4MA0 Higher June 2017 Paper 4 Q17
17 Curve C has equation \(y = 8x^3 - 3x^2 - 25x\)
(a) Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\) (2)
(b) Find the \(x\) coordinates of the points on C where the gradient is 5
Show clear algebraic working. (4)
Show clear algebraic working. (4)
| Scheme | Marks |
|---|---|
| M1 | |
| \(24x^2 - 6x - 25\) | A1 |
| (2) |
Notes
M1: for 2 correct from \(3 \times 8x^2\), \(-3 \times 2x\), \(-25\)
A1: fully correct
| Scheme | Marks |
|---|---|
| \(24x^2 - 6x - 25 = 5\) | M1 |
| \(24x^2 - 6x - 30\;(= 0)\) or \(4x^2 - x - 5\;(= 0)\) or \(12x^2 - 3x - 15\;(= 0)\) | M1 |
\((4x - 5)(6x + 6)\;(=0)\) or \((4x - 5)(x + 1)\;(= 0)\) \((4x - 5)(3x + 3)\;(= 0)\) or \(\dfrac{--1 \pm \sqrt{(-1)^2 - 4 \times 4 \times -5}}{2 \times 4}\) | M1 |
| 1.25 oe, −1 | A1 |
| (4) | |
| (6 marks) |
Notes
M1: ft from (a)
M1: ft from (a) for a 3 term quadratic with no coefficients of zero
M1: ft from (a) for a 3 term quadratic with no coefficients of zero.
If using quadratic formula some simplification may be seen.
A1: cao dep on M1
[ignore attempts to work out y values]