Numeracy Intermediate November 2016 Unit 2 Q7
7.
Bike sheds are built on a rectangular base of width \(x\) metres and length \(y\) metres.
Circle your answer. [1]
\(xy\) metres \(xy\) square metres \(x + y\) metres \(2x + y\) metres \(2x + 2y\) metres
• \(x\) 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]\(y = \dfrac{b-5}{6x}\) \(x = \dfrac{6b}{5y}\) \(y = \dfrac{b+5}{6x}\) \(y = \dfrac{5b}{6x}\) \(y = \dfrac{6x}{5b}\)
He introduces a new sign to pupils in the school newsletter.
The size of the sign in the newsletter is shown below.

Diagram not drawn to scale
A mathematically similar new sign is placed near the side of the playing field.

Diagram not drawn to scale
It is 33·6 cm high.
How wide is this sign? [2]
Width is …………………… cm
| Scheme | Marks | Comments |
|---|---|---|
| (i) 2\(x\) + 2\(y\) metres | B1 | |
| (ii) 48 | B1 | |
| \(y\) = 5\(b\)/6\(x\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 2.6 × 33.6/2.1 or 2.6 ×16 | M1 | |
| 41.6 (cm) | A1 | CAO Award M1, A0 for an answer of 40.32 from PA (33.6 × 1.2 = 40.32) |