CCEA A-Level Mathematics AS 2 Applied Mathematics: a complete overview of mechanics and statistics

What this unit demands

AS 2 Applied Mathematics applies the pure techniques of AS 1 to two real-world fields, mechanics and statistics, weighted equally. The examiners test modelling (turning a physical or data situation into mathematics), accurate calculation, and clear interpretation. The paper is split into Section A (mechanics) and Section B (statistics), so you must be confident in both.

This guide walks through the six dot points of the unit, then sets out the exam patterns CCEA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Mechanics: kinematics and forces

The mechanics half opens with kinematics: displacement, velocity and acceleration in a straight line, the four equations of motion for constant acceleration, motion under gravity with a consistent sign convention, and reading displacement-time and velocity-time graphs (gradient and area). It continues with forces and Newton's laws: forces as vectors, the modelling assumptions (particle, light, inextensible, smooth), the three laws, $F = ma$, the common forces (weight, normal reaction, tension), and connected particles over a smooth pulley.

Statistics: sampling, data and probability

The statistics half begins with statistical sampling: populations, samples and the census, the sampling frame, and the methods (random, systematic, stratified, quota, opportunity) with their trade-offs. Data presentation and interpretation covers the mean, median, mode, the range, interquartile range and standard deviation, histograms (area equals frequency) and box plots, and identifying outliers. Probability covers the addition and multiplication rules, mutually exclusive and independent events, complements, and Venn and tree diagrams. Statistical distributions introduces discrete random variables and the binomial distribution $B(n, p)$ with mean $np$.

How this unit is examined

A typical CCEA profile for AS 2:

• Mechanics calculation. Suvat problems, motion under gravity, and connected-particle systems with $F = ma$.
• Mechanics interpretation. Velocity-time graphs and force diagrams.
• Statistics calculation. Mean and standard deviation, stratified sample sizes, and binomial probabilities.
• Statistics interpretation. Histograms, box-plot comparisons, outliers, and probability via Venn and tree diagrams.

Check your knowledge

A mix of recall and calculation questions covering the unit. Attempt them under timed conditions, then check against the solutions.

1. A car accelerates from rest at $3\,\text{m s}^{-2}$ for $4\,\text{s}$. Find its final speed. (2 marks)
2. State Newton's second law as an equation. (1 mark)
3. A $2\,\text{kg}$ mass hangs from a string. Find the tension when it is in equilibrium. Take $g = 9.8\,\text{m s}^{-2}$. (2 marks)
4. Define stratified sampling. (2 marks)
5. For data with $\sum x = 100$, $\sum x^2 = 1100$ and $n = 10$, find the standard deviation. (3 marks)
6. Events $A$ and $B$ are independent with $P(A) = 0.5$ and $P(B) = 0.4$. Find $P(A \cap B)$. (2 marks)
7. State the four conditions for a binomial distribution. (2 marks)
8. For $X \sim B(20, 0.3)$, find the mean. (1 mark)