AS & A Level Mathematics 9709 · Mechanics (for Paper 4) · 4.1

Forces and equilibrium: past paper questions

139 real questionsasked in 7 of the last 10 exam series2020–2025usually: Find, Show, Draw, Determine, Calculate

Real questions on forces and equilibrium

The newest 20 of 139 written questions. Open one to see it on the real paper.

9709/12 · October/November 2025 · Q7a[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/12 · October/November 2025 · Q7b[3]
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9709/12 · October/November 2025 · Q7c[4]
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9709/31 · October/November 2025 · Q9a[2]
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9709/31 · October/November 2025 · Q9b[2]
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9709/41 · October/November 2025 · Q1a[2]
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9709/41 · October/November 2025 · Q5[6]
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9709/41 · October/November 2025 · Q8b[6]
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9709/42 · October/November 2025 · Q7a[6]
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9709/42 · October/November 2025 · Q7b[5]
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9709/43 · October/November 2025 · Q7a[5]
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9709/43 · October/November 2025 · Q7b[2]
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9709/13 · May/June 2025 · Q8b[3]
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9709/13 · May/June 2025 · Q8c[3]
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9709/41 · May/June 2025 · Q2[4]
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9709/42 · May/June 2025 · Q3[4]
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9709/32 · February/March 2025 · Q3b[3]
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9709/12 · October/November 2024 · Q6[6]
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9709/41 · October/November 2024 · Q1[4]
4-mark “Find” question — its maths and diagrams are best seen on the paper.
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9709/41 · October/November 2024 · Q3[4]
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What examiners said

This part also proved challenging for candidates, with many not attempting a solution at all and only very few gaining full marks. Of those that did score full marks, most found the coordinates of the correct point and then calculated the distance. An alternative method was to use Pythagoras’ Theorem twice.
— Examiner report, February/March 2025, 9709/32 Q3(b) (Cambridge)

The most common error in this question was to assume that the tensions were equal in both strings. There were also signs and trigonometric errors seen when forming the two required simultaneous equations for the two different tensions. Many responses correctly resolved horizontally and vertically to obtain the two equations T1 cos35 = T2 cos 40 and T1 sin35 + T2 sin 40 = 2.4g, but then struggled t...
— Examiner report, October/November 2023, 9709/41 Q2 (Cambridge)

This was a question many candidates found challenging, and it was clear that many were unsure where to begin with this type of extended response. It was frequently unclear in candidate’s responses both how, and to what, different mechanical principles were being applied. It would be extremely beneficial if candidates stated which principle (e.g. resolving parallel to the plane) and to which partic...
— Examiner report, October/November 2023, 9709/41 Q5 (Cambridge)

Practise this topic

Answer these questions online and get each one marked against the official mark scheme, with what you missed and how to fix it.

Practise forces and equilibrium

In the syllabus

4.1 Forces and equilibrium

identify the forces acting in a given situation e.g. by drawing a force diagram.
understand the vector nature of force, and find Calculations are always required, not approximate
solutions by scale drawing.
use the principle that, when a particle is in Solutions by resolving are usually expected, but
equivalent methods (e.g. triangle of forces, Lami’s
Theorem, where suitable) are also acceptable;
these other methods are not required knowledge, and will not be referred to in questions.
understand that a contact force between
use the model of a ‘smooth’ contact, and
understand the concepts of limiting friction Terminology such as ‘about to slip’ may be used to
mean ‘in limiting equilibrium’ in questions.
use Newton’s third law. e.g. the force exerted by a particle on the ground is equal and opposite to the force exerted by the ground on the particle.

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