The parametric equations of a curve are x = tan²2t, y = cos 2t, for 0 < t < ¼π.

Mark scheme

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

1. [M1] Use correct product rule or chain rule to find derivative of x with respect to t
2. [A1] Obtain dx/dt = 4 tan 2t sec² 2t oe
3. [B1] Obtain dy/dt = -2 sin 2t
4. [B1] Use dy/dx = (dy/dt) / (dx/dt) to obtain given answer dy/dx = -½ cos³ 2t
5. [B1] Obtain x = 1 and y = √2/2
6. [B1] State or imply gradient of tangent is -√2/8 or gradient of normal is 4√2
7. [M1] Use correct method to find equation of normal using their values
8. [A1] Obtain equation of normal is y = 4√2x - 7√2/2 or equivalent 3 term equation