June 2024 Paper 1 Q5
5
\[y = \frac{4x^3 + x^7}{x^4}\]Work out \(\quad \dfrac{\mathrm{d}y}{\mathrm{d}x}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(4x^{-1}\) or \(\dfrac{4}{x}\) or \(x^3\) | M1 | either term correct (ignore additional terms) |
| \(-4x^{-2}\) or \(3x^2\) | A1 | a correct term differentiated correctly (must be just two terms before differentiation) accept \(-\dfrac{4}{x^2}\) |
| \(\left(\dfrac{\mathrm{d}y}{\mathrm{d}x} =\right) -4x^{-2} + 3x^2\) | A1 | both terms correct accept \(-\dfrac{4}{x^2}\) |
Additional guidance
| Quotient rule or product rule used to achieve correct simplified answer | M1A2 |
| Quotient rule or product rule used with incorrect or unsimplified answer | M0A0 |
| \(\dfrac{-4 + 3x^4}{x^2}\) | M1A2 |
| Penalise additional incorrect further working eg \(\dfrac{-1}{4x^2}\) for the final A mark |