| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ2.2 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
All the children in a summer camp play at least one sport, from a choice of football (\(F\)) or basketball (\(B\)). 15 children play both sports.
The number of children who play only football is double the number of children who play only basketball.
Let \(x\) be the number of children who play only football.
There are 120 children in the summer camp.
Write down an expression, in terms of \(x\), for the number of children who play only basketball.
Complete the Venn diagram using the above information.
Find the number of children who play only football.
Write down the value of \(n(F)\).
Markscheme
\(\frac{1}{2}x\) (A1) (C1)
[1 mark]
(A1)(A1)(ft) (C2)
Notes: Award (A1) for 15 placed in the correct position, award (A1)(ft) for \(x\) and their \(\frac{1}{2}x\) placed in the correct positions of diagram. Do not penalize the absence of 0 inside the rectangle and award at most (A1)(A0) if any value other than 0 is seen outside the circles. Award at most (A1)(A0) if 35 and 70 are seen instead of \(x\) and their \(\frac{1}{2}x\).
[2 marks]
\(x + \frac{1}{2}x + 15 = 120\) or equivalent (M1)
Note: Award (M1) for adding the values in their Venn and equating to 120 (or equivalent).
\((x = ){\text{ }}70\) (A1)(ft) (C2)
Note: Follow through from their Venn diagram, but only if the answer is a positive integer and \(x\) is seen in their Venn diagram.
[2 marks]
85 (A1)(ft) (C1)
Note: Follow through from their Venn diagram and their answer to part (c), but only if the answer is a positive integer and less than 120.
[1 mark]
