Cambridge International A Level Maths: Mechanics, Paper 4 of 9709

Where Mechanics fits in 9709

Cambridge Mathematics 9709 has six papers: Pure Mathematics 1, 2 and 3, Mechanics (Paper 4), and Probability & Statistics 1 and 2. You take two papers for AS Level and four for A Level:

You can't combine Paper 4 with Paper 6. The pure-only AS route (Papers 1 and 2) cannot be carried forward to A Level. AS grades run from a to e and A Level from A* to E.

The Mechanics paper

• Paper 4: Mechanics, 1 hour 15 minutes, 50 marks, 6 to 8 structured questions.
• Formulae: the list of formulae and statistical tables (MF19) is supplied, and it includes the constant acceleration formulae.
• g: questions are mainly numerical, and Cambridge expects you to use g = 10 m s⁻².
• Equipment: a ruler and a scientific calculator. Calculus is limited to what is in Pure Mathematics 1.

Cambridge A Level Maths exam dates 2027

Paper 2 and Paper 6 are also on Friday 7 May. The June 2027 series runs from 26 April to 11 June, and Cambridge publishes a timetable for each zone, so check yours. From 2027, June AS and A Level results move earlier, to 28 July 2027.

9709 grade thresholds

In June 2026, the Mechanics paper (component 42, out of 50) needed 38 for an A, 29 for a B and 23 for a C. Other versions differed: component 41 needed 43 for an A and 29 for a C. For the whole qualification:

Thresholds change every series and differ between paper versions, so use them as a guide when you mark past papers.

What 9709 Mechanics covers

• 4.1 Forces and equilibrium: force diagrams, resolving, friction and limiting equilibrium with F = μR, Newton's third law.
• 4.2 Kinematics in a straight line: displacement-time and velocity-time graphs, constant acceleration formulae, and calculus for variable acceleration.
• 4.3 Momentum: conservation of momentum in direct impacts, including bodies that coalesce. Impulse and the coefficient of restitution are not required.
• 4.4 Newton's laws of motion: F = ma, connected particles and motion on slopes.
• 4.5 Energy, work and power: work done, kinetic and potential energy, the work-energy principle, and P = Fv.

Projectiles and circular motion are not in 9709 Mechanics; they belong to Further Mathematics.

Worked examples

Friction on a rough surface

A 4 kg block on a rough horizontal floor is pulled by a horizontal force of 30 N. The coefficient of friction is 0.5. The normal reaction is 4 × 10 = 40 N, so the friction force is 0.5 × 40 = 20 N:

Constant acceleration

A particle starts from rest and accelerates at 3 m s⁻² for 4 s. Then v = u + at = 0 + 3 × 4 = 12 m s⁻¹ and s = ut + ½at² = ½ × 3 × 4² = 24 m.

Momentum: bodies that coalesce

A 2 kg particle moving at 5 m s⁻¹ hits a 3 kg particle at rest and they move off together. Momentum is conserved: 2 × 5 = (2 + 3)v, so v = 2 m s⁻¹.

Power

A car moves at a constant 20 m s⁻¹ against a resistance of 800 N, so the driving force is also 800 N. Its power is P = Fv = 800 × 20 = 16 kW.

Practise picking the right constant acceleration equation in our Laws of Motion course, then press Mark to check your answer in the course:

Use the daily paper as a short timed mock

Uni-Sine publishes a free daily paper for Cambridge A-level Maths: Mechanics. It is a short timed mock: 8 questions worth 25 to 35 marks, with a suggested 35 to 45 minutes, marked when you finish. It is not a full Cambridge paper, and the questions are original, not past papers.

• What it covers well: constant acceleration, velocity-time graphs, forces and Newton's laws, friction, connected particles and pulleys, slopes, and variable acceleration with calculus.
• What it does not cover: momentum and energy, work and power, which are both in Paper 4. It also includes projectiles and moments, which are not in 9709 Mechanics, so skip those or treat them as stretch.

Check the value of g each question states, since Cambridge expects 10 m s⁻². For full papers, use Cambridge past papers from your teacher.

Common mistakes in 9709 Mechanics

• Using 9.8 or 9.81 for g. Cambridge expects 10 m s⁻² in this paper.
• Forgetting friction is limiting only when the body is about to slip or moving. Otherwise F ≤ μR.
• Resolving along the wrong axes on a slope. Resolve parallel and perpendicular to the plane.
• Dropping the sign of velocity in momentum. Choose a positive direction and stick to it.

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