WJEC A2 Unit 4 Applied Mathematics B: a complete overview of the A2 statistics, differential equations and mechanics

What Unit 4 actually demands

A2 Unit 4 Applied Mathematics B completes the applied strand, split into a Statistics section and a Differential Equations and Mechanics section. The statistics deepens the AS work into the Normal distribution and tests on correlation and means; the mechanics moves to calculus kinematics, projectiles and the equilibrium of rigid bodies. The differential-equations content sits across the boundary, applying the integration techniques of Unit 3 to real rates of change.

This guide walks through the six topics of the unit (three statistics, one differential equations, two mechanics), then sets out the exam structure. Each topic has a matching dot-point page with worked exam questions; this overview ties them together.

Statistics: conditional probability

The statistics section opens with conditional probability, the chance of one event given another has occurred, $P(A \mid B) = \dfrac{P(A \cap B)}{P(B)}$, the general multiplication rule, the test for independence, and reading conditional probabilities from two-way tables and tree diagrams.

Statistics: the Normal distribution

This topic introduces the Normal distribution $N(\mu, \sigma^2)$ for continuous data, standardising with $z = \dfrac{x - \mu}{\sigma}$, finding probabilities as areas, working backwards to an unknown mean or standard deviation, and the Normal approximation to the binomial.

Statistics: hypothesis testing for correlation and means

Hypothesis testing extends to two new contexts: testing a product moment correlation coefficient against a tabulated critical value, and testing the mean of a Normal distribution using the fact that the sample mean follows $N\!\left(\mu, \dfrac{\sigma^2}{n}\right)$.

Differential equations

This topic covers forming a first-order differential equation from a stated rate of change, solving it by separating the variables and integrating, finding a particular solution from a condition, and applications to exponential growth and decay, cooling and mechanics.

Mechanics: kinematics with calculus and projectiles

Mechanics moves to variable acceleration handled by calculus ($v = \dfrac{ds}{dt}$, $a = \dfrac{dv}{dt}$, and integration to reverse), vector kinematics, and projectile motion resolved into independent horizontal and vertical components linked by time.

Mechanics: forces, friction and moments

The unit closes with resolving forces on inclined planes, the friction model $F \le \mu R$, connected particles on slopes and over pulleys, and moments for the equilibrium of rigid bodies such as rods and beams, where the weight of a uniform body acts at its centre.

How Unit 4 is examined

WJEC Unit 4 Applied Mathematics B is a written paper of 1 hour 45 minutes carrying 80 marks, worth 25 per cent of the full A level. It is split into Section A Statistics (40 marks) and Section B Differential Equations and Mechanics (40 marks), a calculator is allowed, and time can be divided flexibly. Practise each section separately, then under timed conditions to balance the split.

The six topics, dot point by dot point

Each topic has a dot-point answer page with worked exam questions and cross-links. Browse them from this unit overview and the subject hub.

For the official specification

WJEC publishes the full specification, past papers and mark schemes at wjec.co.uk. Always revise from the current specification and WJEC's own past papers, because question style is board-specific.