| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2015 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Curve from derivative information |
| Difficulty | Standard +0.3 This is a straightforward multi-part integration and curve sketching question requiring standard techniques: finding a tangent equation using the given gradient, integrating to find the curve equation with a boundary condition, finding roots and minimum via differentiation, and applying a horizontal stretch transformation. While it has multiple parts, each step follows routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.07m Tangents and normals: gradient and equations1.07n Stationary points: find maxima, minima using derivatives1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
10 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 4 x + 3$. The curve passes through the point ( 2,9 ).\\
(i) Find the equation of the tangent to the curve at the point $( 2,9 )$.\\
(ii) Find the equation of the curve and the coordinates of its points of intersection with the $x$-axis. Find also the coordinates of the minimum point of this curve.\\
(iii) Find the equation of the curve after it has been stretched parallel to the $x$-axis with scale factor $\frac { 1 } { 2 }$. Write down the coordinates of the minimum point of the transformed curve.
\hfill \mbox{\textit{OCR MEI C2 2015 Q10 [13]}}