SPS SPS SM 2025 November — Question 2 12 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2025
SessionNovember
Marks12
TopicCompleting the square and sketching
TypeSketch quadratic curve
DifficultyEasy -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.
Spec1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown

  1. Write \(4x^2 - 24x + 27\) in the form \(a(x - b)^2 + c\). [4]
  2. State the coordinates of the minimum point on the curve \(y = 4x^2 - 24x + 27\). [2]
  3. Solve the equation \(4x^2 - 24x + 27 = 0\). [3]
  4. Sketch the graph of the curve \(y = 4x^2 - 24x + 27\). [3]

\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]}}