Edexcel A Level Maths November 2021 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

   The data in a histogram is grouped into classes. A bar representing the class $100\le x<150$ has a width of $2.5\text{ cm}$ and a height of $4\text{ cm}$. The total area of all bars in the histogram is $90{\text{ cm}}^2$. If the bar for $100\le x<150$ represents a frequency of $20$, calculate the total frequency of the entire data set.

   Worked solution

   1. M1 for calculating the area of the specified bar: $2.5\times 4=10{\text{ cm}}^2$.
   2. M1 for establishing the relationship between area and frequency: $10{\text{ cm}}^2$ represents a frequency of $20$.
   3. A1 for calculating the scale factor: $1{\text{ cm}}^2$ represents $2$ items (since $20/10=2$).
   4. M1 for using the total area to find total frequency: $90{\text{ cm}}^2\times 2$.
   5. A1 for the final answer: $180$ items.

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: 6 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 6 to 11 marks.
• Biggest question: Q4, 11 marks: venn diagram for three college magazines.
• Marks by main topic: Sampling and data 21, Statistical distributions 18, Probability 11.
• More Probability in other sittings: June 2022 Q5 (10 marks), October 2020 Q1 (8 marks), June 2023 Q5 (8 marks).
• Against the other 6 sittings we mapped: more marks on Sampling and data (21 marks here, 14 on average); fewer on Statistical distributions (18 marks here, 24 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. Q1Quota sampling, then a binomial probability (7 marks) · Sampling and data, Statistical distributions
2. Q2Regression of letters against a second variable (6 marks) · Sampling and data
3. Q3Coding large data set pressure readings (8 marks) · Sampling and data
4. Q4Venn diagram for three college magazines (11 marks) · Probability
5. Q5Normal distribution of heights (11 marks) · Statistical distributions
6. Q6Discrete distribution with logarithm probabilities (7 marks) · Statistical distributions, Exponentials and logarithms

What this paper is like

• Shape: 5 questions, 50 marks in 1 h (about 1.2 minutes a mark); questions from 4 to 14 marks.
• Biggest question: Q5, 14 marks: velocity vector: acceleration and position by calculus.
• Marks by main topic: Kinematics 28, Forces and Newton's laws 12, Moments 10.
• More Kinematics in other sittings: June 2022 Q5 (12 marks), October 2020 Q3 (12 marks), June 2023 Q5 (11 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. Q1Constant acceleration with vectors (4 marks) · Kinematics
2. Q2Stones connected over a pulley (12 marks) · Forces and Newton's laws
3. Q3Beam resting on rough ground, moments (10 marks) · Moments, Forces and Newton's laws
4. Q4Projectile from a cliff top (10 marks) · Kinematics
5. Q5Velocity vector: acceleration and position by calculus (14 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.