| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Easy -1.2 This is a straightforward completing the square exercise with standard coefficients, followed by a basic explanation about why a squared term is minimized at zero. Both parts require only routine algebraic manipulation and recall of elementary properties of quadratic functions, making it easier than average for A-level. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
| Answer | Marks | Guidance |
|---|---|---|
| \((x+2)^2 + 3\) | B1 for \(b=2\); B1 for \(c=3\) or FT their \(b\) | AO 1.2, 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Since \((x+b)^2 \geq 0\), the minimum value [or minimum point on the curve] occurs when the expression in the bracket is zero | E1 | AO 2.2a |
**Question 4(a):**
$(x+2)^2 + 3$ | **B1** for $b=2$; **B1** for $c=3$ or FT their $b$ | AO 1.2, 1.1 | [2 marks total]
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**Question 4(b):**
Since $(x+b)^2 \geq 0$, the minimum value [or minimum point on the curve] occurs when the expression in the bracket is zero | **E1** | AO 2.2a | [1 mark total]4
\begin{enumerate}[label=(\alph*)]
\item Express $x ^ { 2 } + 4 x + 7$ in the form $( x + b ) ^ { 2 } + c$.
\item Explain why the minimum point on the curve $y = ( x + b ) ^ { 2 } + c$ occurs when $x = - b$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 Q4 [3]}}