| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find derivative of simple polynomial (integer powers) |
| Difficulty | Easy -1.3 This is a straightforward C1 differentiation question requiring only basic polynomial differentiation (dy/dx = 2x), substitution to find gradient at a point, using gradient formula between two points, and simple reasoning about intermediate gradients. All parts are routine applications of standard techniques with no problem-solving insight required. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07i Differentiate x^n: for rational n and sums |
6\\
\includegraphics[max width=\textwidth, alt={}, center]{918d83c3-1608-4482-9d3d-8af05e65f353-2_394_846_1868_648}
The diagram shows part of the curve $y = x ^ { 2 } + 5$. The point $A$ has coordinates ( 1,6 ). The point $B$ has coordinates ( $a , a ^ { 2 } + 5$ ), where $a$ is a constant greater than 1 . The point $C$ is on the curve between $A$ and $B$.\\
(i) Find by differentiation the value of the gradient of the curve at the point $A$.\\
(ii) The line segment joining the points $A$ and $B$ has gradient 2.3. Find the value of $a$.\\
(iii) State a possible value for the gradient of the line segment joining the points $A$ and $C$.
\hfill \mbox{\textit{OCR C1 2010 Q6 [7]}}