(a) (i) Write 6xy+3y+4x+2 in the form (ax+b)(cy+d), where a, b, c and d are positive integers. (ii) Hence solve the equation 6 sin θ cos θ+3 cos θ+4 sin θ+2 = 0 for 0^(°) < θ < 360^(°). (b) Solve the equation 1/2 sec(2φ+π/4)=1/√3 for -π < φ < π, where φ is in radians. Give your answers in terms of π.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] B1
2. [4] M1 For relating to part (i) and a correct attempt to obtain cosθ =... or sinθ = ...
3. [4] M1 for solving one of the equations to obtain one correct solution
4. [4] A1 for any two correct solutions
5. [4] A1 for a further two correct solutions with no extra solutions within the range
6. [5] B1
7. [5] M1 for solving to obtain one correct positive solution
8. [5] M1 for solving to obtain one correct negative solution
9. [5] A1 for any two correct solutions
10. [5] A1 for a further two correct solutions with no extra solutions within the range