| Date | May 2015 | Marks available | 2 | Reference code | 15M.1.sl.TZ2.15 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 15 | Adapted from | N/A |
Question
A building company has many rectangular construction sites, of varying widths, along a road.
The area, \(A\), of each site is given by the function
\[A(x) = x(200 - x)\]
where \(x\) is the width of the site in metres and \(20 \leqslant x \leqslant 180\).
Site S has a width of \(20\) m. Write down the area of S.
Site T has the same area as site S, but a different width. Find the width of T.
When the width of the construction site is \(b\) metres, the site has a maximum area.
(i) Write down the value of \(b\).
(ii) Write down the maximum area.
The range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\).
Hence write down the value of \(m\) and of \(n\).
Markscheme
\(3600{\text{ (}}{{\text{m}}^2})\) (A1)(C1)
\(x(200 - x) = 3600\) (M1)
Note: Award (M1) for setting up an equation, equating to their \(3600\).
\(180{\text{ (m)}}\) (A1)(ft) (C2)
Note: Follow through from their answer to part (a).
(i) \(100{\text{ (m)}}\) (A1) (C1)
(ii) \(10\,000{\text{ (}}{{\text{m}}^2})\) (A1)(ft)(C1)
Note: Follow through from their answer to part (c)(i).
\(m = 3600\;\;\;\)and\(\;\;\;n = 10\,000\) (A1)(ft) (C1)
Notes: Follow through from part (a) and part (c)(ii), but only if their \(m\) is less than their \(n\). Accept the answer \(3600 \leqslant A \leqslant 10\,000\).
