Higher June 2024 Paper 4 Q9
9 Sasha and Taylor each have a stamp collection.
They organise their stamp collections according to where the stamps come from:
United Kingdom (UK), European Union (EU), Other.
The table shows the number of stamps in each collection and the ratio UK : EU : Other.
| Number of stamps | Ratio UK : EU : Other | |
|---|---|---|
| Sasha’s collection | 1638 | 9 : 3 : 2 |
| Taylor’s collection | 660 | 8 : 1 : 2 |
When they put the two stamp collections together, Sasha and Taylor claim that at least \(\frac{2}{3}\) of all the stamps come from the UK.
Are they correct?
Show how you decide. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct statement with supporting working yes/correct oe and e.g. 1533 with 1532 or 0.667[1]… oe with 0.666… oe or \(\frac{511}{766} - \frac{2}{3} \gt 0\) or \(\frac{511}{766}\) and 510.6 | 5 | B4 for 1533 and 1532 OR | |
| M1 for \(\frac{1638}{9 + 3 + 2}\) [× 9] or better | implied by 117 or 1053 | ||
| M1 for \(\frac{660}{8 + 1 + 2}\) [× 8] or better | implied by 60 or 480 | ||
| M1 for their1053 + their480 or 1638 + 660 | implied by 1533 or 2298 | ||
| M1 for \(\frac{\textit{their } 1533}{\textit{their } 2298}\) or for their 2298 × \(\frac{2}{3}\) or 1532 | implied by 0.667[1]… oe or \(\frac{511}{766}\) | ||
| for those that sum the columns (i.e 17 : 4 : 4); M1 for \(\frac{1638 + 660}{\textit{their}(17 + 4 + 4)}\) [× 17] or better or \(\frac{\textit{their } 17}{\textit{their}(17 + 4 + 4)}\) | implied by 91.92 or1562.64 or \(\frac{17}{25}\) or 0.68 | ||
| M1 for \(\frac{\textit{their } 1562.64}{\textit{their } 2298}\) or for their 2298 × \(\frac{2}{3}\) or 1532 or \(\frac{2}{3}\) [× 25] | implied by 0.68 oe or 1532 or 16.6.. or 0.66… or \(0.\dot{6}\) | ||
| M1 for 0.68 and 0.66… or 1562[.64]/1563 and 1532 | allow 17 and 16.6 to 16.7 | ||