Five topics for early success at A-Level maths

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Five topics for early success at A-Level maths

In this article, I'm going to look at five topics or skills that exhibiting mastery of will significantly improve the start of your time in A-Level mathematics. (Follow the links to see details and examples!)

Completing the square

This topic is significant because it is the first example of algebraic nonsense! The process is probably the first regular encounter with algebra in which an equation is not directly solved, but rather expressions are just manipulated into different forms to reveal information which later needs manipulation or interpretation

Surds and Indices

Learning how to manipulate surds and indices will significantly improve your success on a multitude of later topics; everything to do with logarithms, exponentials and calculus to start with. Surds and indices also expose a large number of misconceptions and allow examinations to quickly discriminate between those who are likely to succeed or fail. Again, like completing the square, this is a topic in which expressions are rewritten without an intention to necessarily solve any equation.

Gradient of a line

A deceptively simple idea; but one which is required for the first explorations of calculus. We slowly replace the requirement for the straightness of a line for the smoothness of a curve to allow us to modify the idea of gradient to one that can be applied to curves.


A recap of trigonometry in the context of a right angled triangle and a discussion of the multiple solutions that arise from the simple equations of the form $\sin(x) = k$ 

Curve Sketching

This is a skill that allows us to graphically represent a huge swathe of problems and simplify their solutions, however, it is not a skill explicitly taught at GCSE and so is important to spend a little time on this.

I've included a mini test with full solutions to enable you to test your familiarity with this material. (The final link in the list below)