Foundation November 2017 Paper 2 Q18
18 Here are five cards.
One of the cards is removed.
The mean of the numbers on the remaining four cards is 6
Which card was removed?
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(6 \times 4\) or 24 stated or implied as target total of the four cards | M1 | Indicating 1, 5, 7 and 11 are the chosen four cards implies M2 |
| \(1 + 5 + 7 + 9 + 11\) or 33 | M1 | |
| 9 | A1 | |
| Alternative method 2 | ||
| 1, 5, 7, 9 \(\rightarrow\) \((1 + 5 + 7 + 9) \div 4\) or 1, 5, 7, 11 \(\rightarrow\) \((1 + 5 + 7 + 11) \div 4\) or 1, 5, 9, 11 \(\rightarrow\) \((1 + 5 + 9 + 11) \div 4\) or 1, 7, 9, 11 \(\rightarrow\) \((1 + 7 + 9 + 11) \div 4\) or 5, 7, 9, 11 \(\rightarrow\) \((5 + 7 + 9 + 11) \div 4\) | M1 | 1, 5, 7, 9 \(\rightarrow\) \(22 \div 4\) or 1, 5, 7, 11 \(\rightarrow\) \(24 \div 4\) or 1, 5, 9, 11 \(\rightarrow\) \(26 \div 4\) or 1, 7, 9, 11 \(\rightarrow\) \(28 \div 4\) or 5, 7, 9, 11 \(\rightarrow\) \(32 \div 4\) |
| 1, 5, 7, 9 \(\rightarrow\) 5.5 or 1, 5, 7, 11 \(\rightarrow\) 6 or 1, 5, 9, 11 \(\rightarrow\) 6.5 or 1, 7, 9, 11 \(\rightarrow\) 7 or 5, 7, 9, 11 \(\rightarrow\) 8 | A1 | |
| 9 | A1 | with no error in the mean of 1, 5, 7, 11 |
Additional guidance
| Use the alternative scheme that awards the better mark | |
| 33 – 24 | M1M1A0 |
| 1 + 5 + 7 + 11 = 28, \(28 \div 4\) = 6, answer 9 (with no other work) | M1A0A0 |