| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Topic | Completing the square and sketching |
| Type | Quadratic inequalities |
| Difficulty | Moderate -0.3 Part (i) is a routine completing the square exercise requiring basic algebraic manipulation. Part (ii) applies this to solve a quadratic inequality, which is standard A-level content but requires careful handling of the inequality direction and set notation. The question is slightly easier than average due to its straightforward structure and standard techniques, though the set notation requirement adds minor complexity. |
| 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=(\roman*)]
\item Write $3x^2 - 6x + 1$ in the form $p(x + q)^2 + r$, where $p$, $q$ and $r$ are integers. [2]
\item Solve $3x^2 - 6x + 1 \leq 0$, giving your answer in set notation. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q3 [6]}}