Numeracy Higher June 2022 Unit 1 Q4
4. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
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 + 2 OCW]
| 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) |
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Area of large sticker) 42 × 42 (= 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 |