June 2016 Paper 2 Q6
6 For the curve \(\quad y = \mathrm{f}(x)\),
\[\frac{\mathrm{d}y}{\mathrm{d}x} = \tfrac{3}{2}x - kx^4 + k \qquad \text{where } k \text{ is a constant.}\]When \(\ x = -2\ \) the gradient of the curve is 12
Work out the value of \(k\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{3}{2} \times (-2) - k \times (-2)^4 + k\) or \(-3 - 16k + k\) or \(-3 - 15k\) | M1 | oe Allow missing brackets even if not recovered eg \(\dfrac{3}{2} \times -2 - k \times -2^4 + k\) or \(-3 + 16k + k\) or \(-3 + 17k\) |
| \(-3 - 16k + k = 12\) or \(-3 - 15k = 12\) or \(-15k = 15\) | A1 | oe correct equation (brackets may be recovered) \(\dfrac{3}{2} \times (-2)\) and \((-2)^4\) must be evaluated Implied by \(k = -1\) |
| \(-1\) | A1 | SC2 \(\dfrac{15}{17}\) or 0.88... or 0.9 |
Additional guidance
| \(-1\) with no errors seen (recovered bracket is not an error) | M1 A2 |
| Substituting \(x = 2\) | M0 A0 |