Foundation November 2021 Paper 2 Q6
6. Ali and Beth have fewer than 12 marbles each.
Ali says to Beth:
| If you had 2 less marbles, we would have the same number of marbles. But, if you had 6 less marbles, I would have double the number of marbles you have. |
How many marbles do they each have?
You must show all your working. [3]
Ali has ………… marbles and Beth has ………… marbles
| Scheme | Marks | Comments |
|---|---|---|
| 8 and 10 in the correct order | B3 | As final answer or last trial Allow B2 for an answer of 10 and 8 B1 for sight of any one of the pairs: 9 and 11, 8 and 10, 7 and 9, 6 and 8, 5 and 7 AND B1 for sight of any one of the pairs: 10 and 11, 6 and 9, 4 and 8, 2 and 7 |
| (3) |
Alternative
| Scheme | Marks | Comments |
|---|---|---|
| \(a = b - 2\) AND \(b - 6 = \dfrac{a}{2}\) or \(2(b - 6) = a\) oe | B1 | |
| Eliminates one variable e.g. \(b - 2 = 2(b - 6)\) or \(a + 2 = \dfrac{a + 12}{2}\) oe | M1 | |
| \(a = 8\) AND \(b = 10\) | A1 | Final answer or in the correct order on the answer line. |
Corrected by Westie's Workshop
- The board's mark scheme printed “\(a + 2 = \dfrac{a}{2} + 12\)”. Changed to “\(a + 2 = \dfrac{a + 12}{2}\)” because from \(2(b - 6) = a\) we get \(b = \frac{a + 12}{2}\), and \(b = a + 2\), so \(a + 2 = \frac{a + 12}{2}\) (check: \(a = 8\) gives 10 = 10). As printed, the 12 is not over the 2 and the equation is false.
Original: see the board's mark scheme PDF (link above).