| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then find vertex/turning point |
| Difficulty | Easy -1.2 This is a straightforward completing the square exercise with integer coefficients, followed by direct reading of the vertex coordinates. Both parts are routine textbook procedures requiring only standard algebraic manipulation with no problem-solving or conceptual insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
| Answer | Marks | Guidance |
|---|---|---|
| \((x-3)^2\) seen | M1 | e.g. in \((x-3)^2 - 9 + 1\) |
| \((x-3)^2 - 8\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \((3, -8)\) | B1FT | FT their completed square |
# Question 2:
## Part (a)
$(x-3)^2$ seen | M1 | e.g. in $(x-3)^2 - 9 + 1$
$(x-3)^2 - 8$ | A1 |
## Part (b)
$(3, -8)$ | B1FT | FT their completed square
---2
\begin{enumerate}[label=(\alph*)]
\item Express $x ^ { 2 } - 6 x + 1$ in the form $( \mathrm { x } - \mathrm { a } ) ^ { 2 } - \mathrm { b }$, where $a$ and $b$ are integers to be determined.
\item Hence state the coordinates of the turning point on the graph of $y = x ^ { 2 } - 6 x + 1$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2023 Q2 [3]}}