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Date November 2014 Marks available 1 Reference code 14N.1.sl.TZ0.9
Level SL only Paper 1 Time zone TZ0
Command term Write down 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 \(y\).

[1]
a.

The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).

Write down a second equation for \(x\) and \(y\).

[1]
b.

Use your graphic display calculator to find the value of \(x\) and the value of \(y\).

[2]
c.

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.

[2]
d.

Markscheme

\(2x + 2y = 44\)     (A1)     (C1)

Note: Accept equivalent forms.

a.

\(xy = 112\)     (A1) (C1)

b.

\(8\), \(14\)     (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.

c.

\(\frac{{112}}{{1250}} \times 100\)     (M1)

Note: Award (M1) for \(112\) divided by \(1250\).

 

\( = 8.96\)     (A1)     (C2)

Note: Do not penalize if percentage sign seen.

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.0 » Simple two-dimensional shapes and their properties, including perimeters and areas of circles, triangles, quadrilaterals and compound shapes.
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