Edexcel IAL M1 June 2025 question paper and mark scheme (WME01/01)

Try 3 M1 questions like these

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1. 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 answer

   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 $t_2$: $5t_2 = 100 \implies t_2 = 20 \text{ s}$. Total time = $30 \text{ s}$.
   5. A1 for finding the total distance: $25 \times 30 = 750 \text{ m}$.

2. Vectors (Mechanics context) · 8 marks

   Ship A starts at position $(0, 5)$ relative to a port and moves with a constant velocity vector of $\begin{pmatrix} 3 \\ -1 \end{pmatrix}\text{ km h}^{-1}$. Ship B starts at $(4, 0)$ and moves with a constant velocity vector of $\begin{pmatrix} 1 \\ 2 \end{pmatrix}\text{ km h}^{-1}$.

   1. Write down the position vectors of Ship A and Ship B at time $t$ hours.
   2. Find an expression for the square of the distance between the ships at time $t$, denoted $D^2(t)$.
   3. Find the exact time $t$ when the two ships are closest to each other.
   Worked answer

   1. M1 for writing the vector equations of motion.
      A1 for $\mathbf{r_A} = \begin{pmatrix} 3t \\ 5-t \end{pmatrix}$ and $\mathbf{r_B} = \begin{pmatrix} 4+t \\ 2t \end{pmatrix}$.
   2. M1 for finding the relative displacement vector $\mathbf{r_B} - \mathbf{r_A} = \begin{pmatrix} 4 - 2t \\ 3t - 5 \end{pmatrix}$.
      M1 for setting up the square of the magnitude: $D^2(t) = (4 - 2t)^2 + (3t - 5)^2$.
      A1 for expanding and simplifying to a quadratic: $D^2(t) = 16 - 16t + 4t^2 + 9t^2 - 30t + 25 = 13t^2 - 46t + 41$.
   3. M1 for recognizing that minimum distance occurs when the derivative of $D^2(t)$ is zero (or using the vertex formula $t = -b/2a$).
      M1 for solving $26t - 46 = 0 \implies 26t = 46$.
      A1 for finding exactly $t = \frac{23}{13}$ hours.

3. Momentum and Impulse · 4 marks

   Two particles A and B, of masses $m$ and $km$ respectively, collide on a smooth horizontal surface. Before the collision, A is moving with speed $3u$ and B is at rest. After the collision, A rebounds with speed $u$ and B moves with speed $u$. Find the value of $k$.

   Worked answer

   1. M1 for applying conservation of momentum, taking A's initial direction as positive.
   2. M1 for the equation: $m(3u) + km(0) = m(-u) + km(u)$.
   3. A1 for simplifying: $3mu = -mu + kmu \implies 4mu = kmu$.
   4. A1 for finding $k = 4$.

More on these topics: Kinematics · Vectors (Mechanics context) · Momentum and Impulse

M1 topics this paper can test

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• Kinematics
• Forces and Newton's Laws
• Moments
• Vectors (Mechanics context)
• Dynamics of a Particle
• Statics of a Particle
• Momentum and Impulse

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• IAL M1

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What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• WME01/01: Momentum (Q1); Moments (Q5); Vectors (Q2, Q7). Official examiner report ↗

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)