| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Quadratic with equal roots |
| Difficulty | Easy -1.3 This is a straightforward completing-the-square question with standard follow-ups. Part (a) is a routine algebraic manipulation, part (a)(ii) requires only reading the completed square form, and part (b) tests basic understanding that equal roots occur at the vertex. All parts are textbook exercises requiring recall of standard techniques with no problem-solving or novel insight. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Express $x^2 - 8x + 11$ in the form $(x - a)^2 + b$ where $a$ and $b$ are constants. [2]
\item Hence write down the minimum value of $x^2 - 8x + 11$. [1]
\end{enumerate}
\item Determine the value of the constant $k$ for which the equation $x^2 - 8x + 11 = k$ has two equal roots. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2023 Q1 [5]}}