AQA A Level Maths June 2024 Paper 3: question paper and mark scheme (7357/3)

Try 3 A Level questions like these

Written and checked by us, not taken from the AQA paper. Tap "Worked answer" to see every step.

1. Trigonometry · 6 marks

   Solve the equation \(\cos 2x = \sin x\) for \(-\pi \le x \le \pi\). Give your answers as exact radian values.

   Worked answer

   Substitute the double angle identity \(\cos 2x = 1 - 2\sin^2 x\). M1
   \(1 - 2\sin^2 x = \sin x \implies 2\sin^2 x + \sin x - 1 = 0\). A1
   Factorise the quadratic: \((2\sin x - 1)(\sin x + 1) = 0\). M1A1
   Case 1: \(2\sin x - 1 = 0 \implies \sin x = \frac{1}{2}\).
   Within the domain \(-\pi \le x \le \pi\), solutions are \(x = \frac{\pi}{6}\) and \(x = \frac{5\pi}{6}\). A1
   Case 2: \(\sin x + 1 = 0 \implies \sin x = -1\).
   Within the domain \(-\pi \le x \le \pi\), the solution is \(x = -\frac{\pi}{2}\). A1

2. Differentiation · 4 marks

   Find the set of values of $x$ for which $f(x) = x^4 - 8x^2$ is an increasing function.

   Worked answer

   1. M1 for finding the derivative $f'(x) = 4x^3 - 16x$.
   2. M1 for setting $f'(x) > 0$ and factorising: $4x(x^2 - 4) > 0 \implies 4x(x-2)(x+2) > 0$.
   3. M1 for finding the critical values $x = -2, 0, 2$ and testing regions.
   4. A1 for stating the correct range: $-2 < x < 0$ or $x > 2$.

3. Probability · 3 marks

   A bag contains 5 green counters and 3 yellow counters. A counter is drawn at random, its colour is noted, and it is replaced. This is done 3 times in total. Find the probability that exactly 2 green counters are drawn.

   Worked answer

   1. M1 for identifying the 3 ways to draw exactly 2 green counters: GGY, GYG, YGG.
   2. M1 for calculating the probability of one such arrangement, e.g., $(\frac{5}{8}) \times (\frac{5}{8}) \times (\frac{3}{8}) = \frac{75}{512}$.
   3. A1 for multiplying by 3 to find the total probability: $\frac{225}{512}$.

More on these topics: Trigonometry · Differentiation · Probability

What this paper covers

Section A is pure mathematics; Section B is statistics (AQA sections K to O), including questions on AQA's large data set.

We haven't mapped this paper question by question yet, so these are the topics it can test, from the specification's paper structure. Each links to a page where you can learn the topic and then practise questions on it.

Pure

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Statistics

• Sampling and data
• Probability
• Statistical distributions
• Hypothesis testing

Practise these topics (opens the practice engine)

• Pure I
• Pure II
• Pure III (calculus)
• Statistics

Some Paper 3 statistics questions use AQA's large data set. We don't write large data set questions, so use your class materials for those.

What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• 7357/3: "Explain" and "interpret" answers without context (Q14); "Show that" (Q5); Conditional probability (Q18). Official examiner report ↗

Question-by-question topics, the top mistakes and what to focus on next →

Formula booklet

Formulae for A-level Mathematics · AQA · Version 1.2 (first issued August 2017), for 7356 / 7357 (current)

Checked against AQA’s own booklet on 11 October 2026.