How is the CCEA A2 2 Applied Mathematics unit structured?

A2 2 Applied Mathematics is assessed by a written examination of 2 hours 15 minutes worth 150 raw marks, counting for 30 percent of the full A-Level. The paper is divided into four sections: Section A Mechanics 1, Section B Mechanics 2, Section C Statistics and Section D Discrete and Decision Mathematics. Students answer questions from two of the sections in permitted combinations, and each chosen section contributes 50 percent of the unit assessment.

Which sections can students choose in A2 2?

Students answer two of the four sections in permitted combinations: A and B, A and C, A and D, or C and D. This lets a centre pair the two mechanics sections, mechanics with statistics or with discrete, or statistics with discrete, but not every combination. Schools usually teach the two sections their students will sit, so check which combination your centre has chosen.

What does the mechanics content of A2 2 cover?

The mechanics sections extend the AS mechanics. Mechanics 1 covers further kinematics with variable acceleration handled by calculus, motion in two dimensions with vectors, and projectile motion with separate horizontal and vertical components. Mechanics 2 covers momentum and impulse, conservation of momentum and Newton's experimental law with the coefficient of restitution, and circular motion and simple harmonic motion with centripetal force, vertical circles and the SHM equations.

What does the statistics and discrete content of A2 2 cover?

The Statistics section covers the Poisson distribution as a model, the normal distribution with standardising, the Central Limit Theorem for the distribution of the sample mean, and hypothesis testing with null and alternative hypotheses, significance levels and conclusions. The Discrete and Decision Mathematics section covers graphs and networks, the minimum spanning tree by Kruskal's and Prim's algorithms, the shortest path by Dijkstra's algorithm, and sorting and route-inspection ideas.

How should I revise the CCEA A2 2 Applied unit?

Revise only the two sections your centre has chosen. For mechanics, drill variable-acceleration calculus, projectiles, momentum and restitution, circular motion and SHM. For statistics, practise Poisson and normal probabilities, the standard error from the Central Limit Theorem, and the full structure of a hypothesis test with a contextual conclusion. For discrete, practise running Kruskal's, Prim's and Dijkstra's algorithms step by step on a network and explaining each step in words.

Northern IrelandFurther Maths

CCEA A-Level Further Mathematics A2 2 Applied Mathematics: a complete overview

A deep-dive CCEA A2 Further Maths guide to the A2 2 Applied Mathematics unit and its four optional sections: further kinematics and projectiles, momentum, impulse and collisions, circular motion and SHM, hypothesis testing and further statistics, and discrete and decision mathematics, with the section-choice rules.

Generated by Claude Opus 4.817 min readCCEAUpdated 2026-06-16

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What this unit demands
Mechanics 1: further kinematics and projectiles
Mechanics 2: momentum, restitution, circular motion and SHM
Statistics: distributions and hypothesis testing
Discrete and decision mathematics
How this unit is examined
Check your knowledge

What this unit demands

A2 2 Applied Mathematics is the A2 applied unit, offered as four optional sections: Mechanics 1 (Section A), Mechanics 2 (Section B), Statistics (Section C) and Discrete and Decision Mathematics (Section D). Students answer two sections in permitted combinations (A and B, A and C, A and D, or C and D). CCEA tests confident modelling and complete, structured methods in whichever pair a centre has chosen.

This guide walks through the dot points for all four sections, then sets out the exam patterns CCEA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together. Revise only the two sections you will sit.

Mechanics 1: further kinematics and projectiles

When acceleration varies, use calculus: $v = \frac{ds}{dt}$ , $a = \frac{dv}{dt}$ , and integrate back with constants from the conditions. In two dimensions, position, velocity and acceleration are vectors. A projectile has constant horizontal velocity and vertical acceleration $-g$ ; apply suvat to each direction separately, linked by time.

Mechanics 2: momentum, restitution, circular motion and SHM

Momentum $m\mathbf{v}$ is conserved in collisions, and impulse is the change in momentum. Newton's experimental law gives separation $= e \times$ approach, with $e = 1$ elastic and $e = 0$ coalescing. Circular motion needs a centripetal force $\frac{mv^2}{r} = m\omega^2 r$ ; SHM satisfies $\ddot{x} = -\omega^2 x$ , with maximum speed $\omega A$ and period independent of amplitude.

Statistics: distributions and hypothesis testing

The Poisson $\text{Po}(\lambda)$ models random events at a constant rate (mean and variance both $\lambda$ ); the normal $N(\mu, \sigma^2)$ is standardised by $Z = \frac{X - \mu}{\sigma}$ . By the Central Limit Theorem, the sample mean is $\approx N(\mu, \frac{\sigma^2}{n})$ with standard error $\frac{\sigma}{\sqrt{n}}$ . A hypothesis test states $H_0$ and $H_1$ , fixes a significance level, computes a statistic, compares with the critical value and concludes in context.

Discrete and decision mathematics

A network is a weighted graph. A minimum spanning tree connects all vertices cheaply by Kruskal's (edge-based) or Prim's (vertex-based) algorithm. Dijkstra's algorithm finds the shortest path by making the smallest temporary label permanent and updating neighbours. Sorting and the route-inspection problem complete the toolkit.

How this unit is examined

A typical CCEA profile for A2 2 (in your chosen sections):

Mechanics 1. A variable-acceleration calculus problem and a projectile question.
Mechanics 2. A collision with restitution and a circular-motion or SHM problem.
Statistics. A Poisson or normal calculation and a full hypothesis test.
Discrete. Running Kruskal's, Prim's or Dijkstra's algorithm with explanation.

Check your knowledge

A mix of recall and technique questions across the sections. Attempt those for your chosen sections under timed conditions, then check against the solutions.

A particle has displacement $s = t^3 - t$ . Find its velocity at $t = 2$ . (2 marks)
A projectile is launched at $20\,\text{m s}^{-1}$ at $30^\circ$ . Find its initial vertical velocity component. (1 mark)
State the principle of conservation of momentum. (2 marks)
State the centripetal force formula in terms of $\omega$ . (1 mark)
For $X \sim \text{Po}(5)$ , write down the variance. (1 mark)
A sample of $36$ has population standard deviation $12$ . Find the standard error. (2 marks)
Which algorithm finds the shortest path between two vertices? (1 mark)

Solutions

Step 1: Differentiate displacement to find velocity

Velocity is the rate of change of displacement with respect to time, so $v = \frac{ds}{dt}$ . Differentiating $s = t^3 - t$ term by term and then substituting $t = 2$ gives the velocity at that instant.

v = \frac{ds}{dt} = 3t^2 - 1, \qquad v(2) = 3(4) - 1 = 11\,\text{m s}^{-1}

Final answer: $11\,\text{m s}^{-1}$

Step 2: Resolve the launch velocity into vertical component

A projectile's initial velocity has two independent components. The vertical component is found by multiplying the speed by the sine of the launch angle, since sine gives the side opposite the angle in the right triangle formed by the velocity vector.

v_{\text{vertical}} = 20\sin 30^\circ = 20 \times 0.5 = 10\,\text{m s}^{-1}

Final answer: $10\,\text{m s}^{-1}$

Step 3: State the principle of conservation of momentum

Conservation of momentum follows from Newton's third law: when two bodies interact, the forces they exert on each other are equal, opposite and act for the same time, so the impulses cancel and the total momentum is unchanged. It applies whenever no external force acts along the line of motion.

When no external force acts along the line of motion, the total momentum before equals the total momentum after.

Final answer: When no external force acts along the line of motion, the total momentum before equals the total momentum after.

Step 4: State the centripetal force formula in terms of angular velocity

A body moving in a circle of radius $r$ at angular velocity $\omega$ has linear speed $v = \omega r$ . Substituting into $F = \frac{mv^2}{r}$ gives the centripetal force in terms of $\omega$ , which is often more convenient when angular velocity is given directly.

F = m\omega^2 r

Final answer: $F = m\omega^2 r$

Step 5: Read off the variance of a Poisson distribution

For the Poisson distribution $\text{Po}(\lambda)$ a defining property is that the mean and variance are both equal to the rate parameter $\lambda$ . This is a fact to recall directly from the distribution's properties.

\text{Var}(X) = \lambda = 5

Final answer: $5$

Step 6: Calculate the standard error using the Central Limit Theorem

The Central Limit Theorem states that the sample mean of a sample of size $n$ drawn from a population with standard deviation $\sigma$ has standard error $\frac{\sigma}{\sqrt{n}}$ . Substituting $\sigma = 12$ and $n = 36$ gives the standard error directly.

\frac{\sigma}{\sqrt{n}} = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2

Final answer: $2$

Step 7: Identify the shortest-path algorithm

Dijkstra's algorithm processes a network by repeatedly making permanent the vertex with the smallest temporary label and updating the labels of its neighbours. This greedy approach guarantees that, once a vertex label is made permanent, it records the shortest distance from the source.

Final answer: Dijkstra's algorithm

Sources & how we know this

CCEA GCE Further Mathematics specification — CCEA (2018)