| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Easy -1.2 Part (a) is a routine completing the square exercise requiring only algebraic manipulation to get (x+3)²-4. Part (b) asks for a standard interpretation of the completed square form as a translation, which is direct recall of transformations. This is a straightforward textbook question with no problem-solving required, making it easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| \((x+3)^2\) | B1 |
| \([-4]\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [Translation or shift] \(\begin{pmatrix}-3\\-4\end{pmatrix}\) | B1, B1 FT | Accept [translation/shift] \(\begin{pmatrix}-\text{their } a\\\text{their } b\end{pmatrix}\) OR translation \(-3\) units in \(x\)-direction and (translation) \(-4\) units in \(y\)-direction. |
## Question 1:
**Part (a):**
$(x+3)^2$ | B1 |
$[-4]$ | B1 |
*Total: 2 marks*
**Part (b):**
[Translation or shift] $\begin{pmatrix}-3\\-4\end{pmatrix}$ | B1, B1 FT | Accept [translation/shift] $\begin{pmatrix}-\text{their } a\\\text{their } b\end{pmatrix}$ OR translation $-3$ units in $x$-direction and (translation) $-4$ units in $y$-direction.
*Total: 2 marks*
---1
\begin{enumerate}[label=(\alph*)]
\item Express $x ^ { 2 } + 6 x + 5$ in the form $( x + a ) ^ { 2 } + b$, where $a$ and $b$ are constants.
\item The curve with equation $y = x ^ { 2 }$ is transformed to the curve with equation $y = x ^ { 2 } + 6 x + 5$.
Describe fully the transformation(s) involved.
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2020 Q1 [4]}}