| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Pure definite integration |
| Difficulty | Moderate -0.8 This is a straightforward integration question testing basic techniques. Part (i) requires standard power rule integration including rewriting 1/√x as x^(-1/2). Part (ii) involves expanding a quadratic and integrating with definite limits. Both parts are routine C2 exercises requiring only direct application of learned rules with no problem-solving or insight needed, making this easier than average. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits |
| Answer | Marks |
|---|---|
| \(= \frac{1}{2}x^2 + 5x + 6x^2 + c\) | M1 A3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(= \int_{-2}^{0} (9x^2 - 6x + 1) \, dx\) | M1 | |
| \(= [3x^3 - 3x^2 + x]_{-2}^{0}\) | M1 A1 | |
| \(= (0) - (-24 - 12 - 2) = 38\) | M1 A1 | (9) |
## (i)
$= \frac{1}{2}x^2 + 5x + 6x^2 + c$ | M1 A3 |
## (ii)
$= \int_{-2}^{0} (9x^2 - 6x + 1) \, dx$ | M1 |
$= [3x^3 - 3x^2 + x]_{-2}^{0}$ | M1 A1 |
$= (0) - (-24 - 12 - 2) = 38$ | M1 A1 | (9)
---\begin{enumerate}[label=(\roman*)]
\item Find
$$\int \left( x + 5 + \frac{3}{\sqrt{x}} \right) dx.$$ [4]
\item Evaluate
$$\int_{-2}^{0} (3x - 1)^2 dx.$$ [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q7 [9]}}