A-LevelMathematicsMechanics9709/41 · May/June 2025 · Q24 Marks

Three coplanar forces of magnitudes PN, 5N and 10N act at a point O, as shown in the diagram. The resultant of the three forces has magnitude QN and acts in a direction perpendicular to the force of magnitude PN.

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Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[M1] For resolving in direction of P. 3 terms; allow sign errors and allow sin/cos mix. (P + 5sin60 - 10sin30 = 0)
[A1] Must be positive. (P = 5 - 5√3/2 or 0.670 [0.66987...])
[M1] For resolving in direction of Q. 3 terms; allow sign errors and allow sin/cos mix. (Q = ±(10cos30 - 5 cos 60))
[A1] Must be positive. (Q = 10√3/2 - 5/2 or 6.16 [6.16025...])

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2025 Paper 4 Variant 1, question 2.

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