A-LevelMathematicsMechanics9709/41 · May/June 2024 · Q27 Marks

Two forces of magnitudes 20N and FN act at a point P in the directions shown in the diagram. [Figure 2.1]

(a)Given that the resultant force has no component in the y-direction, calculate the value of F.[2]
(b)Given instead that F = 10, find the magnitude and direction of the resultant force.[5]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[M1] Attempt to resolve in y-direction; 2 terms; must be 20 cos 60 or 20 sin 60 and must be linked to F (can be implied by the correct answer seen only).
[A1] AWRT 17.3 (17.320508...) or 10√3.
[*M1] Correct number of terms; allow sin/cos mix; allow sign errors.
[A1] For both correct.
[DM1] OE - correct number of terms.
[DM1] OE (e.g. reciprocal) - correct number of terms.
[A1] OE for direction e.g. 36.2° anticlockwise from (positive) x-direction, 36.2° above the horizontal. Possibly seen on a diagram. (Radians: 0.63191... to 3sf or better)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.