| Date | November 2014 | Marks available | 2 | Reference code | 14N.1.sl.TZ0.9 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Determine | Question number | 9 | Adapted from | N/A |
Question
A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.
Write down an equation for \(x\) and \(y\).
The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).
Write down a second equation for \(x\) and \(y\).
Use your graphic display calculator to find the value of \(x\) and the value of \(y\).
An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.
Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.
Markscheme
\(2x + 2y = 44\) (A1) (C1)
Note: Accept equivalent forms.
\(xy = 112\) (A1) (C1)
\(8\), \(14\) (A1)(ft)(A1)(ft) (C2)
Notes: Accept \(x = 8\), \(y = 14\) OR \(x = 14\), \(y = 8\)
Follow through from their answers to parts (a) and (b) only if both values are positive.
\(\frac{{112}}{{1250}} \times 100\) (M1)
Note: Award (M1) for \(112\) divided by \(1250\).
\( = 8.96\) (A1) (C2)
Note: Do not penalize if percentage sign seen.
