| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Prove quadratic always positive/negative |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing standard techniques: solving simultaneous equations by substitution, completing the square, and using the completed square form to identify the minimum value. All parts are routine textbook exercises requiring only direct application of methods with no problem-solving insight needed. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
\begin{enumerate}[label=(\roman*)]
\item Find algebraically the coordinates of the points of intersection of the curve $y = 3x^2 + 6x + 10$ and the line $y = 2 - 4x$. [5]
\item Write $3x^2 + 6x + 10$ in the form $a(x + b)^2 + c$. [4]
\item Hence or otherwise, show that the graph of $y = 3x^2 + 6x + 10$ is always above the $x$-axis. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q1 [11]}}