Easy -1.2 This is a straightforward C1 integration question requiring only direct application of the power rule to three terms. It's routine recall with no problem-solving, simpler than average A-level questions but not trivial since it includes a fractional power.
For either \(\frac{6}{3}x^3\) or \(\frac{x^{\frac{1}{2}}}{\frac{1}{2}}\) or better
A1
For one correct term
\(= 2x^3 + 2x + 2x^{\frac{1}{2}}\)
A1
For all terms in \(x\) correct. Allow \(2\sqrt{x}\) and \(2x^1\)
\(+c\)
B1
For \(+c\), when first seen with a changed expression
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{6x^3}{3} + 2x + \frac{x^{\frac{1}{2}}}{\frac{1}{2}}$ | M1 | For some attempt to integrate $x^n \to x^{n+1}$ |
| For either $\frac{6}{3}x^3$ or $\frac{x^{\frac{1}{2}}}{\frac{1}{2}}$ or better | A1 | For one correct term |
| $= 2x^3 + 2x + 2x^{\frac{1}{2}}$ | A1 | For all terms in $x$ correct. Allow $2\sqrt{x}$ and $2x^1$ |
| $+c$ | B1 | For $+c$, when first seen with a changed expression |
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