Edexcel A Level Maths June 2022 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 · 5 marks

   A histogram is drawn. The class $0\le x<20$ has frequency $10$, and the class $20\le x<30$ has frequency $30$. If the height of the bar for the first class is $2\text{ cm}$, find the height of the bar for the second class, assuming the width of the bars is proportional to the class width.

   Worked solution

   1. M1 for stating the class widths: $20$ and $10$.
   2. M1 for establishing the width ratio: if class width $20$ has a certain drawn width, class width $10$ has half that drawn width. Let drawn width of first bar be $2w$, then second bar is $w$.
   3. M1 for using Area $\propto$ Frequency for the first bar: Area $=2w\times 2=4w$. So $4w$ represents frequency $10$, meaning $w$ represents frequency $2.5$.
   4. M1 for applying to the second bar: Area $=w\times h$. Frequency $=30$. So $w\times h$ represents $30$. Since $w$ represents $2.5$, Area must be $12w$.
   5. A1 for solving for height: $w\times h=12w⟹h=12\text{ cm}$.

3. Kinematics · 6 marks

   A drone is programmed to fly in a straight line. Its position vector $r$ (in km) at time $t$ (in hours) is $r=\left(\begin{array}{c}-5\\ 12\end{array}\right)+t\left(\begin{array}{c}8\\ -6\end{array}\right)$.
   Calculate the exact speed of the drone in km h${}^{-1}$, and find its distance from the origin at $t=2$.

   Worked solution

   Velocity vector $v=\left(\begin{array}{c}8\\ -6\end{array}\right)$. Speed $=|v|=\sqrt{8^2+(-6{)}^2}=\sqrt{64+36}=10$ km h${}^{-1}$. M1A1
   Position at $t=2$: $r(2)=\left(\begin{array}{c}-5\\ 12\end{array}\right)+2\left(\begin{array}{c}8\\ -6\end{array}\right)=\left(\begin{array}{c}11\\ 0\end{array}\right)$. M1A1
   Distance from origin $=\sqrt{{11}^2+0^2}=11$ km. M1A1

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 12 marks.
• Biggest question: Q2, 12 marks: normal model for metal rod lengths.
• Marks by main topic: Statistical distributions 18, Sampling and data 16, Probability 10, Hypothesis testing 6.
• More Statistical distributions in other sittings: November 2021 Q5 (11 marks), June 2023 Q6 (14 marks), October 2020 Q5 (15 marks).
• Against the other 6 sittings we mapped: more marks on Hypothesis testing (6 marks here, 1 on average); fewer on Statistical distributions (18 marks here, 24 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 hitting a target (6 marks) · Statistical distributions
2. Q2Normal model for metal rod lengths (12 marks) · Statistical distributions
3. Q3Large data set: rainfall at Camborne (7 marks) · Sampling and data
4. Q4Binomial test for late arrivals (6 marks) · Hypothesis testing
5. Q5Two-way table and conditional probability (10 marks) · Probability
6. Q6Heart rate and exercise: correlation test (9 marks) · Sampling and data, Hypothesis testing

What this paper is like

• Shape: 5 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 8 to 12 marks.
• Biggest question: Q5, 12 marks: golf ball projectile.
• Marks by main topic: Kinematics 29, Moments 11, Forces and Newton's laws 10.
• More Kinematics in other sittings: November 2021 Q5 (14 marks), June 2023 Q5 (11 marks), October 2020 Q3 (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. Q1Position and velocity vectors with calculus (8 marks) · Kinematics
2. Q2Block on a rough plane held by a horizontal force (10 marks) · Forces and Newton's laws
3. Q3Two forces on a particle, motion with vectors (9 marks) · Kinematics, Forces and Newton's laws
4. Q4Rod with an attached particle, moments (11 marks) · Moments
5. Q5Golf ball projectile (12 marks) · Kinematics

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.