Making the Transition From GCSE To A Level Maths? Make Sure You Know These 11 Important Concepts

Maths GCSE to A Level Transition Tips

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. 


These two deal with the topics mentioned above.

1. Bridging GCSE and ALevel 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 ALevel to undergraduate Mathematics. 

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Rajiv B

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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.

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