| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find tangent at given point (polynomial/algebraic) |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing basic differentiation (sum rule and exponential), finding a tangent line equation at a given point, and calculator work to complete a table. All parts are routine C3 techniques with no problem-solving or insight required, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07m Tangents and normals: gradient and equations |
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(\sqrt{x + \frac{e^x}{5}}\) | 0.45 | 0.91 |
f(x) = $x + \frac{e^x}{5}$, $x \in \mathbb{R}$.
\begin{enumerate}[label=(\alph*)]
\item Find f'(x). [2]
\end{enumerate}
The curve $C$, with equation $y = $f(x), crosses the $y$-axis at the point $A$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find an equation for the tangent to $C$ at $A$. [3]
\item Complete the table, giving the values of $\sqrt{x + \frac{e^x}{5}}$ to 2 decimal places.
\end{enumerate}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & 0 & 0.5 & 1 & 1.5 & 2 \\
\hline
$\sqrt{x + \frac{e^x}{5}}$ & 0.45 & 0.91 & & & \\
\hline
\end{tabular}
[2]
\hfill \mbox{\textit{Edexcel C3 Q7 [7]}}