Easy -1.3 This is a straightforward application of the power rule for integration requiring students to rewrite terms in index form and apply standard formulas. It's routine Core 2 material with no problem-solving element—purely procedural integration of four separate terms with basic algebraic simplification.
cao: All four terms correct simplified with constant of integration on single line
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Attempt to integrate $f(x)$ — one power increased $x^n \to x^{n+1}$ | M1 | At least one power increased |
| $\int(3x^2 + x - 4x^{-\frac{1}{2}} + 6x^{-3})dx = \frac{3x^3}{3} + \frac{x^2}{2} - \frac{4x^{\frac{1}{2}}}{\frac{1}{2}} + \frac{6x^{-2}}{-2}(+c)$ | A1 | Two of four terms correct unsimplified |
| | A1 | Three terms correct (may be unsimplified) |
| | A1 | All four terms correct (may be unsimplified) on single line |
| $= x^3 + \frac{x^2}{2} - 8x^{\frac{1}{2}} - 3x^{-2} + c$ | A1 | cao: All four terms correct simplified with constant of integration on single line |
---