Your progress
Ticks are kept only in this browser: clearing your browsing data or changing device loses them. · ·

Numeracy Intermediate November 2016 Unit 2 Q7

7.

(a) The Headteacher of Ysgol Bro Gwyn investigates building a new bike shed.

Bike sheds are built on a rectangular base of width \(x\) metres and length \(y\) metres.

(i) Which is the correct expression for the perimeter of the bike shed?
Circle your answer. [1]

\(xy\) metres     \(xy\) square metres     \(x + y\) metres     \(2x + y\) metres     \(2x + 2y\) metres

(ii) The Headteacher is given a formula for working out the number of bikes, \(b\), that can be stored in a bike shed that has a base of width \(x\) metres and length \(y\) metres.
He is told the formula only works when
•  \(x\) and \(y\) are whole numbers
•  \(x\) is greater than 3
•  \(y\) is greater than 5

The formula is as follows:

\[b = \frac{6xy}{5}\]
  • According to the formula, how many bikes can be stored in a bike shed 5 metres wide and 8 metres long?
    Circle your answer. [1]

    3     7     42     48     240

  • A bike shed \(x\) metres wide and \(y\) metres long can hold \(b\) bikes.
    According to the details the Headteacher has been given, what is the formula for calculating the length, \(y\) metres?
    Circle your answer. [1]

    \(y = \dfrac{b-5}{6x}\)     \(x = \dfrac{6b}{5y}\)     \(y = \dfrac{b+5}{6x}\)     \(y = \dfrac{5b}{6x}\)     \(y = \dfrac{6x}{5b}\)

(b) The Headteacher decides to place signs around the school site to stop pupils using their bikes on grassed areas.

He introduces a new sign to pupils in the school newsletter.
The size of the sign in the newsletter is shown below.

No-cycling sign in the newsletter: a rectangle 2·6 cm wide and 2·1 cm high

Diagram not drawn to scale

A mathematically similar new sign is placed near the side of the playing field.

The larger, mathematically similar no-cycling sign, 33·6 cm high

Diagram not drawn to scale

It is 33·6 cm high.
How wide is this sign? [2]

Width is …………………… cm