Easy -1.3 This is a straightforward C1 indefinite integration question requiring only direct application of the power rule to three terms. Each term integrates mechanically (x^4, x, x^{-1/2}) with no algebraic manipulation, substitution, or problem-solving needed—purely routine recall of integration formulas.
M1: Some attempt to integrate: \(x^n \to x^{n+1}\) on at least one term (not for \(+c\)). If they think \(\frac{3}{\sqrt{x}}\) is \(3x^{\frac{1}{2}}\) you can still award M1 for \(x^{\frac{1}{2}} \to x^{\frac{3}{2}}\). A1: \(\frac{10x^5}{5}\) and \(\frac{-4x^2}{2}\) or better. A1: \(-\frac{3x^{\frac{1}{2}}}{\frac{1}{2}}\) or better
\(= 2x^5 - 2x^2 - 6x^{\frac{1}{2}} + c\)
A1
Each term correct and simplified and the \(+c\) all appearing together on the same line. Allow \(\sqrt{x}\) for \(x^{\frac{1}{2}}\). Ignore any spurious integral or signs and/or \(dy/dx\)'s.
Total: [4]
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int = \frac{10x^5}{5} - \frac{4x^2}{2} - \frac{3x^{\frac{1}{2}}}{\frac{1}{2}}$ | M1A1, A1 | M1: Some attempt to integrate: $x^n \to x^{n+1}$ on at least one term (not for $+c$). If they think $\frac{3}{\sqrt{x}}$ is $3x^{\frac{1}{2}}$ you can still award M1 for $x^{\frac{1}{2}} \to x^{\frac{3}{2}}$. A1: $\frac{10x^5}{5}$ **and** $\frac{-4x^2}{2}$ or better. A1: $-\frac{3x^{\frac{1}{2}}}{\frac{1}{2}}$ or better |
| $= 2x^5 - 2x^2 - 6x^{\frac{1}{2}} + c$ | A1 | Each term correct and simplified and the $+c$ all appearing together on the same line. Allow $\sqrt{x}$ for $x^{\frac{1}{2}}$. Ignore any spurious integral or signs and/or $dy/dx$'s. |
**Total: [4]**
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