| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Discriminant for real roots condition |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing standard AS-level techniques: discriminant for no real roots (routine application of b²-4ac < 0), solving a quadratic-linear intersection (standard algebraic manipulation), and sketching graphs using found information. All parts are textbook exercises requiring only direct application of well-practiced methods with no problem-solving insight needed. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
\begin{enumerate}[label=(\alph*)]
\item Find the range of values of $k$ for which the quadratic equation $x^2 - kx + 4 = 0$ has no real roots. [4]
\item Determine the coordinates of the points of intersection of the graphs of $y = x^2 - 3x + 4$ and $y = x + 16$. [4]
\item Using the information obtained in parts (a) and (b), sketch the graphs of $y = x^2 - 3x + 4$ and $y = x + 16$ on the same set of axes. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q16 [10]}}