The parametric equations of a curve are x = 3 sin 2θ, y = 1 + 2 tan 2θ, for 0 ≤ θ < π/4.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [B1] Obtain dx/dθ = 6cos 2θ
2. [B1] Obtain dy/dθ = 4 sec² 2θ
3. [M1] Divide dy/dθ by dx/dθ with θ equated to π/6
4. [A1] Obtain 4/9 or exact equivalent
5. [*M1] Equate expression for dy/dx to 2 with only one trigonometry ratio used (Either cos 2θ or sec 2θ)
6. [A1] Obtain cos³ 2θ = 1/3 or sec³ 2θ = 3
7. [DM1] Attempt correct steps to find a value of θ from cos³ 2θ = m, 0 < m < 1
8. [A1] Obtain θ = 0.402 and no others within the range (AWRT, SC: Allow FT if dx/dθ = 3cos 2θ and dy/dθ = 2 sec² 2θ)