Edexcel A Level Maths June 2019 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

   Three independent events $A$, $B$, and $C$ have probabilities $P(A)=0.5$, $P(B)=0.4$, and $P(C)=0.3$. Find the probability that exactly one of these events occurs.

   Worked solution

   1. M1 for identifying the three scenarios: $(A\cap B^{\prime }\cap C^{\prime })$, $(A^{\prime }\cap B\cap C^{\prime })$, and $(A^{\prime }\cap B^{\prime }\cap C)$.
   2. M1 for calculating the probabilities of these scenarios: $(0.5\times 0.6\times 0.7)+(0.5\times 0.4\times 0.7)+(0.5\times 0.6\times 0.3)$.
   3. A1 for evaluating and summing: $0.21+0.14+0.09=0.44$.

2. Sampling and data · 5 marks

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

   Worked solution

   1. M1 for calculating $\overline{x}=\frac{120}{10}=12$.
   2. M1 for finding $\overline{y}=3(12)-2=34$.
   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 $Var(y)=9\times 36=324$.

3. Kinematics · 5 marks

   A particle moving with constant acceleration passes three points $A$, $B$ and $C$, in that order, on a straight line. The distance $AB$ is $20\text{ m}$ and the distance $AC$ is $84\text{ m}$. The speed of the particle at $B$ is $12{\text{ m s}}^{-1}$ and its speed at $C$ is $20{\text{ m s}}^{-1}$. Find the acceleration of the particle and its speed at $A$.

   Worked solution

   1. M1 for $BC=84-20=64\text{ m}$.
   2. M1 for $v^2=u^2+2as$ from $B$ to $C$: ${20}^2={12}^2+2a(64)$.
   3. A1 for $128a=256\Rightarrow a=2{\text{ m s}}^{-2}$.
   4. M1 for $v^2=u^2+2as$ from $A$ to $B$: ${12}^2=u_A^2+2(2)(20)$.
   5. A1 for $u_A^2=64\Rightarrow u_A=8{\text{ m s}}^{-1}$.

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

What this paper covers

What this paper is like

• Shape: 5 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 8 to 13 marks.
• Biggest question: Q5, 13 marks: normal distribution with an unknown standard deviation.
• Marks by main topic: Statistical distributions 22, Sampling and data 20, Probability 8.
• More Statistical distributions in other sittings: October 2020 Q5 (15 marks), November 2021 Q5 (11 marks), June 2022 Q2 (12 marks).
• Against the other 6 sittings we mapped: more marks on Sampling and data (20 marks here, 14 on average).
• Not on this paper: Hypothesis testing.
• 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. Q1Tree diagram for picking marbles (8 marks) · Probability
2. Q2Large data set temperatures and a normal model (11 marks) · Sampling and data, Statistical distributions
3. Q3Testing for correlation (9 marks) · Sampling and data, Hypothesis testing
4. Q4Binomial model for cloud cover (9 marks) · Statistical distributions
5. Q5Normal distribution with an unknown standard deviation (13 marks) · Statistical distributions

What this paper is like

• Shape: 5 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 6 to 13 marks.
• Biggest question: Q5, 13 marks: projectile: speed and direction.
• Marks by main topic: Kinematics 27, Forces and Newton's laws 12, Moments 11.
• More Kinematics in other sittings: October 2020 Q3 (12 marks), November 2021 Q5 (14 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. Q1Velocity vector: differentiate and integrate (6 marks) · Kinematics
2. Q2Direction of motion from a velocity vector (8 marks) · Kinematics
3. Q3Connected particles with friction (12 marks) · Forces and Newton's laws
4. Q4Ramp resting on a smooth drum (11 marks) · Moments, Forces and Newton's laws
5. Q5Projectile: speed and direction (13 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.