| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing standard AS-level skills: sketching a quadratic (factorising or using the formula), reading off an inequality from the graph, and using the discriminant condition. All parts follow routine procedures with no problem-solving insight required, making it easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
7
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = 2 x ^ { 2 } - x - 3$.
\item Hence, or otherwise, solve $2 x ^ { 2 } - x - 3 < 0$.
\item Given that the equation $2 x ^ { 2 } - x - 3 = k$ has no real roots, find the set of possible values of k .
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q7 [8]}}