A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2018 · Q35 Marks
The diagram shows part of the curve y = x(9 – x²) and the line y = 5x, intersecting at the origin O and the point R. Point P lies on the line y = 5x between O and R and the x-coordinate of P is t. Point Q lies on the curve and PQ is parallel to the y-axis.
- (i)Express the length of PQ in terms of t, simplifying your answer.[2]
- (ii)Given that t can vary, find the maximum value of the length of PQ.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] P is (t, 5t)
- [B1] Q is (t, t(9 – t²)) → 4t – t³
- [B1FT] d(PQ)/dt = 4 - 3t²
- [M1] = 0 → t = ±√(2/3)
- [A1] → Maximum PQ = 16/(3√3) or 16√3/9
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →