GCSE Maths Need to know formulas

We know that maths GCSE can be daunting – there’s always plenty to learn!

But Tavistock Tutors have compiled a list of some essential formulas that you’ll need to learn before your exams.

Do I need to learn formulae?

Since the GCSE Maths specifications changed in 2015, formula booklets are no longer provided for most maths GCSE examinations.

This means you’ll need to know the important formulas off by heart. There’s no point only loosely knowing them, as this may mean that you’ll get them wrong in your exam which could easily lose you some vital marks.

This applies to all examination boards whether you’re sitting your maths GCSE with AQA, Edexcel or a different exam board. And could appear in any of your maths exams, whether they require the use of a calculator or not.

Those students sitting the foundation exam will only have to learn some formulae listed, whereas higher students will be expected to learn all formulae. Formulae marked with an asterisk (*) are applicable to higher students only.

These formulas are essential to answering questions – so look out our compiled list and see our tips for remembering formulas below!


Working out areas of shapes

To work out the internal area of a shape, you will need to take into consideration the lengths of the sides of the shape. A = Area of the shape

Rectangle = A = length x width

Parallelogram = A = base x height

Triangle = A = ½ base x height

Trapezium = ½ (a+b)h


Circumference = x diameter

Circumference = 2 x x radius

Area of a circle = x radius squared, r²

Volume of Shapes

The volume of a shape is the total area of a 3D shape. This can often be worked out by working out the area of a 2D side and then multiplying that answer by the total length of the object.

Cuboid = length x width x height

Prism = area of cross section x length

Cylinder = r²h

*Pyramid = 1/3 x area of the base x height


Compound measures

Compound measures are a series of equations in which the different matters can be swapped around to produce multiple different answers.

Speed = distance/Time

Density = mass/Volume

Pressure = force/area


How do I know which part of the equation I need?

The best way to understand a compound measure is by visualising each compound in a different part of the below triangle. If you cover the one compound you wish to find out, you should be able to see which equation you need to do with the information provided in the exam.

For example: See below the speed, distance, time triangle used to visualise a compound measure.

If you want to find out the speed, then divide the distance by time.

If you want to find out the distance, then multiply the speed by time.

If you want to find out the time, then divide the distance by speed.



To find the length of one side of a right-angled triangle, use Pythagoras’ theorem:

a² + b² = c²

Trigonometric ratios (these are new to foundation exams)

This is how you can work out the internal angle of a triangle from the outside lengths

sin = opposite/hypotenuse

cos = adjacent

tan = opposite/adjacent

Quadratic Equations

*The solutions of ax² + bx + c = 0

*Where a isn’t 0, are given by


Trigonometric formulae

*Sine Rule a/Sin A = b/Sin B = c/Sin C

*Cosine Rule a² = b² + c² – 2bc cos A

*Area of triangle = ½ ab sin C


How do I remember these formulae?

Now that you’ve read through the different formulae that you are expected to learn for your maths exam, it’s time to start learning them!

If you have a photographic memory then you’re incredibly lucky, but if you’re looking for some inspiration on different ways to memorise the formulae for your exams, then have a read of our article ‘How to memorise formulae’!

Try and use as many different memorisation techniques as possible so that they really stick in your brain!


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Additional resources:

GCSE Maths Past Papers
How to Memorise Formulae: Maths and Science Exams
GCSE Maths

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