| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then solve equation |
| Difficulty | Moderate -0.8 This is a straightforward completing the square question with standard follow-up parts. Part (i) is routine algebraic manipulation, part (ii) is direct recall from the completed square form, and part (iii) is a simple quadratic equation solved using the completed square form. All techniques are standard C1 content with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
$f(x) = 2x^2 - 4x + 1$.
\begin{enumerate}[label=(\roman*)]
\item Find the values of the constants $a$, $b$ and $c$ such that
$$f(x) = a(x + b)^2 + c.$$ [4]
\item State the equation of the line of symmetry of the curve $y = f(x)$. [1]
\item Solve the equation $f(x) = 3$, giving your answers in exact form. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q6 [8]}}