| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |f(x)| compared to |g(x)| with parameters: equation or inequality only |
| Difficulty | Moderate -0.3 This question involves sketching standard graphs (absolute value and reciprocal), interpreting their intersection graphically, and solving a straightforward absolute value equation by cases. While it requires understanding of transformations and modulus functions, the techniques are routine A-level material with no novel problem-solving required. The case-work in part (c) is mechanical once the modulus is understood, making this slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02s Modulus graphs: sketch graph of |ax+b| |
\begin{enumerate}[label=(\alph*)]
\item Sketch, on a single diagram, the following graphs.
\begin{itemize}
\item $y = |x - 1|$
\item $y = \frac{k}{x}$, where $k$ is a negative constant
\end{itemize} [2]
\item Hence explain why the equation $x|x - 1| = k$ has exactly one real root for any negative value of $k$. [1]
\item Determine the real root of the equation $x|x - 1| = -6$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2021 Q4 [5]}}