| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 5 |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Moderate -0.8 Part (a) is a routine completing the square exercise with straightforward arithmetic. Part (b) requires finding where the parabola crosses the x-axis (using the completed square form) and writing inequalities, which is a standard application. Both parts are mechanical procedures with no problem-solving insight required, making this easier than average but not trivial due to the multi-step nature. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
\begin{enumerate}[label=(\alph*)]
\item Write $3x^2 + 24x + 5$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are constants to be determined. [3]
\end{enumerate}
The finite region R is enclosed by the curve $y = 3x^2 + 24x + 5$ and the $x$-axis.
\begin{enumerate}[label=(\alph*)]
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\item State the inequalities that define R, including its boundaries. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2024 Q2 [5]}}