| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 5 |
| Topic | Completing the square and sketching |
| Type | Complete square then find vertex/turning point |
| Difficulty | Easy -1.3 This is a routine completing-the-square exercise followed by finding a maximum point by inspection. Part (a) requires standard algebraic manipulation with no problem-solving, and part (b) is immediate once (a) is complete. This is easier than average A-level content, requiring only basic technique with no conceptual challenges. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials |
A curve $C$ has equation $y = f(x)$ where
$$f(x) = -3x^2 + 12x + 8$$
\begin{enumerate}[label=(\alph*)]
\item Write $f(x)$ in the form
$$a(x + b)^2 + c$$
where $a$, $b$ and $c$ are constants to be found. [3]
\end{enumerate}
The curve $C$ has a maximum turning point at $M$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the coordinates of $M$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q2 [5]}}