A-LevelMathematicsMechanics9709/41 · May/June 2025 · Q14 Marks

A block of mass 12kg is being pulled by a rope up a rough plane. The plane is inclined at an angle of 20° above the horizontal. The rope pulling the block is parallel to a line of greatest slope of the plane. The coefficient of friction between the block and the plane is 0.4. The acceleration of the block is 2ms⁻².

Mark scheme

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

[B1] R = 12g cos 20 (112.7631145.)
[*M1] For use of N2L with 4 terms. Allow sign errors. Allow sin/cos mix. Allow g missing. Allow with their Friction or just F. (T - F - 12g sin 20 = 12 × 2)
[DM1] Use of F=0.4R where R is a component of weight, to get an equation in T only. (T - 0.4x12g cos 20 - 12g sin 20 = 12×2 [T - 45.1052... - 41.0424.... = 24])
[A1] AWRT 110 CWO. (Tension = 110 N [110.147...])

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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 1.

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