A-LevelMathematicsDifferentiation9709/31 · May/June 2021 · Q68 Marks
The parametric equations of a curve are x = ln(2 + 3t), y = t / (2 + 3t)
- (a)Show that the gradient of the curve is always positive.[5]
- (b)Find the equation of the tangent to the curve at the point where it intersects the y-axis.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Use correct chain rule or correct quotient rule to differentiate x or y
- [A1 OE] Obtain dx/dt = 3 / (2+3t) or dy/dt = 2 / (2+3t)²
- [M1] Use dy/dx = (dy/dt) ÷ (dx/dt)
- [A1 OE] Obtain answer 2 / (3(2+3t))
- [A1] Explain why this is always positive
- [B1] Obtain y = -1/3 when x = 0
- [M1] Use a correct method to form the given tangent
- [A1 OE] Obtain answer 3y = 2x-1
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