Edexcel A Level Maths October 2020 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 · 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 · 5 marks

   Car A travels along a straight road at a constant speed of $25{\text{ m s}}^{-1}$. Car B starts from rest at the same point and accelerates uniformly at $3{\text{ m s}}^{-2}$ until it reaches a speed of $30{\text{ m s}}^{-1}$, after which it maintains this speed. Find the distance Car B travels before it catches up to Car A.

   Worked solution

   1. M1 for finding the time taken for Car B to reach $30{\text{ m s}}^{-1}$: $t=\frac{30}{3}=10\text{ s}$.
   2. M1 for finding the distances covered in the first $10\text{ s}$: Car B covers $\frac{1}{2}\times 10\times 30=150\text{ m}$. Car A covers $25\times 10=250\text{ m}$.
   3. M1 for setting up an equation for the remaining distance where Car B catches A. Let $t_2$ be the additional time: $150+30t_2=250+25t_2$.
   4. M1 for solving to find $t_2$: $5t_2=100⟹t_2=20\text{ s}$. Total time = $30\text{ s}$.
   5. A1 for finding the total distance: $25\times 30=750\text{ m}$.

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 7 to 15 marks.
• Biggest question: Q5, 15 marks: normal model and a test of a health centre's claim.
• Marks by main topic: Statistical distributions 25, Sampling and data 17, Probability 8.
• More Statistical distributions in other sittings: November 2021 Q5 (11 marks), June 2019 Q5 (13 marks), June 2022 Q2 (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.
• 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. Q1Venn diagram with four events (8 marks) · Probability
2. Q2Large data set scatter diagram for Perth (7 marks) · Sampling and data
3. Q3Puzzle times: coding, mean and spread (10 marks) · Sampling and data
4. Q4Discrete distribution with an unknown k (10 marks) · Statistical distributions
5. Q5Normal model and a test of a health centre's claim (15 marks) · Statistical distributions, 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: Q3, 12 marks: variable acceleration using calculus.
• Marks by main topic: Kinematics 31, Moments 10, Forces and Newton's laws 9.
• More Kinematics in other sittings: November 2021 Q5 (14 marks), June 2019 Q5 (13 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. Q1Brick on a rough inclined plane (9 marks) · Forces and Newton's laws
2. Q2Constant acceleration with i and j vectors (8 marks) · Kinematics
3. Q3Variable acceleration using calculus (12 marks) · Kinematics
4. Q4Ladder against a wall, limiting equilibrium (10 marks) · Moments, Forces and Newton's laws
5. Q5Projectile from the top of a cliff (11 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.