| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2023 |
| Session | October |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Find curve equation from derivative |
| Difficulty | Moderate -0.3 This is a straightforward integration problem requiring algebraic simplification of the derivative, followed by routine integration of polynomial terms and application of a boundary condition. Part (a) involves simple substitution and finding a normal line equation. While it requires multiple steps, all techniques are standard P1 procedures with no conceptual challenges or novel insights needed. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums |
\begin{enumerate}
\item The curve $C$ has equation $y = \mathrm { f } ( x )$ where $x > 0$
\end{enumerate}
Given that
\begin{itemize}
\item $f ^ { \prime } ( x ) = \frac { 4 x ^ { 2 } + 10 - 7 x ^ { \frac { 1 } { 2 } } } { 4 x ^ { \frac { 1 } { 2 } } }$
\item the point $P ( 4 , - 1 )$ lies on $C$\\
(a) (i) find the value of the gradient of $C$ at $P$\\
(ii) Hence find the equation of the normal to $C$ at $P$, giving your answer in the form $a x + b y + c = 0$ where $a , b$ and $c$ are integers to be found.\\
(b) Find $\mathrm { f } ( x )$.
\end{itemize}
\hfill \mbox{\textit{Edexcel P1 2023 Q7 [10]}}