Higher November 2017 Paper 1 Q8
8.
(a) Work out \(3\dfrac{1}{5} - 1\dfrac{2}{7}\). [3]
(b) Three two-digit integers \(a\), \(b\) and \(c\) are in the ratios
\(a : b = 4 : 5\) and \(b : c = 7 : 11\).
Find the integers \(a\), \(b\) and \(c\). [3](c) A length of string has been cut into two pieces in the ratio 3 : 5.
The longer piece measures 205 cm.
What was the original length of the string? [2]
The longer piece measures 205 cm.
What was the original length of the string? [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(\left(\dfrac{16}{5} - \dfrac{9}{7} =\right) \dfrac{112}{35} - \dfrac{45}{35}\) or \(2 - \dfrac{3}{35}\) | M2 | M1 for \(\dfrac{112}{35}\) or \(\dfrac{45}{35}\) or \(2 + \dfrac{7}{35} - \dfrac{10}{35}\) |
| \(\dfrac{67}{35}\) or \(1\dfrac{32}{35}\) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| \((a =)\ 28 \quad (b =)\ 35 \quad (c =)\ 55\) | B3 | B1 for each correct value or B2 for 35 and attempting \(4 \times 7\) and \(11 \times 5\) or for a set of values in the correct ratio that are not 2-digit e.g. 56, 70, 110 or B1 for a common multiple of 5 and 7 or for two pairs of two-digit numbers in the ratio 4 : 5 AND 7 : 11 |
| Scheme | Marks | Comments |
|---|---|---|
| \(205 \div 5 \times 8\) or equivalent | M1 | Must be a complete method |
| 328 (cm) or equivalent, CAO | A1 | |
| (8) |