Foundation June 2017 Paper 3 Q27
27 How are the whole number solutions to A and B different?
A \(\qquad\) Solve \(\quad 3 \leqslant 3x \lt 18\)
B \(\qquad\) Solve \(\quad 3 \lt 3x \leqslant 18\)
[2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| A includes 1 or B does not include 1 | B1 | oe Correct statement about 1 without contradiction |
| A does not include 6 or B includes 6 | B1 | oe Correct statement about 6 without contradiction |
| Alternative method 2 | ||
| \(1 \leqslant x \lt 6\) or \(\quad 1 \lt x \leqslant 6\) or \(1 \leqslant x\) and \(1 \lt x\) or \(x \lt 6\) and \(x \leqslant 6\) or A is 1, 2, 3, 4, 5 or B is 2, 3, 4, 5, 6 | M1 | oe eg \(x \geqslant 1\) and \(x \lt 6\) for 1st statement A includes 3 and B includes 18 A is 3, … 17 and B is 4, … 18 |
| A is 1, 2, 3, 4, 5 and B is 2, 3, 4, 5, 6 | A1 | oe eg A = 1 to 5 and B = 2 to 6 |
Additional guidance
| For 2 marks, must have clearly indicated both sets of integer solutions | M1A1 |
| For 2 marks, must have clearly indicated both differences | B1B1 |
| A could be 1 but not 6, B could be 6 but not 1 | B1B1 |
| A is \(x = 1\) and B is \(x = 6\) | B1B1 |
| A: 3, 6, 9, 12, 15 and B: 6, 9, 12, 15, 18 | M1A0 |
| Comment that inequality signs are switched with no other working | B0B0 |
| ‘1 and 6 don’t appear in both’ – need to be correctly linked to A and B | B0B0 |