Easy -1.8 This is a straightforward application of the power rule for differentiation requiring only direct recall of a basic formula. It's a single-step C1 question with no problem-solving element, making it significantly easier than average A-level questions.
\(x^4 \to kx^3\) or \(x^{1/3} \to kx^{-2/3}\) or \(3 \to 0\) (\(k\) a non-zero constant)
M1
\(\frac{dy}{dx} = 4x^3\ldots\) with '3' differentiated to zero (or 'vanishing')
A1
1st A1 requires \(4x^3\), and 3 differentiated to zero; having '+C' loses the 1st A mark
\(\frac{dy}{dx} = \ldots + \frac{1}{3}x^{-2/3}\) or equivalent e.g. \(\frac{1}{3\sqrt[3]{x^2}}\) or \(\frac{1}{3(\sqrt[3]{x})^2}\)
A1
Terms not added, but otherwise correct e.g. \(4x^3\), \(\frac{1}{3}x^{-2/3}\) loses the 2nd A mark
Total: [3]
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^4 \to kx^3$ or $x^{1/3} \to kx^{-2/3}$ or $3 \to 0$ ($k$ a non-zero constant) | M1 | |
| $\frac{dy}{dx} = 4x^3\ldots$ with '3' differentiated to zero (or 'vanishing') | A1 | 1st A1 requires $4x^3$, and 3 differentiated to zero; having '+C' loses the 1st A mark |
| $\frac{dy}{dx} = \ldots + \frac{1}{3}x^{-2/3}$ or equivalent e.g. $\frac{1}{3\sqrt[3]{x^2}}$ or $\frac{1}{3(\sqrt[3]{x})^2}$ | A1 | Terms not added, but otherwise correct e.g. $4x^3$, $\frac{1}{3}x^{-2/3}$ loses the 2nd A mark |
**Total: [3]**
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