4MA0 Higher January 2018 Paper 4 Q17
17 The curve C has equation \(y = 2x^3 - 9x^2 + 7\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
The point \(P\) lies on the curve C.
The gradient at point \(P\) of the curve C is \(-\dfrac{27}{2}\)
(b) Find the coordinates of \(P\).
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| \(6x^2 - 18x\) | B2 |
| (2) |
Notes
B2: B1 for \(3 \times 2x^2\) (= \(6x^2\)) or \(-9 \times 2x\) (= \(-18x\))
| Scheme | Marks |
|---|---|
| \(6x^2 - 18x = -\dfrac{27}{2}\) oe | M1 |
| e.g. \((2x \pm 3)(2x \pm 3)\;(= 0)\) or correct substitution into quadratic formula (condone one sign error) | M1 |
| \(x = 1.5\) oe | M1 |
| (1.5, −6.5) oe | A1 |
| (4) |
Notes
M1: ft from (a)
M1: method to solve correct quadratic equation
(terms may not all be ‘on the same side’)
(\(12x^2 - 36x = -27\) or \(4x^2 - 12x + 9\) (=0) or \(6x^2 - 18x + 13.5\) (=0) oe) by factorising or correct substitution into formula
M1: dep on M1 for correct value of \(x\)
A1: dep on correct quadratic equation