Mathematics

Mathematics

Pure mathematics, mechanics, and statistics for A Level

Resources›A Level›Mathematics

Pure

12 topics

Proof

AS

Proof by deduction, exhaustion, contradiction, and counter-example

proofdeductioncontradiction+1

Algebra and Functions

AS

Indices, surds, quadratics, inequalities, graphs, transformations

algebrafunctionsgraphs+1

Coordinate Geometry

AS

Straight lines, circles, parametric equations

coordinate geometrystraight linescircles+1

Sequences and Series

AS

Binomial expansion, arithmetic and geometric sequences

sequencesseriesbinomial+2

Trigonometry

AS

Trigonometric functions, identities, equations, small angle approximations

trigonometryidentitiesequations+1

Exponentials and Logarithms

AS

Laws of logarithms, exponential functions, natural logarithms

exponentialslogarithmse+1

Calculus

AS

Differentiation (first principles, chain rule, product rule, quotient rule) and integration (standard integrals, substitution, by parts)

calculusdifferentiationintegration+9

Numerical Methods

A2

Location of roots, iteration, Newton-Raphson method

numerical methodsiterationNewton-Raphson+1

Vectors

AS

3D vectors, scalar product, vector equations of lines

vectorsscalar product3D+1

Advanced Algebra and Functions

A2

Partial fractions, functions, modulus function, composite and inverse functions

partial fractionsmoduluscomposite functions+1

Further Calculus

A2

Parametric differentiation, implicit differentiation, differential equations

parametricimplicitdifferential equations+1

Further Trigonometry

A2

Compound angles, double angle formulae, R sin(x + α) form

compound anglesdouble angleharmonic form+1

Mechanics

6 topics

Kinematics

AS

Motion in straight line, SUVAT equations, velocity-time graphs

kinematicsSUVATmotion+1

Forces and Newton's Laws

AS

Force diagrams, equilibrium, Newton's laws, connected particles

forcesNewton's lawsequilibrium+1

Moments

A2

Moments about a point, equilibrium of rigid bodies

momentsequilibriumrigid bodies+1

Kinematics in 2D

A2

Projectile motion, motion in two dimensions with constant acceleration

projectiles2D motiontrajectories+1

Variable Acceleration

A2

Motion with variable acceleration using calculus

variable accelerationcalculusvelocity+1

Energy, Work and Power

A2

Work done, kinetic and potential energy, power, conservation of energy

workenergypower+1

Statistics

8 topics

Statistical Sampling

AS

Populations, samples, sampling techniques

samplingpopulationsample+1

Data Presentation and Interpretation

AS

Histograms, cumulative frequency, box plots, outliers

histogramsbox plotsoutliers+1

Probability

AS

Conditional probability, independent events, tree diagrams

probabilityconditionalindependent+1

Statistical Distributions

AS

Binomial distribution, normal distribution, hypothesis testing

binomialnormal distributionhypothesis testing+1

Statistical Hypothesis Testing

A2

One and two-tailed tests, critical values, Type I and II errors

hypothesis testingcritical valuesType I error+1

Correlation and Regression

A2

Scatter diagrams, correlation, linear regression

correlationregressionPMCC+1

Conditional Probability

A2

Conditional probability formulae, probability distributions

conditional probabilityBayes theoremprobability distributions

The Normal Distribution

A2

Properties, standardising, inverse normal, approximations

normal distributionstandardisingz-scores+1