| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indefinite & Definite Integrals |
| Type | Curve properties and tangent/normal |
| Difficulty | Moderate -0.8 This is a straightforward C1 integration question requiring standard power rule integration, using a boundary condition to find the constant, then finding a normal equation. All techniques are routine with no problem-solving insight needed, making it easier than average but not trivial due to the fractional powers and multiple steps. |
| Spec | 1.07m 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 |
10. A curve with equation $y = \mathrm { f } ( x )$ passes through the point (4,25).
Given that
$$f ^ { \prime } ( x ) = \frac { 3 } { 8 } x ^ { 2 } - 10 x ^ { - \frac { 1 } { 2 } } + 1 , \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item find $\mathrm { f } ( x )$, simplifying each term.
\item Find an equation of the normal to the curve at the point ( 4,25 ).
Give your answer in the form $a x + b y + c = 0$, where $a$, $b$ and $c$ are integers to be found.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q10 [10]}}