| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| 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 completing the square exercise followed by routine curve sketching. Part (a) requires a standard algebraic manipulation (completing the square), and part (b) involves identifying the vertex from completed square form and finding axis intercepts by substitution. These are textbook procedures with no problem-solving or novel insight required, making it easier than average but not trivial since it requires multiple steps and careful execution. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
\begin{enumerate}[label=(\alph*)]
\item Express $x^2 - 10x + 27$ in the form $(x + p)^2 + q$. [3]
\item Sketch the curve with equation $y = x^2 - 10x + 27$, showing on your sketch
\begin{enumerate}[label=(\roman*)]
\item the coordinates of the vertex of the curve,
\item the coordinates of any points where the curve meets the coordinate axes. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q3 [6]}}