| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial intersection with algebra |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing basic curve intersection (solving a quadratic equation), sketching parabolas, and shading regions defined by inequalities. All techniques are routine for AS-level with no problem-solving insight required, making it easier than average but not trivial due to the multiple components. |
| Spec | 1.02i Represent inequalities: graphically on coordinate plane1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations |
The curve $C_1$ has equation $y = -x^2 + 2x + 3$ and the curve $C_2$ has equation $y = x^2 - x - 6$. The two curves intersect at the points $A$ and $B$.
\begin{enumerate}[label=(\alph*)]
\item Determine the coordinates of $A$ and $B$. [4]
\item On the same set of axes, sketch the graphs of $C_1$ and $C_2$. Clearly label the points where the two curves intersect. [3]
\item In the diagram drawn in part (b), shade the region satisfying the following inequalities: [2]
$$x > 0,$$
$$y < -x^2 + 2x + 3,$$
$$y > x^2 - x - 6.$$
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q5 [9]}}