We know that maths GCSE can be daunting â thereâs always plenty to learn!

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

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

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

This applies to all examination boards whether youâre 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 â so look out our compiled list and see our tips for remembering formulas below!

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 = Â˝ base x height

Trapezium = Â˝ (a+b)h

Circles

Circumference = x diameter

Circumference = 2 x x radius

Area of a circle = x radius squared, rÂ˛

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 = rÂ˛h

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

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

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 Pythagorasâ theorem:

aÂ˛ + bÂ˛ = cÂ˛

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

hypotenuse

tan = opposite/adjacent

Quadratic Equations

*The solutions of axÂ˛ + bx + c = 0

*Where a isnât 0, are given by

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

*Cosine Rule aÂ˛ = bÂ˛ + cÂ˛ â 2bc cos A

*Area of triangle = Â˝ ab sin C

Now that youâve read through the different formulae that you are expected to learn for your maths exam, itâs time to start learning them!

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

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

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