A-LevelMathematicsDifferentiation9709/33 · May/June 2022 · Q68 Marks
The parametric equations of a curve are x = 1/cos t, y = ln tan t, where 0 < t < ½π.
- (a)Show that dy/dx = cos t / sin² t.[5]
- (b)Find the equation of the tangent to the curve at the point where y = 0.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [M1] Use chain rule at least once
- [A1] Obtain dx/dt = sec t tan t
- [A1] Obtain dy/dt = sec² t / tan t
- [M1] Use dy/dx = dy/dt ÷ dx/dt
- [A1] Obtain given answer cos t / sin² t
- [B1] State or imply t = ¼π when y = 0
- [M1] Form the equation of the tangent at y = 0 or find c
- [A1] Obtain answer y = √2 x – 2
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