Maths made easy - Your pathway to success

A

Algebra

factorising expanding one or more brackets

Algebraic

Area

between a curve and the x-axis between a curve and the y-axis between a parametric curve sector segment triangle Argand diagram Arithmetic Progression (Series)

Asymptotes

horizontal and vertical

B

Binomial Expansion rational powers validity

Brackets

expanding

C

Cast Diagram Chain rule Change of sign Circle equation Cofactor, matrix Completing the square Complex Numbers argument Argand diagram equations locus modulus Composite functions Compound angles Compound interest Connected rates of change Cosecant Cosine Rule Cotangent

Cubic

graphs Curve, gradient

Curve Sketching

cubic graphs quadratic graphs reciprocal graphs

D

Definite integrals De Moivre's Theorem Derivative, second order Determinant of a matrix Difference of two Squares

Differential

second

Differential equations

first order separable type forming separable Differentiation chain rule connected rates of change product rule quotient rule reciprocal function

Differentiation of

axn exponential functions ax exponential functions ex implicit functions log functions sec(x), cosec(x), cot(x)trigonometric functions Discriminant

Distance

between points

Division

algebraic algebraic long division Double-angle formula Domain

E

ex

Equations

complex numbers linear equations simultaneous equations quadratic equations

Even functions

Expanding

brackets

Exponential

differential: See differentiation of

functions and graphs

integration: See Integrals of the form

Exponents

F

Factorising (Factoring)difference of two squares grouping quadratics Factor theorem

Fractions

partial simplifying algebraic

Functions

composite domain increasing, decreasing inverse modulus notation range

G

Geometric Progression (series)

Gradient of

curve parallel lines perpendicular lines straight lines (line segment)

Graphs

cubic quadratic reciprocal transformations

H

Half-angle formulae Harmonic identities

I

Identity

identity or equation – what's the difference?Imaginary numbers

Implicit functions

differentiation Indices

Inequalities

double linear modulus quadratic

Integral

definite

Integrals of the form

axn (ax + b)n exponential: ex, eax and e(ax+b)f '(x) / f(x)f '(x) ef(x)f [g(x)] g '(x)reciprocal: 1/x and 1/(ax + b)trigonometric functions

Integration

by parts change of variable definite equation of a curve given dy/dx general methods partial fractions type substitution

Integration – applications

area bounded by a curve and x-axis area between a curve and the y-axis area between a parametric curve

Inverse

function trigonometric functions

Iteration

iteration – fixed point Newton-Raphson

L

Linear transformations, matrices

Line

equation of gradient of mid-point Locus – complex plane Logarithms change of base

differential – see differentiation of

rules simplifying and expanding simultaneous equations

Long Division

algebraic

M

Matrices addition and subtraction cofactor determinant 3×3 inverse linear transformations minors multiplication transpose

Maximum and minimum – see stationary points

Mid-point of a line Modelling curves Modulus Functions

N

Newton-Raphson

Normal

to a curve to parametric curves

Numerical methods for equations

change of sign graphical iteration Newton-Raphson

Numerical methods for integration

trapezium rule

P

Parametric

differentiation equations tangents and normals Polynomials roots and coefficients Product rule Prime factorisation

Proof

counter example exhaustion identities Pythagorean identities / equations Pythagoras' theorem

Q

Quadrant Rule

Quadratic Equations – solution by:-

completing the square discriminant factorising formula sum and product of roots

Quadratic Expressions

completing the square factorising

Quadratic Graphs

sketching Quotient rule

R

Radians Range

Rationalising

surds

Reciprocal

function of dy/dx graphs

Reflection – see transformations

Roots

discriminant – quadratic equations

Rotation – see transformations

S

Secant Sector – area Segment – area

Sequences

recurrence relationships nth term Sequences and Series

Series

arithmetic binomial geometric sum of – sigma notation

Simultaneous Equations

elimination method substitution method Sine rule Small angles Stationary points

Stretch – see transformations

Surds

T

Tangent

to a circle to a curve to a parametric curve t-substitution Terms

Transformations

graphs

Translation see transformations

Trapezium rule

Trigonometric identities / equations

basic Pythagorean compound angles double angles half angles triple angles harmonic

Trigonometric functions

differential – see differentiation of

integration – see integrals of the form

inverse (arcsin, arccos, arctan)small angles Trigonometric ratios Trigonometry applications cosine rule graphs and transformations right angled triangles sine rule

V

Vectors addition equal magnitude multiplication by a scalar notation position unit

Maths Index

A

B

C

D

E

F

G

H

I

L

M

N

P

Q

R

S

T

V