| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Single transformation sketch |
| Difficulty | Standard +0.3 This question tests understanding of even functions and basic algebraic manipulation. Part (a) requires sketching using symmetry properties (routine for C3), part (b) involves direct substitution and applying the even function property f(-x)=f(x), and part (c) is a straightforward quadratic equation. All components are standard textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
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 $y = \text{f}(x)$, 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 Q3 [9]}}