In this question, i is a unit vector due east and j is a unit vector due north. A cyclist rides at a speed of 4ms⁻¹ on a bearing of 015°. Write the velocity vector of the cyclist in the form xi + yj, where x and y are constants.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [B2] 4cos75i + 4sin75j
2. [B1] for x = 4cos75 or x = 4sin15 oe, soi
3. or y=4sin 75 or y = 4cos15 oe, soi
4. or B1 for a correct pair of implicit statements for x and y e.g. both x/4 = sin15 and y/4 = cos15 oe
5. or both x/4 = cos 75 and y/4 = sin 75 oe
6. If 0 scored, SC1 for a correct expression with missing brackets such as √6-√2i +√6+√2j or for (1.04 / 3.86) oe
7. [B1] (-6cos30-2cos40)i +(6sin30 – 2sin40)j or (-6sin60-2sin50)i +(6sin30 -2sin40)j or (-6cos30-2cos40)i +(6cos60 -2cos50)j or (-3√3-1.532...)i+ (3–1.285...)j oe, soi
8. [M1] [r² =] (-6.7282...)² + (1.7144...)² FT their (−6.728... i + 1.714...j)
9. [A1] [r = ] 6.94 or 6.9432329... rot to 4 or more sf dep on B1
10. [M1] α = tan⁻¹(1.7144... / 6.7282...) or awrt 75.7 or β= tan⁻¹(1.7144... / 6.7282...) or awrt 14.3 FT their (−6.728... i + 1.714...j)
11. [A1] 284 or 284.2[95...] rot to 4 or more sf dep on B1