June 2024 Paper 2 Q8
8
\[y = \frac{1}{2}x^2 + \frac{3}{4x^4}\]Work out \(\quad \dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}\)
Give your answer in the form \(\quad a + bx^n \quad\) where \(a\), \(b\) and \(n\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(1 + 15x^{-6}\) | B3 | B2 answer \((\ldots +)\ 15x^{-6}\) or answer \((\ldots +)\ \dfrac{15}{x^6}\) or \(x\) and \(-3x^{-5}\) B1 \(x\) or \(-3x^{-5}\) SC2 \(1 - 15x^{-6}\) |
Additional guidance
| Answer must be in the required form | |
| eg \(1 + 15x^{-6}\) in working with answer \(1 + \dfrac{15}{x^6}\) | B2 |
| Accept equivalents for \(x\) eg \(\dfrac{1}{2} \times 2x^{2-1}\) | |
| Accept equivalents for \(-3x^{-5}\) eg \(-\dfrac{3}{x^5}\) or \(\dfrac{3}{4} \times -4 \times x^{-4-1}\) | |
| \(\ldots\) may be incorrect or blank | |
| Condone \(15x^{-6} + 1\) | B3 |
| Condone \(1 + -15x^{-6}\) or \(1 + -\dfrac{15}{x^6}\) | SC2 |
| Condone eg \(y = x - 3x^{-5}\) | B2 |