Higher June 2018 Paper 3 Q5
5 \(a\) is a common factor of 72 and 120
\(b\) is a common multiple of 6 and 9
Work out the highest possible value of \(\;\dfrac{a}{b}\) [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| At least two common factors of 72 and 120 from 2, 3, 4, 6, 8, 12, 24 or \(72 = 2\ (\times)\ 2\ (\times)\ 2\ (\times)\ 3\ (\times)\ 3\) or \(120 = 2\ (\times)\ 2\ (\times)\ 2\ (\times)\ 3\ (\times)\ 5\) | M1 | May be seen on a diagram, eg factor tree |
| At least two common multiples of 6 and 9 from 18, 36, 54… | M1 | |
| (HCF =) 24 selected from factors or \(a = 24\) or (LCM =) 18 selected from multiples or \(b = 18\) | M1 | oe eg HCF \(= 2\ (\times)\ 2\ (\times)\ 2\ (\times)\ 3\) 24 can be implied from their numerator oe eg LCM \(= 2\ (\times)\ 3\ (\times)\ 3\) 18 can be implied from their denominator oe eg \(\dfrac{2 \times 2 \times 2 \times 3}{2 \times 3 \times 3}\) |
| \(1\dfrac{1}{3}\) or \(\dfrac{4}{3}\) or 1.33… | A1 | oe Accept \(\dfrac{24}{18}\) Ignore further incorrect cancelling |
Additional guidance
| HCF = 24 and LCM = 18 | M1M1M1 |
| HCF = 24 | M1M0M1 |
| LCM = 18 | M0M1M1 |