| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Tangent parallel to given line |
| Difficulty | Standard +0.3 This is a straightforward two-part differentiation question requiring chain rule application and solving a cubic equation. While it involves multiple steps (differentiate, find gradient at P, find equation, then solve for Q where gradient matches), each step uses standard techniques with no conceptual challenges beyond typical C3 level. |
| Spec | 1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
3. A curve has the equation $y = ( 3 x - 5 ) ^ { 3 }$.\\
(i) Find an equation for the tangent to the curve at the point $P ( 2,1 )$.
The tangent to the curve at the point $Q$ is parallel to the tangent at $P$.\\
(ii) Find the coordinates of $Q$.\\
\hfill \mbox{\textit{OCR C3 Q3 [7]}}