| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2023 |
| Session | October |
| Marks | 5 |
| Topic | Curve Sketching |
| Type | Solve f(x) > g(x) using sketch |
| Difficulty | Easy -1.3 This is a straightforward question requiring a basic sketch of a reciprocal function (standard curve knowledge) and solving a simple rational inequality using either the graph or algebraic manipulation. Both parts are routine A-level techniques with minimal problem-solving demand, making it easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve with equation
$$y = \frac{k}{x} \quad x \neq 0$$
where $k$ is a positive constant. [2]
\item Hence or otherwise, solve
$$\frac{16}{x} \leq 2$$ [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2023 Q7 [5]}}