| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Line-curve intersection points |
| Difficulty | Moderate -0.3 This is a straightforward C1 question testing standard techniques: completing the square to show no real roots, solving a quadratic inequality, and finding intersection points. All three parts use routine methods with no novel insight required, though part (iii) involves slightly more algebraic manipulation than typical. Slightly easier than average due to the mechanical nature of the tasks. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
\begin{enumerate}[label=(\roman*)]
\item Show that the graph of $y = x^2 - 3x + 11$ is above the $x$-axis for all values of $x$. [3]
\item Find the set of values of $x$ for which the graph of $y = 2x^2 + x - 10$ is above the $x$-axis. [4]
\item Find algebraically the coordinates of the points of intersection of the graphs of
$$y = x^2 - 3x + 11 \quad\text{and}\quad y = 2x^2 + x - 10.$$ [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q12 [12]}}