Everything you need to memorise for Edexcel A Level Maths Pure

Index Laws

laws used in algebra involving numbers and letters to a power (index)

log laws

Factor Theorem

A polynomial f(x) has a factor x - k if and only if f(k) = 0

Inequalities

Algebraic statements that have ≠, <, >, ≤, or ≥ as their symbols of comparison.

Partial Fractions

Two or more fractions that add or subtract to result in a given rational expression.

Triangle Geometry

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

Circle theorems

Functions

Simple linear equation rules

Reciprocal graphs

y=1/x

Equation of a circle

(x-h)²+(y-k)²=r²

Trig graphs

F(x) transformations

Vector Laws

binomial expansion

Arithmetic Series Formula

Sn=n/2(a1+an) or Sn=n/2(2a1+(n-1)d)

Geometric Series

Other series sequences

Radians conversions

small angle approximation

Exact Trig Values

tangent definition

Solving trig equations

Trig Functions

Pythagorean Identities

sin²∅ + cos²∅ = 1

tan²∅ + 1 = sec²∅

cot²∅ + 1 = cosec²∅

addition formula

Double Angle Formulas

sin(2x)=2sin(x)cos(x)

cos(2x)=cos^2-sin^2

=1-2sin^2

=2cos^2-1

tan(2x)=2tanx/1-tan^2

Rearranged double angle formula

Harmonic identity

Differentiation by first principles

First derivatives

Second derivatives

you differentiate then differentiate again.

Denoted by d^2y/dx^2 or f''(x).

pronounced: dee two y dee x squared.

Functions and their derivatives

Reciprocal derivative

Parametric Differentiation

(dy/dt)/(dx/dt)

Connected rates of change

Numerical methods- roots

staircase/cobweb diagrams

Newton Raphson formula

Xn+1 = Xn - f(Xn)/f'(Xn)

Integrals of functions

Reverse chain rule

Integration by substitution

Like in chain rule of derivatives, using "u" finding "du", spotting it in the integral, replacing it and solving. After taking the integral, re-substitute "u"

Integration by parts

∫ u dv = uv - ∫ v du

Parametric integration

Trapezium rule

AREA = 0.5(Width of strips)(FirstHeight + 2(Σ Middle Heights) + FinalHeight)