A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2023 · Q66 Marks
The parametric equations of a curve are x = √t + 3, y = ln t, for t > 0.
- (a)Obtain a simplified expression for dy/dx in terms of t.[3]
- (b)Hence find the exact coordinates of the point on the curve at which the gradient of the normal is -2.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [B1] (a) State correct derivative of x or y with respect to t dx/dt = 1/(2√t), dy/dt = 1/t
- [M1] (a) Use dy/dx = (dy/dt) x (dt/dx) Use correct chain rule.
- [A1] (a) Obtain answer dy/dx = 2/√t Or simplified equivalent e.g. 2t⁻¹/² or 2√t / t.
- [M1] (b) State or imply their dy/dx = 1/2
- [A1] (b) Obtain √t = 4 Or equivalent.
- [A1] (b) Obtain answer (7, ln 16) Or exact equivalent. Can state the two components separately.
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