| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |linear| < |linear| |
| Difficulty | Moderate -0.3 Part (a) requires solving an absolute value inequality by considering cases (x < 2, 2 ≤ x < 3, x ≥ 3), which is a standard A-level technique but involves careful algebraic manipulation. Part (b) tests understanding of transformations of modulus functions, requiring recognition that |2x - 6| = 2|x - 3| and identifying the horizontal translation and vertical stretch. Both parts are routine applications of core techniques with no novel insight required, making this slightly easier than average. |
| Spec | 1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07n Stationary points: find maxima, minima using derivatives1.08i Integration by parts1.09d Newton-Raphson method1.09f Trapezium rule: numerical integration |
\begin{enumerate}[label=(\alph*)]
\item In this question you must show detailed reasoning.
Solve the inequality $|x - 2| \leqslant |2x - 6|$. [4]
\item Give full details of a sequence of two transformations needed to transform the graph of $y = |x - 2|$ to the graph of $y = |2x - 6|$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2019 Q3 [7]}}