| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Areas by integration |
| Type | Area involving absolute values |
| Difficulty | Standard +0.8 This question requires understanding of modulus function transformations, careful case analysis for absolute value equations (splitting into 4 cases based on signs), and algebraic manipulation. While the sketching is relatively standard, solving the equation systematically requires methodical reasoning beyond routine procedures, placing it moderately above average difficulty for C3. |
| 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 |
\begin{enumerate}[label=(\roman*)]
\item Sketch on the same diagram the graphs of $y = |x| - a$ and $y = |3x + 5a|$, where $a$ is a positive constant.
Show on your diagram the coordinates of any points where each graph meets the coordinate axes. [5]
\item Solve the equation
$$|x| - a = |3x + 5a|.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [9]}}