| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | November |
| Marks | 12 |
| Topic | Completing the square and sketching |
| Type | Sketch quadratic curve |
| Difficulty | Easy -1.3 This is a straightforward completing-the-square question with standard follow-up parts. Part (i) is routine algebraic manipulation, parts (ii) and (iv) are direct consequences requiring minimal additional work, and part (iii) is a standard quadratic equation solve. All techniques are basic A-level content with no problem-solving insight required, making this easier than average. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
\begin{enumerate}[label=(\roman*)]
\item Write $4x^2 - 24x + 27$ in the form $a(x - b)^2 + c$. [4]
\item State the coordinates of the minimum point on the curve $y = 4x^2 - 24x + 27$. [2]
\item Solve the equation $4x^2 - 24x + 27 = 0$. [3]
\item Sketch the graph of the curve $y = 4x^2 - 24x + 27$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q2 [12]}}