| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Factorise then sketch |
| Difficulty | Moderate -0.8 This is a straightforward C2 curve sketching question involving a quadratic function. Part (a) requires basic substitution and solving a quadratic equation, part (b) is routine sketching, and part (c) involves standard differentiation and solving f'(x)=0. All techniques are procedural with no problem-solving insight required, making it easier than average but not trivial due to the multi-part nature and 8 total marks. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials1.07n Stationary points: find maxima, minima using derivatives |
Given that $f(x) = 15 - 7x - 2x^2$,
\begin{enumerate}[label=(\alph*)]
\item find the coordinates of all points at which the graph of $y = f(x)$ crosses the coordinate axes. [3]
\item Sketch the graph of $y = f(x)$. [2]
\item Calculate the coordinates of the stationary point of $f(x)$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q23 [8]}}