Edexcel A Level Maths June 2024 Paper 3: question paper and mark scheme (9MA0/31, 9MA0/32)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the Pearson Edexcel paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. 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 solution

   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: $\frac{225}{512}$.

2. Sampling and data · 4 marks

   A dataset $x$ has mean $\overline{x}=5$ and standard deviation ${\sigma }_x=2$. A new dataset $y$ is formed using the linear transformation $y=ax+b$, where $a>0$. The new dataset has mean $\overline{y}=15$ and standard deviation ${\sigma }_y=6$. Find the values of $a$ and $b$.

   Worked solution

   1. M1 for linking the standard deviations: ${\sigma }_y=a{\sigma }_x$.
   2. A1 for solving for $a$: $6=a(2)⟹a=3$.
   3. M1 for linking the means: $\overline{y}=a\overline{x}+b$.
   4. A1 for substituting $a=3$ to find $b$: $15=3(5)+b⟹b=0$.

3. Kinematics · 7 marks

   At time $t$ hours after 09:00, a boat $P$ has position vector $((1+2t)\mathbf{i}+(5-t)\mathbf{j})$ km relative to a fixed origin. A lighthouse $L$ is at the point with position vector $(8\mathbf{i}+7\mathbf{j})$ km.

   (a) Find $\overrightarrow{PL}$ in terms of $t$. [2]

   (b) Show that $P{L}^2=5t^2-24t+53$. [2]

   (c) Find the shortest distance between the boat and the lighthouse, and the time at which it occurs. [3]

   Worked solution

   (a) $\overrightarrow{PL}=(8\mathbf{i}+7\mathbf{j})-((1+2t)\mathbf{i}+(5-t)\mathbf{j})$ M1

   $(7-2t)\mathbf{i}+(2+t)\mathbf{j}$ A1

   (b) $P{L}^2=(7-2t{)}^2+(2+t{)}^2$ M1

   $=49-28t+4t^2+4+4t+t^2=5t^2-24t+53$ A1 (cso)

   (c) $5t^2-24t+53=5(t-2.4{)}^2+24.2$ (or any complete method for the minimum) M1

   $t=2.4$, i.e. 11:24 A1

   Shortest distance $\sqrt{24.2}=4.92$ km A1

More on these topics: Probability · Sampling and data · Kinematics

What this paper covers

What this paper is like

• Shape: 6 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 6 to 11 marks.
• Biggest question: Q1, 11 marks: binomial model for rolling sixes.
• Marks by main topic: Statistical distributions 21, Sampling and data 12, Probability 11, Hypothesis testing 6.
• More Statistical distributions in other sittings: June 2023 Q6 (14 marks), June 2025 Q6 (11 marks), June 2022 Q2 (12 marks).
• Against the other 6 sittings we mapped: more marks on Hypothesis testing (6 marks here, 1 on average).
• Coverage: every topic on the list came up.
• Calculator: allowed.

9MA0/31: question by question

Labels and topics are ours, read from the 9MA0/31 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Binomial model for rolling sixes (11 marks) · Statistical distributions
2. Q2Regression model of a bird's flight (6 marks) · Sampling and data
3. Q3Large data set: Perth summary statistics (6 marks) · Sampling and data
4. Q4Binomial test for left-handed adults (6 marks) · Hypothesis testing
5. Q5Normal model for high-jump heights (10 marks) · Statistical distributions
6. Q6Venn diagram with four events (11 marks) · Probability

What this paper is like

• Shape: 6 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 3 to 12 marks.
• Biggest question: Q5, 12 marks: stone projected from the ground.
• Marks by main topic: Kinematics 31, Forces and Newton's laws 10, Moments 9.
• More Kinematics in other sittings: June 2023 Q5 (11 marks), June 2025 Q4 (9 marks), June 2022 Q5 (12 marks).
• Against the other 6 sittings we mapped: a typical spread of marks, with no topic 4 or more marks away from its average.
• Coverage: every topic on the list came up.
• Calculator: allowed.

9MA0/32: question by question

Labels and topics are ours, read from the 9MA0/32 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Particle on a rough horizontal plane (3 marks) · Forces and Newton's laws
2. Q2Speed-time graph of a 200 m race (8 marks) · Kinematics
3. Q3Particle held on a rough inclined plane (7 marks) · Forces and Newton's laws
4. Q4Motion with i vectors and calculus (11 marks) · Kinematics
5. Q5Stone projected from the ground (12 marks) · Kinematics
6. Q6Uniform rod resting on a peg (9 marks) · Moments, Forces and Newton's laws

Some Paper 3 statistics questions use Edexcel's large data set (weather data). 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).

• 9MA0/31: Premature rounding and truncating (Q2, Q3, Q4); Binomial probabilities (Q1, Q4); Normal distribution (Q5). Official examiner report ↗
• 9MA0/32: "Show that" (Q3); Mechanics; Moments (Q6). Official examiner report ↗

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