Easy -1.3 This is a straightforward C1 integration question requiring only the power rule applied to three terms with simple coefficients. It's routine recall with no problem-solving, conceptual challenges, or multi-step reasoning—purely mechanical application of ∫x^n dx = x^(n+1)/(n+1) + c.
M1 for some attempt to integrate a term in \(x\): \(x^n \to x^{n+1}\); 1st A1 for correct possibly unsimplified \(x^4\) or \(x^{\frac{3}{2}}\) term
\(= 2x^4 + 4x^{\frac{3}{2}}, -5x + c\)
A1 A1
2nd A1 for both \(2x^4\) and \(4x^{\frac{3}{2}}\) correct and simplified on same line; 3rd A1 for \(-5x+c\), accept \(-5x^1+c\); \(+c\) must appear on same line as \(-5x\)
Note: \(4\sqrt{x^3}\) or \(4x^{1\frac{1}{2}}\) fine for A1; ignore ISW if correct answer followed by incorrect version; condone poor notation e.g. \(\int 2x^4 + 4x^{\frac{3}{2}} - 5x + c\) scores full marks
Total
4
## Question 2:
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $\frac{8x^4}{4} + \frac{6x^{\frac{3}{2}}}{\frac{3}{2}} - 5x + c$ | M1 A1 | M1 for some attempt to integrate a term in $x$: $x^n \to x^{n+1}$; 1st A1 for correct possibly unsimplified $x^4$ or $x^{\frac{3}{2}}$ term |
| $= 2x^4 + 4x^{\frac{3}{2}}, -5x + c$ | A1 A1 | 2nd A1 for both $2x^4$ and $4x^{\frac{3}{2}}$ correct and simplified on same line; 3rd A1 for $-5x+c$, accept $-5x^1+c$; $+c$ must appear on same line as $-5x$ |
| | | Note: $4\sqrt{x^3}$ or $4x^{1\frac{1}{2}}$ fine for A1; ignore ISW if correct answer followed by incorrect version; condone poor notation e.g. $\int 2x^4 + 4x^{\frac{3}{2}} - 5x + c$ scores full marks |
| **Total** | **4** | |