| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Topic | Modulus function |
| Type | Find range of k for number of roots |
| Difficulty | Moderate -0.8 This is a straightforward modulus function question requiring basic understanding of absolute value graphs. Part (a) is direct reading from the graph, part (b) involves solving a linear equation in two cases (standard modulus technique), and part (c) requires identifying where a horizontal line intersects the V-shaped graph twice. All parts are routine applications of modulus function properties with no novel problem-solving required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
\includegraphics{figure_2}
Figure 2 shows a sketch of part of the graph $y = f(x)$, where
$$f(x) = 2|3 - x| + 5, \quad x \geq 0$$
\begin{enumerate}[label=(\alph*)]
\item State the range of $f$
[1]
\item Solve the equation
$$f(x) = \frac{1}{2}x + 30$$
[3]
Given that the equation $f(x) = k$, where $k$ is a constant, has two distinct roots,
\item state the set of possible values for $k$.
[2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q9 [6]}}