| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Write down | Question number | 7 | Adapted from | N/A |
Question
A tetrahedral (four-sided) die has written on it the numbers 1, 2, 3 and 4. The die is rolled many times and the scores are noted. The table below shows the resulting frequency distribution.
The die was rolled a total of 100 times.
The mean score is 2.71.
Write down an equation, in terms of \(x\) and \(y\), for the total number of times the die was rolled.
Using the mean score, write down a second equation in terms of \(x\) and \(y\).
Find the value of \(x\) and of \(y\).
Markscheme
\(18 + x + y + 22 = 100\) or equivalent (A1) (C1)
[1 mark]
\(\frac{{18 + 2x + 3y + 88}}{{100}} = 2.71\) or equivalent (M1)(A1) (C2)
Note: Award (M1) for a sum including \(x\) and \(y\), divided by 100 and equated to 2.71, (A1) for a correct equation.
[2 marks]
\(x + y = 60\) and \(2x + 3y = 165\) (M1)
Note: Award (M1) for obtaining a correct linear equation in one variable from their (a) and their (b).
This may be implied if seen in part (a) or part (b).
\(x = 15;{\text{ }}y = 45\) (A1)(ft)(A1)(ft) (C3)
Notes: Follow through from parts (a) and (b), irrespective of working seen provided the answers are positive integers.
[3 marks]
