| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Quadratic with equal roots |
| Difficulty | Easy -1.2 Both parts are straightforward applications of standard techniques: (i) uses the discriminant condition b²-4ac=0 for repeated roots, requiring simple substitution and arithmetic; (ii) is a routine quadratic inequality solved by factorizing and testing regions. These are textbook exercises testing basic recall with minimal problem-solving, making them easier than average A-level questions. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
\begin{enumerate}[label=(\roman*)]
\item The equation $x^2 + 3x + k = 0$ has repeated roots. Find the value of the constant $k$. [2]
\item Solve the inequality $6 + x - x^2 > 0$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q2 [4]}}