| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Completing square from standard form |
| Difficulty | Easy -1.2 This is a straightforward completing the square exercise requiring routine algebraic manipulation to rewrite y = x² + 8x - 7 as y = (x+4)² - 23, then identifying the translation and turning point. It's below average difficulty as it's a standard textbook procedure with no problem-solving or conceptual challenges beyond basic recall. |
| 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 |
| \(x^2 + 8x - 7 = (x+4)^2 - 16 - 7\) | M1 | For \((x+4)^2\); or from differentiation |
| \((x+4)^2 - 23\) | A1 | Correct completion of square |
| Translation | B1 | More than one transformation loses last two marks |
| \(\begin{pmatrix} -4 \\ -23 \end{pmatrix}\) | B1 | Must be vector |
| [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((-4, -23)\) | B1 | Correct or FT *their* translation or vector |
| [1] |
## Question 2:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x^2 + 8x - 7 = (x+4)^2 - 16 - 7$ | M1 | For $(x+4)^2$; or from differentiation |
| $(x+4)^2 - 23$ | A1 | Correct completion of square |
| Translation | B1 | More than one transformation loses last two marks |
| $\begin{pmatrix} -4 \\ -23 \end{pmatrix}$ | B1 | Must be vector |
| **[4]** | | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(-4, -23)$ | B1 | Correct or FT *their* **translation** or vector |
| **[1]** | | |
---2
\begin{enumerate}[label=(\alph*)]
\item Find the transformation which maps the curve $y = x ^ { 2 }$ to the curve $y = x ^ { 2 } + 8 x - 7$.
\item Write down the coordinates of the turning point of $y = x ^ { 2 } + 8 x - 7$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2019 Q2 [5]}}