| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Moderate -0.3 This is a straightforward integration question requiring students to integrate a simple expression, apply an initial condition to find the constant, then substitute x=4. The integration is routine (power rule only), and the algebraic manipulation is minimal. Slightly easier than average due to its mechanical nature, though the fractional powers require care. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums |
Given that
$$\frac{dy}{dx} = 3\sqrt{x} - x^2,$$
and that $y = \frac{4}{3}$ when $x = 1$, find the value of $y$ when $x = 4$. [7]
\hfill \mbox{\textit{OCR C2 Q3 [7]}}