3 Maths Concepts You Need to Understand if You Want to Take Maths at A-Level

3 Maths Concepts You Need to Understand if You Want to Take Maths at A-Level

A-level maths will enhance your ability to solve complex scientific problems and analyse information more effectively. You will apply problem-solving skills to a variety of scientific fields, ranging from physics to medicine.

Studying maths, even if only up to A-level, will be useful for further studies and your future career. Maths has been described as the ideal “facilitating subject”, giving you access to a vast range of job opportunities in fields that would seem unrelated.

For instance, strong mathematical skills are required in planning and constructing buildings – from homes to skyscrapers. Moreover, just as maths couples nicely with science, it is also a necessary requirement in any job related to medicine, engineering, scientific research, and accounting.

Your maths skills will also enhance your ability to code, opening the door to careers in the world of software.

This article will discuss 3 GCSE topics you should be confident with before starting your A-levels. These topics will only be briefly revised in the classroom. There are several reasons for this. Firstly, you are expected to have obtained the relevant knowledge during your GCSEs. Secondly, an A-Level student is supposed to have a good degree of independence regarding prerequisite learning. Thirdly, there is simply not enough time.



Maths is the language of numbers and algebra represents its grammar. The universe, from planets to subatomic particles, “moves” mathematically and motion can be represented by complex systems of equations. Algebraic manipulation will remain a fundamental skill for many years to come. This makes it is paramount that you have a sound knowledge of linear and quadratic equations and rearranging processes.



During your GCSEs you will have applied trigonometry to right angle triangles. You will also have briefly investigated vectors. Vectors are widely used in physics and engineering to embody entities such as forces and can be represented using trigonometric functions such as sine and cosine.

You will extensively use trigonometry in mechanics and experience its application to mechanical or structural engineering.  For instance, you might think that a bridge is a stationary object. However, any structure vibrates because of the effects exerted by seismic waves or vehicles. Broadly speaking, engineers try to minimise movement to preserve the structural integrity of constructions.



So far you will have applied probability theory to events such as throwing a fair die or the landing of a spinner. However, probability theories are used in many different fields of physics, engineering, and science.

You might be surprised to learn that modern science does not have a deterministic solution for everything. Many physical phenomena can only be investigated and comprehended using a probabilistic approach.

For instance, the way chemical elements form depends on how different atoms bond, and bonding processes depend on the motion of electrons. The trajectories of electrons around nuclei cannot be established with certainty, but the information obtained by using probabilistic theories is sufficient to understand these phenomena. This is what Quantum Mechanics does.

Finally, probability is widely used to investigate how viruses attack our immune system and how certain diseases develop. This helps scientists research and prevent medical issues such as Covid-19.


A robust understanding of these three concepts will set students in good stead for their A Level maths course. As a TuitionWorks tutor, I work with students to help them master these core concepts, and more, through a course of personalised, one-to-one lessons.

If you think you could benefit from advanced A-Level maths tutoring from a qualified teacher, get in touch for a free consultation.   

Federico Antonelli

Federico Antonelli

Maths tutor at TuitionWorks

I am an applied mathematician and qualified secondary teacher. I have done research in the field of nuclear energy and am currently studying toward a PhD with the University of Cranfield in aerospace materials.

Book Federico today →

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