Edexcel A Level Maths June 2018 Paper 3: question paper and mark scheme (9MA0/03)

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

   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 · 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: 10 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 5 to 15 marks.
• Biggest question: Q10, 15 marks: projectile thrown at a target.
• Marks by main topic: Statistical distributions 30, Kinematics 29, Sampling and data 20, Moments 13, Forces and Newton's laws 8.
• Not on this paper: Probability, Hypothesis testing.
• Calculator: allowed.

9MA0/03: question by question

Labels and topics are ours, read from the 9MA0/03 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Modelling cloud cover from the large data set (5 marks) · Statistical distributions, Sampling and data
2. Q2Sales against temperature: correlation and a test (7 marks) · Sampling and data, Hypothesis testing
3. Q3Binomial model for darts hitting a target (11 marks) · Statistical distributions
4. Q4Sampling methods and a summary of travel times (13 marks) · Sampling and data
5. Q5Normal model for battery life (14 marks) · Statistical distributions, Hypothesis testing
6. Q6Variable acceleration with i and j vectors (6 marks) · Kinematics
7. Q7Crate pulled at an angle on a rough floor (8 marks) · Forces and Newton's laws
8. Q8Constant acceleration with vectors (8 marks) · Kinematics
9. Q9Plank against a rough wall, moments (13 marks) · Moments, Forces and Newton's laws
10. Q10Projectile thrown at a target (15 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.