| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Transformations of quadratic graphs |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question on completing the square and graph transformations. Part (a) is routine algebraic manipulation, part (b) requires reading the minimum from completed square form, and part (c) involves identifying a simple translation. All parts are standard textbook exercises requiring only recall and basic application of well-practiced techniques. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(f(x) = x^2 - 3x + 2 = \left(x - \frac{3}{2}\right)^2 + b\) | M1 | Begins process of completing the square as far as \(\left(x-\frac{3}{2}\right)^2\). Also allow for \(\left(x+\frac{3}{2}\right)^2\) |
| \(= \left(x-\frac{3}{2}\right)^2 - \frac{1}{4}\) | A1 | All correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Minimum point \(\left(\frac{3}{2}, -\frac{1}{4}\right)\) | B1 | \(x\)-coordinate FT their (a) |
| B1 | \(y\)-coordinate FT their (a) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| translation | B1 | Correct term must be seen |
| \(\begin{pmatrix} -\frac{5}{2} \\ 0 \end{pmatrix}\) | B1 | Also allow for 2.5 to the left |
## Question 4:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $f(x) = x^2 - 3x + 2 = \left(x - \frac{3}{2}\right)^2 + b$ | M1 | Begins process of completing the square as far as $\left(x-\frac{3}{2}\right)^2$. Also allow for $\left(x+\frac{3}{2}\right)^2$ |
| $= \left(x-\frac{3}{2}\right)^2 - \frac{1}{4}$ | A1 | All correct |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Minimum point $\left(\frac{3}{2}, -\frac{1}{4}\right)$ | B1 | $x$-coordinate FT their (a) |
| | B1 | $y$-coordinate FT their (a) |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| translation | B1 | Correct term must be seen |
| $\begin{pmatrix} -\frac{5}{2} \\ 0 \end{pmatrix}$ | B1 | Also allow for 2.5 to the left |
---4 The quadratic function $\mathrm { f } ( x )$ is given by $\mathrm { f } ( x ) = x ^ { 2 } - 3 x + 2$.
\begin{enumerate}[label=(\alph*)]
\item Write $\mathrm { f } ( x )$ in the form $( \mathrm { x } + \mathrm { a } ) ^ { 2 } + \mathrm { b }$, where $a$ and $b$ are constants.
\item Write down the coordinates of the minimum point on the graph of $y = f ( x )$.
\item Describe fully the transformation that maps the graph of $y = f ( x )$ onto the graph of $y = ( x + 1 ) ^ { 2 } - \frac { 1 } { 4 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 1 2022 Q4 [6]}}