| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Line-curve intersection points |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing standard techniques: simultaneous equations with substitution, completing the square (with coefficient of x² given), and reading off vertex properties. All parts are routine textbook exercises requiring only direct application of learned methods with no problem-solving or insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02q Use intersection points: of graphs to solve equations |
\begin{enumerate}[label=(\roman*)]
\item Find algebraically the coordinates of the points of intersection of the curve $y = 4x^2 + 24x + 31$ and the line $x + y = 10$. [5]
\item Express $4x^2 + 24x + 31$ in the form $a(x + b)^2 + c$. [4]
\item For the curve $y = 4x^2 + 24x + 31$,
\begin{enumerate}[label=(\Alph*)]
\item write down the equation of the line of symmetry, [1]
\item write down the minimum $y$-value on the curve. [1]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2011 Q11 [11]}}