OCR MEI C1 2011 January — Question 9 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2011
SessionJanuary
Marks5
PaperDownload PDF ↗
TopicSolving quadratics and applications
TypeGeometric area leads to quadratic
DifficultyModerate -0.8 This is a straightforward application of the trapezium area formula followed by solving a simple quadratic equation. The question explicitly tells students what equation to derive (removing problem-formulation difficulty) and the quadratic factors easily as (x+7)(x-5)=0. This is easier than average A-level work, being a routine C1 exercise with clear scaffolding.
Spec1.02f Solve quadratic equations: including in a function of unknown1.02z Models in context: use functions in modelling

9 Fig. 9 shows a trapezium ABCD , with the lengths in centimetres of three of its sides. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{754d34e4-2f47-48b7-9fbb-6caa7ac21eb7-3_464_878_347_632} \captionsetup{labelformat=empty} \caption{Fig. 9}
\end{figure} This trapezium has area \(140 \mathrm {~cm} ^ { 2 }\).
  1. Show that \(x ^ { 2 } + 2 x - 35 = 0\).
  2. Hence find the length of side AB of the trapezium.

9 Fig. 9 shows a trapezium ABCD , with the lengths in centimetres of three of its sides.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{754d34e4-2f47-48b7-9fbb-6caa7ac21eb7-3_464_878_347_632}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\end{center}
\end{figure}

This trapezium has area $140 \mathrm {~cm} ^ { 2 }$.\\
(i) Show that $x ^ { 2 } + 2 x - 35 = 0$.\\
(ii) Hence find the length of side AB of the trapezium.

\hfill \mbox{\textit{OCR MEI C1 2011 Q9 [5]}}