| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find tangent given derivative expression |
| Difficulty | Moderate -0.3 This is a straightforward C1 question requiring basic integration and tangent line calculation. Part (a) involves substituting x=4 into the given derivative to find the gradient, then using point-slope form. Part (b) requires integrating a polynomial and x^(-1/2) term, then finding the constant using the given point. Both parts are standard textbook exercises with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08b Integrate x^n: where n != -1 and sums |
7. The point $P ( 4 , - 1 )$ lies on the curve $C$ with equation $y = \mathrm { f } ( x ) , x > 0$, and
$$f ^ { \prime } ( x ) = \frac { 1 } { 2 } x - \frac { 6 } { \sqrt { } x } + 3$$
\begin{enumerate}[label=(\alph*)]
\item Find the equation of the tangent to $C$ at the point $P$, giving your answer in the form $y = m x + c$, where $m$ and $c$ are integers.
\item Find $\mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2012 Q7 [8]}}