Edexcel IAL M1 Maths Revision: Mechanics 1
Everything for Edexcel International A Level M1 (Mechanics 1) in one place: what each topic covers, an exam-style question with its mark scheme for each topic, and 256 practice questions with instant marking.
- 1h 30min written paper (75 marks), calculator permitted
- 7 topics
- 256 questions
M1 topics
M1 Kinematics
Constant-acceleration (suvat) formulae; vertical motion under gravity; displacement-time and velocity-time graphs (variable acceleration and projectiles are M2).
Example question
A car travels at a constant speed of $20 \text{ m s}^{-1}$ for $T$ seconds, and then decelerates uniformly to rest in $5$ seconds. If the total distance travelled is $400 \text{ m}$, find the value of $T$.
Show the mark scheme
- M1 for drawing a velocity-time graph or setting up the total distance as the sum of a rectangle and a triangle.
- M1 for forming the equation: $20T + \frac{1}{2} \times 5 \times 20 = 400$.
- M1 for simplifying to $20T + 50 = 400 \implies 20T = 350$.
- A1 for finding $T = 17.5 \text{ s}$.
M1 Forces and Newton's Laws
Newton's three laws, resolving forces on inclines, connected particles (pulleys), friction with coefficient μ.
Example question
The velocity of a particle, $v\text{ ms}^{-1}$, moving in a straight line is given by $v(t) = 6t - 2$, where $t$ is the time in seconds. Find the exact displacement of the particle from $t = 0$ to $t = 3$.
Show the mark scheme
[M1] for recognizing that displacement is the definite integral of velocity: $\int_0^3 (6t - 2) \,dt$.
[M1] for integrating the function correctly: $[3t^2 - 2t]_0^3$.
[M1] for substituting the limits: $(3(3)^2 - 2(3)) - (0)$.
[A1] for evaluating to $27 - 6 = 21\text{ m}$.
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.
Example question
A triangle has an area of \(10 \text{ cm}^2\). It is transformed by the matrix \(M = \begin{pmatrix} 4 & -1 \\ 2 & 3 \end{pmatrix}\).
Calculate the area of the transformed image triangle.
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Area Scale Factor \(= |\det(M)|\). [M1]
\(\det(M) = (4)(3) - (-1)(2) = 12 - (-2) = 14\). [M1][A1]
New Area \(= 10 \times 14 = 140 \text{ cm}^2\). [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.
Example question
A particle moves with a constant velocity of \(v = 4i - 3j\) m s^{-1}. Its initial position at time \(t=0\) is given by the position vector \(r_0 = -2i + 7j\) m.
Write down the vector equation of the particle’s path and find its position vector at \(t = 5\) seconds.
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Equation of motion: \(r = r_0 + vt = \begin{pmatrix} -2 \\ 7 \end{pmatrix} + t \begin{pmatrix} 4 \\ -3 \end{pmatrix}\). M1A1
At \(t=5\): \(r(5) = \begin{pmatrix} -2 \\ 7 \end{pmatrix} + 5 \begin{pmatrix} 4 \\ -3 \end{pmatrix} = \begin{pmatrix} -2 \\ 7 \end{pmatrix} + \begin{pmatrix} 20 \\ -15 \end{pmatrix}\). M1
\(r(5) = \begin{pmatrix} 18 \\ -8 \end{pmatrix}\) or \(18i - 8j\). A1
M1 Dynamics of a Particle
F = ma in a straight line; connected particles over pulleys; tow-bars; lifts.
Example question
Two particles A and B of masses $3 \text{ kg}$ and $5 \text{ kg}$ 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.
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- M1 for forming the equation for B (moving downwards): $5g - T = 5a$.
- M1 for forming the equation for A (moving upwards): $T - 3g = 3a$.
- M1 for adding the equations to eliminate $T$: $2g = 8a$.
- A1 for calculating $a = 0.25g = 2.45 \text{ m s}^{-2}$.
M1 Statics of a Particle
Resolving forces; equilibrium of a particle; friction and limiting equilibrium (F ≤ μR).
Example question
A particle of mass $10 \text{ kg}$ is suspended in equilibrium by two light inextensible strings. The strings make angles of $30^{\circ}$ and $45^{\circ}$ with the horizontal ceiling. Find the tension in the string making the $45^{\circ}$ angle. (Take $g = 9.8 \text{ m s}^{-2}$)
Show the mark scheme
- M1 for resolving horizontally: $T_1 \cos 30^{\circ} = T_2 \cos 45^{\circ}$.
- M1 for resolving vertically: $T_1 \sin 30^{\circ} + T_2 \sin 45^{\circ} = 10g$.
- M1 for substituting $T_1 = T_2 \frac{\cos 45^{\circ}}{\cos 30^{\circ}}$ into the vertical equation.
- A1 for calculating $T_2 = \frac{10g}{\frac{\cos 45^{\circ}}{\cos 30^{\circ}} \sin 30^{\circ} + \sin 45^{\circ}} = 87.9 \text{ N}$ (to 3 s.f.).
M1 Momentum and Impulse
Momentum, impulse = change in momentum, conservation of momentum in direct collisions.
Example question
A particle of mass $2 \text{ kg}$ has its velocity changed from $(\mathbf{i} + 3\mathbf{j}) \text{ m s}^{-1}$ to $(4\mathbf{i} - \mathbf{j}) \text{ m s}^{-1}$ by an impulse $\mathbf{I}$. Calculate the magnitude of $\mathbf{I}$.
Show the mark scheme
- M1 for setting up $\mathbf{I} = m(\mathbf{v} - \mathbf{u}) = 2((4\mathbf{i} - \mathbf{j}) - (\mathbf{i} + 3\mathbf{j}))$.
- M1 for finding the vector $\mathbf{I} = 2(3\mathbf{i} - 4\mathbf{j}) = 6\mathbf{i} - 8\mathbf{j}$.
- M1 for finding the magnitude $|\mathbf{I}| = \sqrt{6^2 + (-8)^2}$.
- A1 for evaluating to $10 \text{ N s}$.
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. You still need to show full method to earn the M marks.
How many M1 practice questions are there?
256 exam-style M1 questions across 7 topics, each with an Edexcel-style mark scheme (M, A and B marks).