Solve 10 cos²x + 3 sinx = 9 for 0° < x < 360°.

Mark scheme

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

1. [1] (a) 10(1-sin²x) + 3 sin x = 9
2. [1] (a) Solves 10sin²x - 3sinx - 1 = 0 oe
3. [1] (a) Solves their three term quadratic in sin x
4. [1] (a) sin x = 1/2, sin x = -1/5
5. [2] (a) 30°, 150° and 191.5°, 348.5° awrt
6. [1] (a) A1 for any two correct solutions
7. [1] (b) 3 sin(2y)/cos(2y) = 4 sin(2y) oe
8. [1] (b) Solves 3 sin 2y - 4 sin 2y cos 2y [= 0]
9. [1] (b) sin 2y = 0 OR cos 2y = 3/4
10. [1] (b) Any two of π, 0.72273..., 5.56045... nfww
11. [1] (b) π/2, 0.361, 2.78 awrt nfww
12. [1] (b) SC: cancels out sin2y after M1M0 allow SC1 for 0.72273... and 5.56045... and SC1for 0.361 and 2.78