Foundation June 2019 Paper 1 Q19
19 You are given that \(\quad 4a - 2b = 10\)
(a) Write down the value of \(\quad 2a - b\) [1 mark]
(b) Write down the value of \(\quad 2b - 4a\) [1 mark]
(c) You are given that \(\quad 4a - 2b = 10 \quad\) and \(\quad a + c = 3\)
Write an expression in \(a\), \(b\) and \(c\) that is equal to 23
Give your answer in its simplest form.
You must show your working. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| 5 | B1 |
Additional guidance
| Condone \(10 - 5 = 5\) | B1 |
| Condone \(x = 5\) | B1 |
| \(\dfrac{10}{2}\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(-10\) | B1 |
| Answer | Mark | Comments |
|---|---|---|
| Unsimplified expression in \(a\), \(b\) and \(c\) which would evaluate to 23 | M1 | eg \(2(4a - 2b) + a + c\) or \(8a - 4b + a + c\) or \(11(a + c) - (4a - 2b)\) or \(11a + 11c - 4a + 2b\) |
| Simplified expression in \(a\), \(b\) and \(c\) which would evaluate to 23 | A1 | eg \(9a - 4b + c\) \(7a + 2b + 11c\) SC2 Values assigned to \(a\), \(b\) and \(c\) which satisfy original equations and expression given which has value 23 eg \(a = 3, b = 1, c = 0\) and \(7a + 2b + c\) |
Additional guidance
| There are infinitely many correct solutions. Allow solutions where the coefficients are not integers if initial working is shown. eg \(3(4a - 2b) - \dfrac{7}{3}(a + c) = \dfrac{29}{3}a - 6b - \dfrac{7}{3}c\) | M1A1 |
| \(5a - 2b + c + 10 = 23\) | M1A1 |
| Condone ‘= 23’ after the expression | |
| Answer using only two variables eg \(2.3(4a - 2b)\) | M0A0 |