What does the CCEA A2 2 Applied Mathematics unit cover?

A2 2 is the applied half of the A2 year, split equally between mechanics and statistics. The mechanics content covers projectile motion in two dimensions and motion with variable acceleration using calculus, and forces, friction and moments including motion on an inclined plane and the equilibrium of a rigid body. The statistics content covers conditional probability and independence, the normal distribution with standardising and the normal approximation to the binomial, and hypothesis testing.

How is the CCEA A2 2 Applied Mathematics unit assessed?

Unit A2 2 is assessed by a written examination, typically of 1 hour 30 minutes worth 100 raw marks. The paper has two sections, with Section A assessing mechanics and Section B assessing statistics, each carrying 50 percent of the unit. It assumes the content of AS 1, AS 2 and A2 1. A calculator is allowed and a formulae and statistical tables booklet is provided.

What is the difference between a one-tailed and a two-tailed hypothesis test?

A one-tailed test has an alternative hypothesis in a single direction, such as the probability being greater than a stated value, and places the whole significance level in one tail. A two-tailed test has an alternative hypothesis that the value has simply changed in either direction, and splits the significance level into two equal tails, so a 5 percent test uses 2.5 percent in each tail.

What is the most common mistake in A2 2?

In mechanics, the common errors are mixing the horizontal and vertical motions of a projectile, using the constant-acceleration equations when acceleration varies, and swapping sine and cosine on an inclined plane. In statistics, the frequent slips are confusing the two directions of a conditional probability, forgetting that standardising uses the standard deviation not the variance, and comparing a two-tailed tail probability with the full significance level instead of half.

How should I revise the A2 2 Applied Mathematics unit?

Revise the two halves to equal depth, because the paper splits the marks evenly. For mechanics, drill projectile problems by resolving into components, variable-acceleration problems using differentiation and integration, and friction and moment problems with clear diagrams. For statistics, practise conditional probability from tables and trees, standardising for normal probabilities and inverse-normal values, and the full structure of a binomial hypothesis test with a conclusion in context.

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CCEA A-Level Mathematics A2 2 Applied Mathematics: a complete overview of advanced mechanics and statistics

A deep-dive CCEA A-Level Mathematics guide to the A2 2 Applied Mathematics unit. Covers the mechanics half - projectiles and variable acceleration, and forces, friction and moments - and the statistics half - conditional probability, the normal distribution and hypothesis testing, with the methods CCEA examines in Sections A and B.

Generated by Claude Opus 4.818 min readCCEAUpdated 2026-06-16

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

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What this unit demands
Mechanics: projectiles, variable acceleration, friction and moments
Statistics: conditional probability, the normal distribution and testing
How this unit is examined
Check your knowledge

What this unit demands

A2 2 Applied Mathematics is the applied half of the second year, weighted equally between mechanics and statistics. It deepens the AS 2 applied content: mechanics gains projectiles, variable acceleration and rigid-body work with friction and moments; statistics gains conditional probability, the normal distribution and formal hypothesis testing. The paper splits into Section A (mechanics) and Section B (statistics), so fluency across both is essential.

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: projectiles, variable acceleration, friction and moments

The mechanics half covers projectiles and variable acceleration: resolving projectile motion into independent horizontal and vertical components, finding the time of flight, range and maximum height, and using calculus ( $v = \frac{ds}{dt}$ , $a = \frac{dv}{dt}$ , and their integrals) when acceleration varies. It continues with forces, friction and moments: resolving forces, the friction model $F \le \mu R$ , motion and equilibrium on an inclined plane, and the moment of a force with the two conditions for the equilibrium of a rigid body.

Statistics: conditional probability, the normal distribution and testing

The statistics half covers conditional probability: the formula $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ , the general multiplication rule, the independence test, and tree diagrams and two-way tables. The normal distribution introduces $N(\mu, \sigma^2)$ , standardising to $Z$ , finding probabilities and inverse-normal values, and the normal approximation to the binomial. Hypothesis testing sets up null and alternative hypotheses, the significance level and critical region, one- and two-tailed tests, and the binomial hypothesis test.

How this unit is examined

A typical CCEA profile for A2 2:

Mechanics calculation. Projectile range and flight time, variable-acceleration calculus, and friction or moment problems.
Mechanics modelling. Inclined-plane diagrams and rigid-body equilibrium.
Statistics calculation. Conditional probabilities, normal probabilities and inverse-normal values.
Statistics reasoning. A full binomial hypothesis test with a conclusion in context.

Check your knowledge

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

A projectile is launched at $25\,\text{m s}^{-1}$ at $40^\circ$ . Find the horizontal component of velocity. (2 marks)
A particle has velocity $v = 4t - t^2$ . Find its acceleration when $t = 3$ . (2 marks)
A block on a $25^\circ$ slope weighs $80\,\text{N}$ . Find the component of weight down the slope. (2 marks)
State the two conditions for the equilibrium of a rigid body. (2 marks)
Given $P(A \cap B) = 0.15$ and $P(B) = 0.5$ , find $P(A \mid B)$ . (2 marks)
For $X \sim N(100, 15^2)$ , find the $z$ -value of $X = 130$ . (2 marks)
State the mean and variance of the normal approximation to $B(200, 0.5)$ . (2 marks)
Write suitable hypotheses to test whether a coin is biased towards tails. (2 marks)

Solutions

Step 1: Resolve the velocity into its horizontal component

A velocity at an angle can be split into independent horizontal and vertical parts using trigonometry. The horizontal component is found by multiplying the speed by the cosine of the launch angle, because cosine gives the adjacent side of the right-angled triangle.

\text{Horizontal component} = 25\cos 40^\circ = 25 \times 0.766 = 19.2\,\text{m s}^{-1}

Final answer: $19.2\,\text{m s}^{-1}$

Step 2: Find acceleration by differentiating the velocity function

Acceleration is the rate of change of velocity with respect to time, so differentiating $v$ with respect to $t$ gives $a$ . Substitute the given value of $t$ after differentiating.

a = \frac{dv}{dt} = 4 - 2t

At $t = 3$ :

a = 4 - 6 = -2\,\text{m s}^{-2}

Final answer: $-2\,\text{m s}^{-2}$

Step 3: Resolve the weight along the slope

The weight of the block acts vertically, but only the component parallel to the slope drives motion along it. That component is found by multiplying the weight by the sine of the angle of inclination.

\text{Component down the slope} = 80\sin 25^\circ = 80 \times 0.4226 = 33.8\,\text{N}

Final answer: $33.8\,\text{N}$

Step 4: State the two equilibrium conditions for a rigid body

A rigid body is in equilibrium when there is no tendency either to translate or to rotate. Two independent vector conditions capture this completely: one for forces and one for moments.

The resultant force is zero (in two directions) and the resultant moment about any point is zero.

Final answer: Resultant force = 0 in every direction; resultant moment about any point = 0.

Step 5: Apply the conditional probability formula

Conditional probability $P(A \mid B)$ gives the probability of $A$ given that $B$ has already occurred. It is calculated by dividing the probability of both events happening together by the probability of the conditioning event.

P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{0.15}{0.5} = 0.3

Final answer: $P(A \mid B) = 0.3$

Step 6: Standardise to find the z-value

To use the standard normal distribution, convert the observed value to a $z$ -score by subtracting the mean and dividing by the standard deviation. This tells you how many standard deviations the value lies from the mean.

z = \frac{130 - 100}{15} = 2

Final answer: $z = 2$

Step 7: State the mean and variance of the normal approximation

When $n$ is large and $p$ is not too close to 0 or 1, the binomial distribution $B(n,p)$ is approximated by a normal distribution with mean $np$ and variance $np(1-p)$ . Substituting $n = 200$ and $p = 0.5$ gives these values directly.

\text{Mean} = np = 200 \times 0.5 = 100, \quad \text{Variance} = np(1 - p) = 200 \times 0.5 \times 0.5 = 50

Final answer: Mean $= 100$ , variance $= 50$ .

Step 8: Write hypotheses to test for bias towards tails

In a hypothesis test the null hypothesis $H_0$ states no effect (a fair coin), while the alternative hypothesis $H_1$ states the direction of the suspected bias. Since we suspect bias towards tails, the test is one-tailed with $H_1$ asserting $p > 0.5$ .

H_0: p = 0.5 \quad \text{versus} \quad H_1: p > 0.5

where $p$ is the probability of tails (a one-tailed test).

Final answer: $H_0: p = 0.5$ ; $H_1: p > 0.5$ (one-tailed).

Sources & how we know this

CCEA GCE Mathematics specification — CCEA (2018)