| Date | May 2012 | Marks available | 3 | Reference code | 12M.1.sl.TZ1.1 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The following six integers are arranged from smallest to largest
1 , x , 3 , y , 14 , z
The mode is 1 , the median is 5 and the mean is 7.
Find x ;
Find y ;
Find z .
Markscheme
x = 1 (A1) (C1)
[1 mark]
\(\frac{{3 + y}}{2} = 5\) (M1)
Note: Award (M1) for setting the correct equation or equivalent.
y = 7 (A1) (C2)
[2 marks]
1 + 1 + 3 + 7 + 14 + z = 6 × 7 (M1)(M1)
Note: Award (M1) for the sum of their 5 numbers and z, and (M1) for 6 × 7.
z = 16 (A1)(ft) (C3)
Note: Follow through from their x and y found in part (b) provided y is a positive integer less than 14.
[3 marks]
Examiners report
In part (a), the majority of candidates were able to identify the correct value for x. In part (b), many candidates seemed to think that the median was the same as the value of y. Consequently the value 5 proved to be a popular, but incorrect, answer. The majority of candidates wrote down the correct value of 7 and went on to give the required answer of 16 in part (c). A cautionary note here though: A common set of responses to this question was 1, 5 and 18. Without working this earned 1 mark, with working (in part (c)) this earned 4 marks.
In part (a), the majority of candidates were able to identify the correct value for x. In part (b), many candidates seemed to think that the median was the same as the value of y. Consequently the value 5 proved to be a popular, but incorrect, answer. The majority of candidates wrote down the correct value of 7 and went on to give the required answer of 16 in part (c). A cautionary note here though: A common set of responses to this question was 1, 5 and 18. Without working this earned 1 mark, with working (in part (c)) this earned 4 marks.
In part (a), the majority of candidates were able to identify the correct value for x. In part (b), many candidates seemed to think that the median was the same as the value of y. Consequently the value 5 proved to be a popular, but incorrect, answer. The majority of candidates wrote down the correct value of 7 and went on to give the required answer of 16 in part (c). A cautionary note here though: A common set of responses to this question was 1, 5 and 18. Without working this earned 1 mark, with working (in part (c)) this earned 4 marks.
