OCR C1 — Question 3 6 marks

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeSketch quadratic curve
DifficultyModerate -0.8 This is a straightforward completing the square exercise followed by routine curve sketching. Part (a) requires a standard algebraic manipulation (completing the square), and part (b) involves identifying the vertex from completed square form and finding axis intercepts by substitution. These are textbook procedures with no problem-solving or novel insight required, making it easier than average but not trivial since it requires multiple steps and careful execution.
Spec1.02e Complete the square: quadratic polynomials and turning points1.02n Sketch curves: simple equations including polynomials

  1. Express \(x^2 - 10x + 27\) in the form \((x + p)^2 + q\). [3]
  2. Sketch the curve with equation \(y = x^2 - 10x + 27\), showing on your sketch
    1. the coordinates of the vertex of the curve,
    2. the coordinates of any points where the curve meets the coordinate axes. [3]

\begin{enumerate}[label=(\alph*)]
\item Express $x^2 - 10x + 27$ in the form $(x + p)^2 + q$. [3]

\item Sketch the curve with equation $y = x^2 - 10x + 27$, showing on your sketch
\begin{enumerate}[label=(\roman*)]
\item the coordinates of the vertex of the curve,

\item the coordinates of any points where the curve meets the coordinate axes. [3]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{OCR C1  Q3 [6]}}