| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 5 |
| Topic | Curve Sketching |
| Type | Solve f(x) > g(x) using sketch |
| Difficulty | Easy -1.2 Part (a) is a basic sketch of a rectangular hyperbola requiring only recall of standard curve shapes. Part (b) is a straightforward inequality solved by rearranging to x ≥ 8 (considering x > 0) or using the sketch, requiring minimal problem-solving beyond routine algebraic manipulation. This is easier than average A-level content. |
| 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 FM 2024 Q2 [5]}}