| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Stationary points after transformation |
| Difficulty | Standard +0.3 This is a standard C3 transformations question requiring application of well-defined transformation rules to identify new stationary points. Part (a) involves systematic application of modulus and composite transformations, while part (b) requires working backwards from given conditions. The techniques are routine for C3 students who have learned transformation rules, making this slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
| Answer | Marks | Guidance |
|---|---|---|
| (a) (i) Graph showing U-shape with vertex below x-axis, passing through \((-2, -4)\) and \((2, -4)\) | B3 | |
| (ii) Graph showing curve with maximum at \((-\frac{3}{2}, 6)\), minimum at \((1, -12)\) | M2 A2 | |
| (b) \(a = 4, b = 2\) | B2 | (9 marks) |
**(a)** (i) Graph showing U-shape with vertex below x-axis, passing through $(-2, -4)$ and $(2, -4)$ | B3 |
(ii) Graph showing curve with maximum at $(-\frac{3}{2}, 6)$, minimum at $(1, -12)$ | M2 A2 |
**(b)** $a = 4, b = 2$ | B2 | (9 marks)
---5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{de511dda-d00f-4881-94c3-9ee643d10f3f-3_529_806_248_408}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the curve $y = \mathrm { f } ( x )$ which has a maximum point at ( $- 3,2$ ) and a minimum point at $( 2 , - 4 )$.
\begin{enumerate}[label=(\alph*)]
\item Showing the coordinates of any stationary points, sketch on separate diagrams the graphs of
\begin{enumerate}[label=(\roman*)]
\item $y = \mathrm { f } ( | x | )$,
\item $y = 3 \mathrm { f } ( 2 x )$.
\end{enumerate}\item Write down the values of the constants $a$ and $b$ such that the curve with equation $y = a + \mathrm { f } ( x + b )$ has a minimum point at the origin $O$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q5 [9]}}