| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing routine completing the square technique, reading minimum from completed square form, finding intercepts by factoring/substitution, and solving a linear equation from equating two quadratics. All parts are standard textbook exercises requiring only direct application of learned procedures with no problem-solving insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials |
\begin{enumerate}[label=(\roman*)]
\item Write $x^2 - 7x + 6$ in the form $(x - a)^2 + b$. [3]
\item State the coordinates of the minimum point on the graph of $y = x^2 - 7x + 6$. [2]
\item Find the coordinates of the points where the graph of $y = x^2 - 7x + 6$ crosses the axes and sketch the graph. [5]
\item Show that the graphs of $y = x^2 - 7x + 6$ and $y = x^2 - 3x + 4$ intersect only once. Find the $x$-coordinate of the point of intersection. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2006 Q11 [13]}}