Higher November 2020 Paper 2 Q19
19 \(a\) and \(b\) are positive values.
Show that \(\quad \dfrac{7a + 2b - 3a}{8a + 6b + 2a - b} \quad\) always simplifies to the same value. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(4a + 2b\) and \(10a + 5b\) | M1 | |
| \(2(2a + b)\) or \(5(2a + b)\) | M1 | |
| \(\dfrac{2(2a + b)}{5(2a + b)}\) and \(\dfrac{2}{5}\) or \(\dfrac{2(2a + b)}{5(2a + b)}\) and 0.4 | A1 |
Additional guidance
| \(\dfrac{2}{5}\) with no working or only from substitution of values | M0M0A0 |
| Ignore substitution of values eg \(\dfrac{2(2a + b)}{5(2a + b)} = \dfrac{2}{5}\) followed by substitution of values | M1M1A1 |
| \(\dfrac{4a + 2b}{10a + 4b} = \dfrac{2}{5}\) | M1M0A0 |
| \(2b + 4a\) and \(5b + 10a\) are equivalent to \(4a + 2b\) and \(10a + 5b\) etc |