A-LevelMathematicsMechanics9709/42 · Feb/Mar 2018 · Q24 Marks

The three coplanar forces shown in the diagram are in equilibrium.

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

[M1] (EITHER) Resolve vertically (2 terms): 2P sin θ = P sin 60
[A1] θ = 25.7
[M1] Resolve horizontally (3 terms): 2P cos θ + P cos 60 = 10
[A1] P = 4.34
(M1) (OR1) Attempt Lami's theorem using one pair of terms (e.g., 2P / sin 120 = P / sin(180-θ) = 10 / sin(60+θ))
(A1) Solve for θ = 25.7
(M1) Use a second Lami equation
(A1) P = 4.34
(M1) (OR2) Use sine or cosine rule with triangle of forces using forces P, 2P and 10 and with angles 60, θ and 120 – θ between
(A1) θ = 25.7
(M1) Use a second relationship from the triangle of forces
(A1) P = 4.34

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Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Feb/Mar 2018 Paper 4 Variant 2, question 2.

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