Formulae to be learnt for A level Mathematics

Learners must be able to use the following formulae and identities for A level mathematics, without these formulae and identities being provided, either in these forms or in equivalent forms. These formulae and identities may only be provided where they are the starting point for a proof or as a result to be proved.

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Pure Mathematics

Quadratic Equations

Laws of Indices

Laws of Logarithms

for and

Coordinate Geometry

A straight line graph, gradient m passing through has equation:
Straight lines with gradients and are perpendicular when:

Sequences

General term of an arithmetic progression:
General term of a geometric progression:

Trigonometry

In the triangle ABC

Sine rule:
Cosine rule:
Area of the triangle:

Mensuration

Circumference and Area of circle, radius r and diameter d:
Pythagoras’ Theorem: In any right-angled triangle where a, b and c are the lengths of the sides and c is the hypotenuse:
Area of a trapezium, where a and b are the lengths of the parallel sides and h is their perpendicular separation:
Volume of a prism =	area of cross section × length
For a circle of radius r, where an angle at the centre of θ radians subtends an arc of length s and encloses an associated sector of area A:

Calculus and Differential Equations
Differentiation

Function	Derivative

Integration

Function	Integral
Area under a curve

Vectors

Mechanics

Forces and Equilibrium

Weight =
Friction
Newton’s second law in the form:

Kinematics

For motion in a straight line with variable acceleration:

Statistics

The mean of a set of data:
The standard Normal variable:	where