Higher November 2022 Paper 1 Q6
6 Rizwan writes down three numbers \(a\), \(b\) and \(c\)
\(a : b = 1 : 3\)
\(b : c = 6 : 5\)
(a)
(i) Find \(a : b : c\) (2)
(ii) Express \(a\) as a fraction of the total of the three numbers \(a\), \(b\) and \(c\) (2)
Emma writes down three numbers \(m\), \(n\) and \(p\)
\(n = 2m\)
\(p = 5n\)
(b) Find \(m : p\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| (i) 2 : 6 : 5 | P1 | for process to compare ratios, eg \(a : b = 2 : 6\) or \(b : c = 3 : 2.5\) |
| A1 | for 2 : 6 : 5 oe | |
| (ii) \(\dfrac{2}{13}\) | M1 | for process to find fraction, eg \(\dfrac{[2]}{[2 + 6 + 5]}\) or for \(\dfrac{a}{a + b + c}\) |
| A1 | for \(\dfrac{2}{13}\) oe or ft (a)(i) |
Additional guidance
(i) Could use 3 or any common multiple of 3 and 6
| Answer | Mark | Mark scheme |
|---|---|---|
| 1 : 10 | P1 | for process to express all numbers in terms of one number, eg \(p = 5 \times 2m\ (= 10m)\) or \(m = \dfrac{n}{2}\) or for \(2m = \dfrac{p}{5}\) or for assigning values in the ratio given, eg \(m = 1\), \(n = 2\), \(p = 10\) or for \(n : m : p = 2 : 1 : 10\) oe or 10 : 1 oe |
| A1 | for 1 : 10 oe |