Numeracy Intermediate June 2022 Unit 1 Q12
12. Rectangular stickers with warnings written on them are often placed near water taps.
The rectangular sticker shown below warns of hot water.
It has a length of 14 cm and an area of 42 cm2.
Diagram not drawn to scale
The sticker below is mathematically similar to the first sticker.
It is an enlargement of the first sticker, with scale factor 4.
Diagram not drawn to scale
Calculate the length and the width of the larger sticker.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Width of small sticker is) 42 ÷ 14 | M1 | |
| 3 (cm) | A1 | Must be for the small label (check the diagram) |
| (Length or width of large sticker) 4 × 14 OR 4 × 3 | M1 | FT ‘their 42 ÷ 14’ |
| 56 (cm) AND 12 (cm) | A1 | (Note: Incorrect logic 42 × 4 = 168 with 168 ÷ 56 = 3 does not give the width of the small label! M0 A0) |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Area of large sticker) \(42 \times 4^{2}\) (= 672cm2) | M1 | |
| (Length of large sticker) 14 × 4 (= 56cm) | M1 | |
| (Width of large sticker) \(\dfrac{42 \times 4^{2}}{14 \times 4}\) or \(\dfrac{672}{56}\) | M1 | |
| (Length and width of large sticker) 56 (cm) AND 12 (cm) | A1 |
The alternative method is printed in italics in the original.