| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Transformations of quadratic graphs |
| Difficulty | Easy -1.3 This is a straightforward completing-the-square question with standard follow-up parts requiring only routine recall and application of basic transformations. Part (a) is a textbook exercise, part (b) requires simply reading off the turning point from completed square form, and part (c) involves stating standard translations—no problem-solving or novel insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = 4\) | B1 (1.1a) | May be seen as \((x+4)^2 - 14\) |
| \(b = -14\) | B1 (1.1) |
| Answer | Marks | Guidance |
|---|---|---|
| \((-4, -14)\) | B1 (2.2a) | FT their (a) |
| Answer | Marks | Guidance |
|---|---|---|
| Translation | B1 (1.2) | If other transformations as well (e.g. stretch) then B0; 'Shift' does not score; Or B1 for translation 4 to left oe |
| \(\begin{pmatrix}-4\\-14\end{pmatrix}\) oe | B1 (2.2a) | FT their (a); Or B1 for translation 14 down oe; B0 B1 can be awarded for e.g. Translation, correct vector & stretch |
## Question 1:
**Part (a):**
$a = 4$ | B1 (1.1a) | May be seen as $(x+4)^2 - 14$
$b = -14$ | B1 (1.1) |
[2 marks]
**Part (b):**
$(-4, -14)$ | B1 (2.2a) | FT their (a)
[1 mark]
**Part (c):**
Translation | B1 (1.2) | If other transformations as well (e.g. stretch) then B0; 'Shift' does not score; Or B1 for translation 4 to left oe
$\begin{pmatrix}-4\\-14\end{pmatrix}$ oe | B1 (2.2a) | FT their (a); Or B1 for translation 14 down oe; B0 B1 can be awarded for e.g. Translation, correct vector & stretch
[2 marks]
---1
\begin{enumerate}[label=(\alph*)]
\item Express $x ^ { 2 } + 8 x + 2$ in the form $( x + a ) ^ { 2 } + b$.
\item Write down the coordinates of the turning point of the curve $y = x ^ { 2 } + 8 x + 2$.
\item State the transformation(s) which map(s) the curve $y = x ^ { 2 }$ onto the curve $y = x ^ { 2 } + 8 x + 2$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2021 Q1 [5]}}