topics.
But don’t let any of this put you off. To progress with the A-Level it’s important that you have a good grounding and that you enjoy Maths. Though the first few topics will seem like GCSE revision, you will go into them in more detail than before.
The secret to starting the A-Level is to be organised and prepared. One way to be organised is to get yourself some folders of blank, lined and graph paper, and several notebooks to jot down ideas. One way to be prepared is to thoroughly practice certain topics before you start the A-Level course. Some of those topics are listed below.
If you practise these topics, you’ll start off well. If you don’t know them, A-Level will most likely be tough and you may get left behind. So make sure you have a thorough grasp of the following as you start your transition from GCSE to A Level Maths.
Algebra – a vital area of Maths is getting to grips with manipulating formulae and equations.
Practice algebra – a lot! Get good at it, and much of the rest will follow.
Indices and Surds – you need to be confident with the laws of indices, and how to manipulate surds.
Expanding and Simplifying Brackets – try double, triple, and more brackets.
Factorising and Completing the Square – essential skills for sketching curves and solving quadratics.
Solving Linear and Quadratic Equations – work on these before moving on to the more complex ones in A-Level.
Sketching Curves – a sketch will often help you to make sense of a problem and help solve it.
Co-ordinate Geometry – this is almost anything to do with straight lines and their equations.
Graphs and Transformations – A Level students need to know how to manipulate graphs. This knowledge will help you to visualise many common problems.
Sine and Cosine Rules – just two of the many trigonometric rules you will come across.
Area of a triangle – there are several formulae and methods for finding the area of any triangle. Look up as many as you can. You’ll be surprised at how many you find.
Vectors – these appeared in your Maths GCSE at an elementary level. Make sure you revise them as they’ll come up again in Pure Maths and in Mechanics.
Two more topics, called Differentiation and Integration, come under the heading of Calculus, and are two of the most important topics in Mathematics. You won’t have done them at GCSE but now’s the time to start. If you learn to Differentiate and Integrate some simple functions, you’ll be way ahead when you come to doing them in class.
Recommended Reading
There are a great deal of books written about Mathematics, many of which are very readable. Many public libraries will have a good selection. Here are just a few of my favourites.
Textbooks
These two deal with the topics mentioned above.
1. Bridging GCSE and A–Level Maths, by Mark Rowland
2. Head Start to A-Level Maths, CGP Books
General Reading
These are just some of the books I hope will raise your interest in Mathematics.
Any book by Ian Stewart – too many to mention!
Aha! Solutions, by Martin Erikson
Alex’s Adventures in Numberland, by Alex Bellos
Alex Through The Looking-Glass, by Alex Bellos
A Mathematical Tapestry, by Peter Hilton & Jean Pedersen
A Mathematician’s Apology, by G H Hardy
A Number For Your Thoughts, by Malcolm E Lines
Fermat’s Last Theorem, by Simon Singh
Go Figure!, by Clint Brookhart
How Big Is Infinity, by Tony Crilly
How Long Is A Piece of String?, by Rob Eastway & Jeremy Wyndham
How To Lie With Statistics, by Darrell Huff
How Math Can Save Your Life, by James D Stein
Humble Pi, by Matt Parker
In Code, by Sarah Flannery
Magnificent Mistakes in Mathematics, by A S Posamentier & I Lehmann
Mathematician’s Delight, by W W Sawyer
Mathematics for the Million, by Lancelot Hogben
Mathematics From the Birth of Numbers, by Jan Gullberg
Riddles in Mathematics, by Eugene P Northrop
Statistics Without Tears, by Derek Rowntree
The Music of the Primes, by Marcus du Sautoy
The Penguin Dictionary of Curious and Interesting Geometry, by David Wells
The Penguin Dictionary of Curious and Interesting Numbers, by David Wells
The Pleasures of Pi, E and Other Interesting Numbers, by Y.E.O. Adrian
The Simpsons and their Mathematical Secrets, by Simon Singh
The Tiger That Isn’t, by Michael Blastland & Andrew Dilnot
Think of a Number, by Malcolm E Lines
Why Do Buses Come In Threes?, by Rob Eastway & Jeremy Wyndham
Later on…
If eventually you decide to study Mathematics at university then make sure you check out the book “Bridging the Gap to University Mathematics” by Martin Gould & Edward Hurst. It talks about the transition from A–Level to undergraduate Mathematics.
Rajiv B
Maths tutor at TuitionWorks
I have been teaching and tutoring for over 35 years now, with an excellent rate of success and glowing references from literally scores of past pupils.
About me: At the age of 10, I was awarded a 7-year scholarship to Loughborough Grammar School and went on to study Mathematics at Keele University and then at Oxford University.
