| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Basic factored form sketching |
| Difficulty | Standard +0.3 This question tests understanding of even functions and basic curve sketching with straightforward algebraic manipulation. Part (a) requires recognizing that an even function is symmetric about the y-axis and sketching a parabola for x≥0 then reflecting it. Parts (b) and (c) involve direct substitution and solving a quadratic equation. While it requires multiple concepts (even functions, symmetry, solving quadratics), each step is routine with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02m Graphs of functions: difference between plotting and sketching |
The function $f$ is even and has domain $\mathbb{R}$. For $x \geq 0$, $f(x) = x^2 - 4ax$, where $a$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item In the space below, sketch the curve with equation $y = f(x)$, showing the coordinates of all the points at which the curve meets the axes. [3]
\item Find, in terms of $a$, the value of $f(2a)$ and the value of $f(-2a)$. [2]
\end{enumerate}
Given that $a = 3$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item use algebra to find the values of $x$ for which $f(x) = 45$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q34 [9]}}