| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2022 |
| Session | February |
| Marks | 10 |
| Topic | Modulus function |
| Type | Sketch y=|linear| and y=linear with unknown constants, then solve |
| Difficulty | Standard +0.3 This is a multi-part question on transformations of modulus functions requiring graph sketching, solving modulus inequalities, and applying function transformations. While it involves several steps, the techniques are standard A-level content (modulus graphs, transformations, solving inequalities) with no novel insight required. The algebraic manipulation is straightforward once the approach is identified, making it slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x) |
\includegraphics{figure_4}
Figure 4
Figure 4 shows a sketch of the graph with equation
$$y = |2x - 3k|$$
where $k$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph with equation $y = f(x)$ where
$$f(x) = k - |2x - 3k|$$
stating
• the coordinates of the maximum point
• the coordinates of any points where the graph cuts the coordinate axes
[4]
\item Find, in terms of $k$, the set of values of $x$ for which
$$k - |2x - 3k| > x - k$$
giving your answer in set notation.
[4]
\item Find, in terms of $k$, the coordinates of the minimum point of the graph with equation
$$y = 3 - 5f\left(\frac{1}{2}x\right)$$
[2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Mechanics 2022 Q10 [10]}}