Pure Edexcel a level maths

Laws of indices

Manipulating surds

Rationalising denominators

Quadratic formula

Completing the square

Name of inputs and outputs for a function

Inputs = domain

Outputs = range

Turning point coordinates from completing the square

Discriminant - how many roots?

Number line circle notation

Regions line notation

Reciprocal graphs

Translating graphs

Gradient formula

Equation of a straight line

Gradient of parallel lines vs perpendicular lines

Parallel = the same

Perpendicular = m and -1/m

Distance between two points on a line

Modelling with straight lines - proportionality

Two quantities are in direct proportion when they increase at the same rate. The grapg of the quantites is a straight line through the origin

Midpoint of a line segment

Perpendicular bisector

Perpenmdicular to AB and passes through the midpoint of AB

Equation of a circle with centre (a,b) and radius r

Perpendicular bisector of a chord

Always goes through the centre of the circle

Triangles in a circle

Factor theorem

Proof by deduction

Starting from knwon facts or defenitions, then using logical steps to reach the desired conclusion

Proof by exhaustion

Breaking the statement into smaller cases and proving each case seperately

Proof by counter-example

Using an example that does not work for the statement (just one example is adequate)

General term for the expansion of (a + b)^n

Cosine rule (when you have 2 sides and the angle between them)

Cosine rule (when you know all 3 sides)

Sine rule

(Can also be used the other way round i.e. sinA/a = sinB/b etc)

Area of a triangle (using sine)

Area of a triangle

1/2 x base x height

Graph of y = sinθ

Graph of y = cosθ

Graph of y = tanθ

When the sine rule produces two possible solutions for a missing angle

Sinθ/ cosθ = ?

Tanθ

Sin (squared)θ + cos (squared)θ = ?

1

If PQ = RS (vectors)

The line segments are equal in length and are parallel

Multiplying and adding column vectors

Two dimensional vectors

Magnitude of a vector

Unit vector

Position vectors

If a and b are two non-parallel vectors and pa + qb = ra + sb

P = r, q = s

Gradient of a curve at any given point is the equivalent to...

The gradient of the tangent

Basic differentiation formula

Tangent to the curve y = f(x) at point (a,f(a))

Normal to the curve y = f(x) at point (a,f(a))

The function f(x) is decreasing/ increasing when...

Decreasing = f'(x) < 0 (less than or equal to 0)

Increasing = f'(x) > 0 (larger than or equal to 0)

Second order derivative notation

Identifying types of stationary points

If a function f(x) has a stationary point when x = a, then...

If f''(a) > 0, the point is a local minimum

If f''(a) < 0, the point is a local maximum

If f''(a) = 0, the point could be a local min or local max or point of inflection - need to do other method

Sketching gradient functions

General integration formula

Definite integration

When the area bounded by a curve and the x-axis is below the x-axis

Integrated answer gived a negaitve answer - state the area as a positive quanity

f(x) = a^x

Exponential function

Exponential and logarithmic graphs

Exponential growth and decay

If f(x) = e^x / if f(x) = e^kx

Logarithm general formula

Laws of logarithms

Graph of y = Inx and y = e^x

Proof by contradiction

Start by assuming the statement is not true

Rational number can be written as

A/b where a and b are integers

Mapping of a function

A mapping is a function if every input has a distinct output. Functions can either be one to one, or one to many

Inverse functions

Sketching y = If(x)I and y = f(IxI)

Nth term arithmetic sequence

Un = a + (n-1)d

Sum of n terms arithmetic (one that isnt given)

Sn = n/2 (a+l)

Nth term geometric sequence

A sequence is periodic when

Un+k = Un

1 radian =

180/π degrees

The expansion of (1+bx)^n is valid when...

The expansion of (a+bx)^n is valid when...

π radians =

180°

Arc length

L = rθ

Area of a sector

A = 1/2r^2θ

Area of a segment in a circle

A = (1/2)r²(θ - sinθ)

(θ given in radians)

Sec x

1/cos x

Cosec x

1/sin x

Cot x

1/tan x or cos x/ sin x

Sec graph

1 + tan^2x

sec^2x

Cosec graph

Sin 2A

2sinAcosA

Cot graph

Arcsin x

Tan 2A

(2 tan A) / (1 - tan² A)

Cos 2A

cos^2 A - sin^2 A // 2cos^2 A - 1 // 1 - 2sin^2 A

Arccos x

Arctan x

Differentiate sin x // sinkx

Cos x // k coskx

Differentiate cos x // coskx

- sin x // -k sinkx

Differentiate e^kx

Ke^kx

Simplifying asin x +/- bcos x

Differentiate In x

1/ x

Differentiate a ^kx

A^(kx) x k In a

Dy/ dx can be written as

1 / (dx/dy)