WJEC AS Unit 2 Applied Mathematics A: a complete overview of the statistics and mechanics sections

What Unit 2 actually demands

AS Unit 2 Applied Mathematics A is the applied half of the AS year, split into a Statistics section and a Mechanics section. Statistics rewards careful definitions and accurate calculator use with distributions; mechanics rewards clear force diagrams, a consistent sign convention, and fluent use of the constant-acceleration equations. The two sections are examined in one paper but cover quite different skills, so both need dedicated practice.

This guide walks through the six topics of the unit (four statistics, 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: sampling and data presentation

The statistics section opens with the difference between a population and a sample, the main sampling methods (simple random, systematic, stratified, quota, opportunity), and how to present and interpret data using measures of location (mean, median, mode), measures of spread (range, interquartile range, standard deviation), histograms (area equals frequency) and box plots.

Statistics: probability

Probability covers the probability of events, Venn diagrams and set notation, the addition rule $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, mutually exclusive and independent events (tested by $P(A \cap B) = P(A)P(B)$), and tree diagrams for sequences of events with and without replacement.

Statistics: the binomial distribution

This topic introduces discrete random variables and their probability distributions, the conditions for a binomial distribution $X \sim B(n, p)$ (fixed $n$, two outcomes, independence, constant $p$), and the calculation of binomial probabilities $P(X = r) = \binom{n}{r}p^r(1-p)^{n-r}$, including cumulative cases and the mean $np$.

Statistics: hypothesis testing

The statistics section closes with hypothesis testing using the binomial distribution: stating a null and alternative hypothesis, choosing a one-tailed or two-tailed test, working at a significance level, finding a critical region or comparing a tail probability, and writing a conclusion in context.

Mechanics: kinematics

The mechanics section opens with quantities and units (SI units, scalars and vectors), the definitions of displacement, velocity and acceleration, motion graphs (gradients and areas), and the constant-acceleration (suvat) equations, including vertical motion under gravity with $a = g \approx 9.8\,\text{m s}^{-2}$.

Mechanics: forces and Newton's laws

The unit closes with Newton's three laws, force diagrams, and the standard forces of weight ($W = mg$), normal reaction, tension and friction ($F \le \mu R$). You apply $F = ma$ to single bodies and to connected particles linked by a light string over a smooth pulley, solving the resulting equations simultaneously.

How Unit 2 is examined

WJEC Unit 2 Applied Mathematics A is a written paper of 1 hour 45 minutes carrying 75 marks, worth 15 per cent of the full A level. It is split into Section A Statistics (40 marks) and Section B Mechanics (35 marks), a calculator is allowed, and time can be divided flexibly between the sections. 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.