FormulaeGCSE Mathematics

1 Know these…The following formulae are included in the subject content.

Candidates are expected to know these formulae; they will not be given in the examination.

The quadratic formula

The solutions of 𝑎𝑥2+ + = 0 where ≠0 𝑏𝑥 𝑐 𝑎

Circumference and area of a circle

Where r is the radius andd is the diameter:

Circumference of a circle = 2 = 𝜋𝑟 𝜋𝑑

Area of a circle= 𝜋𝑟2

Pythagoras’s theorem

In any right-angled triangle where a, b and c are the length of the sides and c is the hypotenuse:

a2 + b2 = c2

In any right-angled triangle ABC where a, b and c are the length of the sides and c is the hypotenuse:

Trigonometry formulae

In any triangle ABC where a, b and c are the length of the sides

Trigonometry formulae

Trigonometry formulae

In any triangle ABC where a, b and c are the length of the sides

Trigonometry formulae

In any triangle ABC where a, b and c are the length of the sides

2 Understand these…The following formulae are not specified in the content but should be derived or informally understood by candidates.

These formulae will not be given in the examination.

Perimeter, area, surface area and volume formulae

Area of a trapezium =

Volume of a prism = area of cross section × length

Compound interest

Where P is the principal amount, r is the interest rate over a given period and n is number of times that the interest is compounded:

Probability

Where P(A) is the probability of outcome A and P(B) is the probability of outcome B:

𝑃( ) = ( ) + ( ) − ( 𝐴 𝑜𝑟 𝐵 𝑃 𝐴 𝑃 𝐵 𝑃 𝐴 ) 𝑎𝑛𝑑 𝐵

𝑃( ) = ( ) ( ) 𝐴 𝑎𝑛𝑑 𝐵 𝑃 𝐴 𝑔𝑖𝑣𝑒𝑛 𝐵 𝑃 𝐵

3 Use these…Candidates should be able to use the following formulae, but need not memorise them. These may be given in the exam, either in the relevant question, or in a list from which candidates select and apply as appropriate.

Perimeter, area, surface area and volume formulae

Information from the DfE has been used in accordance with the terms of the Open Government Licence

Kinematics formulae Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the positionwhen t = 0 and t is time taken:

CalculatorsThere are several specialist calculators available online including calculators for the various formulae required for GCSE.

For a collection of these see Calculators on Mathematics for Students.

Colleen Young