| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| 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 multi-part question covering standard C1 techniques: factorising a quadratic (routine), sketching from factorised form (straightforward), using the discriminant (direct recall), and solving a quadratic by completing the square or formula (standard procedure). While it has 12 marks total and requires multiple techniques, each individual part is textbook-standard with no novel insight required, making it slightly easier than the average A-level question. |
| 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 polynomials1.02q Use intersection points: of graphs to solve equations |
\begin{enumerate}[label=(\roman*)]
\item Solve, by factorising, the equation $2x^2 - x - 3 = 0$. [3]
\item Sketch the graph of $y = 2x^2 - x - 3$. [3]
\item Show that the equation $x^2 - 5x + 10 = 0$ has no real roots. [2]
\item Find the $x$-coordinates of the points of intersection of the graphs of $y = 2x^2 - x - 3$ and $y = x^2 - 5x + 10$. Give your answer in the form $a \pm \sqrt{b}$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2010 Q10 [12]}}