Manipulating Formulae/ Changing the Subject: WJEC GCSE Numeracy Higher November 2016 Unit 2 Q1

Numeracy Higher November 2016 Unit 2 Q1

WJECHigherCurrent spec3 marksManipulating Formulae/ Changing the Subject Similar Shapes

(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.

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:

\[b = \dfrac{6xy}{5}\]

According to the details the Headteacher has been given, what is the formula for calculating the length, \(y\) metres, of a bike shed \(x\) metres wide that can hold \(b\) bikes?
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.

Rectangular no-cycling sign 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.

Larger 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