Numeracy Higher June 2023 Unit 1 Q1
1. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Mari and Huw share a prize of £2700 in the ratio 4 : 5 respectively.
Mari decides to donate 24% of her share of the prize to charity.
Huw decides to give the same amount of money as Mari to charity.
What fraction of Huw’s share of the prize money does he give to charity?
Express your answer in its simplest form.
You must show all your working. [6 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| (Mari’s share of the prize) 4 × 2700 ÷ (4 + 5) OR (Huw’s share of the prize) 5 × 2700 ÷ (4 + 5) | M1 | (4 × 300) (5 × 300) |
| (Mari’s share is £) 1200 | A1 | Allow for sight of (£)1200 irrespective of the name assigned May be implied in later calculation (Huw’s share is £1500) |
| (Mari donates) 0.24 × 1200 | M1 | FT 0.24 × ‘their smaller share’ (Note: ‘their smaller share’ < 1350) |
| (£) 288 | A1 | |
| (Fraction of his prize Huw donates) \(\dfrac{0.24 \times 1200}{5 \times 2700 \div (4 + 5)}\) or \(\dfrac{0.24 \times 1200}{2700 - 1200}\) or \(\dfrac{288}{1500}\) or 1 – \(\dfrac{(1500 - 0.24 \times 1200)}{2700 - 1200}\) or 1 – \(\dfrac{1212}{1500}\) | M1 | FT ‘their 0.24 × ‘their smaller share’’ and 2700 – ‘their smaller share’ |
| \(\dfrac{24}{125}\) | A1 | Must be a simplified fraction, ISW (e.g. 19.2%) An unsimplified fraction (144/750 or 96/500 or 72/375 or 48/250) is awarded M1 A0 Only FT if there are at least 2 different common prime factors for the numerator and denominator for simplifying, and not both numerator and denominator being a multiple of 10, i.e. equivalent level of difficulty If consistently working with Mari’s getting the larger share, initially possible M1, A1 or M1, A0, but then M0, A0, M0, A0. However, also award SC2 for a final answer of 3/10 or SC1 for (donation) (£)360. Mari with larger share leads to: \(\dfrac{0.24 \times 1500}{2700 - 1500}\) = \(\dfrac{360}{1200}\) = \(\dfrac{3}{10}\) |
| 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 |
|---|---|---|
| (Fraction of his prize Huw donates) \(\dfrac{4}{5}\) × \(\dfrac{24}{100}\) | M3 | M2 for sight of ⅘ of 24% M1 for sight of ⅘ of 24 |
| \(\dfrac{24}{125}\) | A3 | Must be a simplified fraction A2 for correct unsimplified fraction, e.g. \(\dfrac{96}{500}\) Only FT if there are at least 2 different common prime factors for the numerator and denominator for simplifying, i.e. equivalent level of difficulty ISW (e.g. 19.2%) |