Edexcel C1 — Question 41 8 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks8
PaperDownload PDF ↗
TopicInequalities
TypePerimeter or area constraint inequality
DifficultyModerate -0.8 This is a straightforward C1 inequality question requiring basic algebraic setup (perimeter and area formulas), forming simple linear and quadratic inequalities, and solving them. The quadratic factorizes easily and all steps are routine with no conceptual challenges beyond standard GCSE/early A-level techniques.
Spec1.02g Inequalities: linear and quadratic in single variable

The width of a rectangular sports pitch is \(x\) metres, \(x > 0\). The length of the pitch is 20 m more than its width. Given that the perimeter of the pitch must be less than 300 m,
  1. form a linear inequality in \(x\). [2]
Given that the area of the pitch must be greater than 4800 m²,
  1. form a quadratic inequality in \(x\). [2]
  2. by solving your inequalities, find the set of possible values of \(x\). [4]

The width of a rectangular sports pitch is $x$ metres, $x > 0$. The length of the pitch is 20 m more than its width. Given that the perimeter of the pitch must be less than 300 m,

\begin{enumerate}[label=(\alph*)]
\item form a linear inequality in $x$. [2]
\end{enumerate}

Given that the area of the pitch must be greater than 4800 m²,

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item form a quadratic inequality in $x$. [2]
\item by solving your inequalities, find the set of possible values of $x$. [4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C1  Q41 [8]}}