Foundation June 2017 Paper 3 Q19
19 The value of \(x\) can be 2 or 5
The value of \(y\) can be 3 or 12
(a) List the possible values of \(\quad xy\) [2 marks]
(b) Work out the least possible value of \(\quad \dfrac{x - y}{x}\)
You must show your working. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| 6, 15, 24, 60 in any order | B2 | B1 for 6, 15, 24, 60 with no more than one additional value or three correct values with no more than one incorrect value |
Additional guidance
| Ignore repeated values for B2 and B1 | |
| 6, 10, 15, 24, 60 | B1 |
| 6, 10, 15, 24 | B1 |
| 6, 10, 15, 24, 36 | B0 |
| \(2 \times 3,\ 5 \times 3,\ 2 \times 12,\ 5 \times 12\) | B0 |
| \(6xy,\ 15xy,\ 24xy,\ 60xy\) | B0 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{2 - 12}{2}\) or one correctly evaluated trial with correct substitutions for \(x = 2\) or 5 and \(y = 3\) or 12 or two correct values from \(-\dfrac{10}{2},\ -\dfrac{1}{2},\ -\dfrac{7}{5},\ \dfrac{2}{5}\) oe or two correct values from \(-5,\ -0.5,\ -1.4,\ 0.4\) oe | M1 | \(\dfrac{2 - 3}{2} = -\dfrac{1}{2}\) oe or \(\dfrac{5 - 12}{5} = -\dfrac{7}{5}\) oe or \(\dfrac{5 - 3}{5} = \dfrac{2}{5}\) oe |
| \(-\dfrac{10}{2}\) or \(-5\) | A1 |
Additional guidance
| Two separate correct values can be in either fraction or decimal form | |
| \(2 - 12 \div 2 = -5\) (recovered) | M1A1 |
| \(2 - 12 \div 2\) | M0A0 |
| An example of an incorrect substitution with different values of \(x\) eg \(\dfrac{5 - 12}{2} = -\dfrac{7}{2}\) |