November 2021 Paper 1 Q2
2
\[y = x(2x^4 - 7x^3)\]Work out an expression for the rate of change of \(y\) with respect to \(x\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(2x^5 - 7x^4\) | M1 | |
| \(10x^4\) or \((-)\ 28x^3\) | M1 | oe eg \(5 \times 2x^{5-1}\) |
| \(\left(\dfrac{\mathrm{d}y}{\mathrm{d}x} =\right)\ 10x^4 - 28x^3\) with no additional terms | A1 | do not award for \(y =\) or \(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2} =\) on the answer line SC2 \(2x^4 - 7x^3 + 8x^4 - 21x^3\) SC1 \(2x^4 - 7x^3 + x(8x^3 - 21x^2)\) |
Additional guidance
| Allow \(y = \ldots\) for M marks but must be recovered for A1 | |
| \(\left(\dfrac{\mathrm{d}y}{\mathrm{d}x} =\right)\ 10x^4 - 28x^3 + c\) | M2A0 |