Edexcel IAL M1 Maths Revision: Mechanics 1

Edexcel International A Level M1 (Mechanics 1): every topic with an exam-style question and its mark scheme, and 278 practice questions with mark schemes.

1h 30min written paper (75 marks), calculator permitted
7 topics
278 questions

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Kinematics · M1 paper · 5 marks · hard

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

Worked answer

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

M1 topics

"Tested in" counts come from our question-by-question mapping of the 4 Pearson M1 papers from June 2024 to June 2025.

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M1 past papers

Official Pearson M1 papers and mark schemes, with a timer: all IAL M1 past papers. Most recent: June 2025 · January 2025 · October 2024 · June 2024.

Examiner Insights for IAL M1: every examiner report since June 2024, the top mistakes and what to focus on next →

Knowledge organiser: Mechanics 1 (M1) on one page (key facts, formulas and mistakes to avoid; printable PDF)

M1 Kinematics

Constant-acceleration (suvat) formulae; vertical motion under gravity; displacement-time and velocity-time graphs (variable acceleration and projectiles are M2).

37 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise kinematics →

Example question · 5 marks · hard

Show the mark scheme

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

M1 Forces and Newton's Laws

Newton's three laws, resolving forces on inclines, connected particles (pulleys), friction with coefficient μ.

45 practice questions with mark schemes · Worked examples → · Notes → · Practise forces and newton's laws →

Example question · 7 marks · hard

Two particles $A$ ( $4 kg$ ) and $B$ ( $6 kg$ ) are connected by a light inextensible string that passes over a smooth pulley at the edge of a rough horizontal table. $A$ rests on the table (coefficient of friction $μ = 0.2$ ); $B$ hangs freely. The system is released from rest. Find the acceleration and the tension in the string. Take $g = 9.8 {m s}^{- 2}$ .

A (4 kg) on a rough horizontal table joined by a string over a pulley at the edge to B (6 kg) hanging freely

Show the mark scheme

For $A$ : $R = 4 g = 39.2 N$ ; friction $= 0.2 \times 39.2 = 7.84 N$ M1 A1. Newton II on $A$ : $T - 7.84 = 4 a$ M1. Newton II on $B$ : $6 g - T = 6 a$ , i.e. $58.8 - T = 6 a$ M1. Add: $58.8 - 7.84 = 10 a \Rightarrow a = 5.10 {m s}^{- 2}$ A1. Then $T = 4 (5.10) + 7.84 = 28.24 N$ A1 A1.

M1 Moments

Moment of a force; equilibrium of a rod under parallel coplanar forces, including non-uniform rods and rods on the point of tilting.

43 practice questions with mark schemes · Worked examples → · Notes → · Practise moments →

Example question · 7 marks · hard

A uniform plank of length $4 m$ and mass $18 kg$ rests horizontally on two supports at $A$ (left end) and $B$ ( $3 m$ from $A$ ). A boy of mass $40 kg$ stands on the plank at a distance $x$ from $A$ .
(a) Find, in terms of $x$ , the reactions at $A$ and $B$ . (5)
(b) State the maximum value of $x$ for which the plank does not tip. (2) Take $g = 9.8 {m s}^{- 2}$ .

Plank 4 m on supports at A (left end) and B (3 m from A); a 40 kg boy at distance x from A

Show the mark scheme

(a) Moments about $A$ : $R_{B} \times 3 = 18 g \times 2 + 40 g \times x \Rightarrow R_{B} = \frac{(36 + 40 x) g}{3}$ M1 A1. Total: $R_{A} + R_{B} = 58 g \Rightarrow R_{A} = 58 g - R_{B} = \frac{(174 - 36 - 40 x) g}{3} = \frac{(138 - 40 x) g}{3}$ M1 A1 A1.
(b) On point of tipping about $B$ when $R_{A} = 0$ : $138 - 40 x = 0 \Rightarrow x = 3.45$ ; but plank ends at $x = 4$ , so max $x = 3.45 m$ M1 A1.

M1 Vectors (Mechanics context)

Position, velocity and force vectors in i, j form; magnitude and direction; r = r₀ + vt for constant velocity; resultant forces.

63 practice questions with mark schemes · Worked examples → · Notes → · Calculator steps → · Practise vectors (mechanics context) →

Example question · 8 marks · hard

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

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

Show the mark scheme

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

M1 Dynamics of a Particle

F = ma in a straight line; connected particles over pulleys; tow-bars; lifts.

30 practice questions with mark schemes · Worked examples → · Notes → · Practise dynamics of a particle →

Example question · 4 marks · hard

Two particles A and B of masses $3 kg$ and $5 kg$ respectively are connected by a light inextensible string passing over a smooth fixed peg. The system is released from rest. Find the acceleration of the particles.

Particles A (3 kg) and B (5 kg) hanging from a string over a smooth fixed peg

Show the mark scheme

M1 for forming the equation for B (moving downwards): $5 g - T = 5 a$ .
M1 for forming the equation for A (moving upwards): $T - 3 g = 3 a$ .
M1 for adding the equations to eliminate $T$ : $2 g = 8 a$ .
A1 for calculating $a = 0.25 g = 2.45 {m s}^{- 2}$ .

M1 Statics of a Particle

Resolving forces; equilibrium of a particle; friction and limiting equilibrium (F ≤ μR).

30 practice questions with mark schemes · Worked examples → · Notes → · Practise statics of a particle →

Example question · 5 marks · hard

A particle of mass $2 kg$ is held in limiting equilibrium on a rough plane inclined at $40^{\circ}$ to the horizontal by a horizontal force $H$ . The particle is on the point of sliding up the plane. The coefficient of friction is $0.3$ . Find the value of $H$ .

Particle of mass 2 kg on a rough plane inclined at 40 degrees held by a horizontal force H

Show the mark scheme

M1 for resolving perpendicular to the plane: $R = 2 g \cos 40^{\circ} + H \sin 40^{\circ}$ .
M1 for resolving parallel to the plane (friction acts down): $H \cos 40^{\circ} = 2 g \sin 40^{\circ} + F$ .
M1 for substituting $F = 0.3 R$ : $H \cos 40^{\circ} = 2 g \sin 40^{\circ} + 0.3 (2 g \cos 40^{\circ} + H \sin 40^{\circ})$ .
M1 for rearranging to isolate $H$ : $H (\cos 40^{\circ} - 0.3 \sin 40^{\circ}) = 2 g \sin 40^{\circ} + 0.6 g \cos 40^{\circ}$ .
A1 for calculating $H = \frac{12.60 + 4.50}{0.766 - 0.193} = \frac{17.10}{0.573} = 29.8 N$ (to 3 s.f.).

M1 Momentum and Impulse

Momentum, impulse = change in momentum, conservation of momentum in direct collisions.

30 practice questions with mark schemes · Worked examples → · Notes → · Practise momentum and impulse →

Example question · 4 marks · hard

A ball of mass $0.5 kg$ is dropped from rest from a height of $19.6 m$ above horizontal ground. It rebounds to a height of $4.9 m$ . Calculate the magnitude of the impulse exerted by the ground on the ball. (Take $g = 9.8 {m s}^{- 2}$ )

Show the mark scheme

M1 for finding the velocity just before impact using $v^{2} = u^{2} + 2 a s$ : $v_{1}^{2} = 0 + 2 (9.8) (19.6) = {19.6}^{2} ⟹ v_{1} = 19.6 {m s}^{- 1}$ downwards.
M1 for finding the velocity just after impact using $v^{2} = u^{2} + 2 a s$ : $0 = v_{2}^{2} - 2 (9.8) (4.9) ⟹ v_{2}^{2} = {9.8}^{2} ⟹ v_{2} = 9.8 {m s}^{- 1}$ upwards.
M1 for calculating the impulse: $I = m (v_{2} - v_{1}) = 0.5 (9.8 - (- 19.6))$ .
A1 for evaluating $I = 0.5 (29.4) = 14.7 N s$ .

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FAQ

What is on the Edexcel IAL M1 exam?

M1 Mechanics 1 is assessed by a 1h 30min written paper (75 marks), calculator permitted. It covers Kinematics, Forces and Newton's Laws, Moments, Vectors (Mechanics context), Dynamics of a Particle, Statics of a Particle, Momentum and Impulse.

Can I use a calculator in M1?

Yes, a calculator is permitted in M1, as in every IAL maths unit. You still need to show full method to earn the M marks.

How many M1 practice questions are there?

278 exam-style M1 questions across 7 topics, each with an Edexcel-style mark scheme (M, A and B marks).

Which M1 topics come up most?

In our mapping of the 4 Pearson M1 papers from June 2024 to June 2025, Vectors (Mechanics context) (6 questions), Kinematics (5 questions), Dynamics of a Particle (5 questions) were tested most. Every topic can be examined in any series.

Where can I find M1 past papers?

Pearson publishes them. Our IAL M1 past papers page links to each official paper and mark scheme by series, with an exam timer.

How should I revise for M1?

Read the note for a topic, study the worked example and its mark scheme, practise that topic's questions, then sit a timed M1 past paper and check the common mistakes examiners report.

What is free on this page?

Everything here, with no sign-in: one example question with its mark scheme for every M1 topic, the worked examples on the topic pages and a quick quiz.

What does a free account add?

A free account (no card) adds 5 more practice questions on every topic with instant feedback, answers and mark schemes on free questions, 3 AI-marked answers a week, free, and your streak and progress on any device. The rest of the M1 bank with its mark schemes is part of the paid plans.

Other IAL units: IAL P1 Pure Mathematics 1 · IAL P2 Pure Mathematics 2 · IAL P3 Pure Mathematics 3 · IAL P4 Pure Mathematics 4 · IAL S1 Statistics 1

Exam season: Mock exam guides · January 2027 prediction papers · 12-day mock revision plan · Final exam countdown · Results day: what next? · All exam-season plans

Edexcel IAL M1 Maths Revision: Mechanics 1

Try one now

M1 topics

Try it now

M1 past papers

M1 Kinematics

Example question · 5 marks · hard

M1 Forces and Newton's Laws

Example question · 7 marks · hard

M1 Moments

Example question · 7 marks · hard

M1 Vectors (Mechanics context)

Example question · 8 marks · hard

M1 Dynamics of a Particle

Example question · 4 marks · hard

M1 Statics of a Particle

Example question · 5 marks · hard

M1 Momentum and Impulse

Example question · 4 marks · hard

Your M1 revision kit

FAQ

What is on the Edexcel IAL M1 exam?

Can I use a calculator in M1?

How many M1 practice questions are there?

Which M1 topics come up most?

Where can I find M1 past papers?

How should I revise for M1?

What is free on this page?

What does a free account add?