| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Moderate -0.8 This is a straightforward integration question requiring students to integrate a linear function and use a point to find the constant, followed by solving a simple quadratic equation. Both parts are routine C2 techniques with no conceptual challenges beyond basic integration and substitution. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
2 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x - 4$. The curve passes through the distinct points ( 2,5 ) and ( $p , 5$ ).\\
(i) Find the equation of the curve.\\
(ii) Find the value of $p$.
\hfill \mbox{\textit{OCR C2 2010 Q2 [7]}}