CAIE P1 2011 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionNovember
TopicQuadratic Functions

7
\includegraphics[max width=\textwidth, alt={}, center]{56d376c5-b91f-488d-89e2-18edcb14052d-3_534_895_255_625} The diagram shows the dimensions in metres of an L-shaped garden. The perimeter of the garden is 48 m .
  1. Find an expression for \(y\) in terms of \(x\).
  2. Given that the area of the garden is \(A \mathrm {~m} ^ { 2 }\), show that \(A = 48 x - 8 x ^ { 2 }\).
  3. Given that \(x\) can vary, find the maximum area of the garden, showing that this is a maximum value rather than a minimum value.