OCR MEI C1 2011 June — Question 11 11 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2011
SessionJune
Marks11
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeLine-curve intersection points
DifficultyModerate -0.8 This is a straightforward C1 question testing standard techniques: simultaneous equations with substitution, completing the square (with coefficient of x² given), and reading off vertex properties. All parts are routine textbook exercises requiring only direct application of learned methods with no problem-solving or insight needed.
Spec1.02e Complete the square: quadratic polynomials and turning points1.02q Use intersection points: of graphs to solve equations

  1. Find algebraically the coordinates of the points of intersection of the curve \(y = 4x^2 + 24x + 31\) and the line \(x + y = 10\). [5]
  2. Express \(4x^2 + 24x + 31\) in the form \(a(x + b)^2 + c\). [4]
  3. For the curve \(y = 4x^2 + 24x + 31\),
    1. write down the equation of the line of symmetry, [1]
    2. write down the minimum \(y\)-value on the curve. [1]

\begin{enumerate}[label=(\roman*)]
\item Find algebraically the coordinates of the points of intersection of the curve $y = 4x^2 + 24x + 31$ and the line $x + y = 10$. [5]
\item Express $4x^2 + 24x + 31$ in the form $a(x + b)^2 + c$. [4]
\item For the curve $y = 4x^2 + 24x + 31$,
\begin{enumerate}[label=(\Alph*)]
\item write down the equation of the line of symmetry, [1]
\item write down the minimum $y$-value on the curve. [1]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C1 2011 Q11 [11]}}