Higher November 2020 Paper 1 Q6
6.
(a) Eric currently spends £36 each week playing ten pin bowling.
He wants to decrease this amount by \(\dfrac{3}{8}\).
He writes:
He wants to decrease this amount by \(\dfrac{3}{8}\).
He writes:
New amount : Current amount
3 : 8
13.50 : 36
I will now spend £13.50 each week playing ten pin bowling
3 : 8
13.50 : 36
I will now spend £13.50 each week playing ten pin bowling
(i) Explain why Eric’s method is not correct. [1]
(ii) Describe what Eric's answer of £13.50 actually represents. [1]
(b) Three integers \(a\), \(b\) and \(c\) are in the ratios
Find the integers \(a\), \(b\) and \(c\). [3]
\(a : b = 9 : 2\) and \(b : c = 6 : 7\).
It is known that \(a + b + c = 200\).Find the integers \(a\), \(b\) and \(c\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| (i) Valid criticism of method e.g. ‘He should have used the ratio 5 : 8’ or ‘He should have divided by 8 and multiplied by 5’ or ‘He has forgotten to subtract it from 36.’ | E1 | Do not accept e.g. ‘Because the answer should be £22.50’ or ‘That is not 36 decreased by \(\frac{3}{8}\).’ Allow e.g. ‘He has (only) found \(\frac{3}{8}\)’ or ‘36 – 13.50 = 22.50, 13.50 is only the amount of the decrease.’ |
| (ii) Valid description of what £13.50 is e.g. ‘He has found the amount of the reduction.’ or ‘He has found the amount decreased by \(\frac{5}{8}\)’ | E1 | Allow e.g. ‘He has found what \(\frac{3}{8}\) is, he needs to subtract it,’ (as implying the ‘reduction’) or ‘How much he needs to take off.’ or ‘How much he saves each week.’ or ‘It is \(\frac{3}{8}\)’ |
| Scheme | Marks | Comments |
|---|---|---|
| \((a =)\ 135\) \((b =)\ 30\) \((c =)\ 35\) | B3 | B1 for each correct value OR B1 for \(a : b : c = 27 : 6 : 7\), oe si; and B1 FT for \(\dfrac{200}{27+6+7}\times27\) or \(\dfrac{200}{27+6+7}\times6\) or \(\dfrac{200}{27+6+7}\times7\); FT ‘their \(27 : 6 : 7\)’ OR B1 for \(2a = 9b\) and \(7b = 6c\) and finding e.g. \(a = \dfrac{9}{2}b\) and \(c = \dfrac{7}{6}b\) and B1 for solving e.g. \(\dfrac{9}{2}b + b + \dfrac{7}{6}b = 200\) OR B1 for trials leading to 3 values in the ratio 27 : 6 : 7 and B1 for at least 2 further trials to attempt find 3 values in this ratio that sum to 200 |
| (5) |