| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2023 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch two |linear| functions and solve related equation/inequality |
| Difficulty | Moderate -0.3 Part (a) is trivial algebra (equating two linear functions). Part (b) requires sketching modulus functions and finding intersections, which is standard A-level content. Part (c) involves calculating area between modulus graphs using integration or geometry, requiring careful consideration of regions but following routine methods. The 10-mark total and multi-step nature elevate it slightly, but all techniques are standard textbook exercises with no novel insight required. |
| Spec | 1.02i Represent inequalities: graphically on coordinate plane1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b| |
\begin{enumerate}[label=(\alph*)]
\item The graphs of $y = 5x - 3$ and $y = 2x + 3$ intersect at the point A. Show that the coordinates of A are $(2, 7)$. [2]
\item On the same set of axes, sketch the graphs of $y = |5x - 3|$ and $y = |2x + 3|$, clearly indicating the coordinates of the points of intersection of the two graphs and the points where the graphs touch the $x$-axis. [4]
\item Calculate the area of the region satisfying the inequalities
$$y \geqslant |5x - 3| \quad \text{and} \quad y \leqslant |2x + 3|.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2023 Q7 [10]}}