AQA A Level Maths June 2025 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. Coordinate geometry · 6 marks

   The circle $C$ has centre $(a, b)$ and passes through the points $P(0, 0)$, $Q(6, 0)$, and $R(0, 8)$. Find the values of $a$, $b$, and the radius of $C$.

   Worked answer

   $P$ and $Q$ both on circle ⇒ centre lies on the perpendicular bisector of $PQ$, so $a = 3$   M1 A1. Similarly $P$ and $R$ give $b = 4$   M1 A1. Radius $= |CP| = \sqrt{9 + 16} = 5$   M1 A1.

2. Sequences and series · 5 marks

   The second term of a geometric series is 12 and its sum to infinity is 64. Find the two possible values of the common ratio, $r$, and the corresponding values of the first term, $a$.

   Worked answer

   1. M1 for setting up the two equations: $ar = 12$ and $\frac{a}{1-r} = 64$.
   2. M1 for substituting $a = \frac{12}{r}$ to get $\frac{12/r}{1-r} = 64 \implies 12 = 64r(1-r)$.
   3. M1 for forming the quadratic $16r^2 - 16r + 3 = 0$.
   4. A1 for finding $r = 0.25$ and $r = 0.75$.
   5. A1 for finding the corresponding first terms: $a = 48$ and $a = 16$.

3. Sampling and data · 5 marks

   For a sample of $n=10$ observations, $\Sigma x = 120$ and $\Sigma x^2 = 1800$. A new variable $y$ is defined as $y = 3x - 2$. Calculate the mean and variance of $y$.

   Worked answer

   1. M1 for calculating $\bar{x} = \frac{120}{10} = 12$.
   2. M1 for finding $\bar{y} = 3(12) - 2 = 34$.
   3. M1 for calculating $Var(x) = \frac{1800}{10} - 12^2 = 180 - 144 = 36$.
   4. M1 for applying the variance transformation rule $Var(y) = 3^2 \times Var(x)$.
   5. A1 for finding $Var(y) = 9 \times 36 = 324$.

More on these topics: Coordinate geometry · Sequences and series · Sampling and data

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; "Show that" (Q11); Proof by contradiction (Q12). 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.