4400 Higher November 2006 Paper 3 Q19
19 Each student in a group plays at least one of hockey, tennis and football.
10 students play hockey only
9 play football only.
13 play tennis only.
6 play hockey and football but not tennis.
7 play hockey and tennis.
8 play football and tennis.
\(x\) play all three sports.
(a) Write down an expression, in terms of \(x\), for the number of students who play hockey and tennis, but not football. (1)
There are 50 students in the group.
(b) Find the value of \(x\). (3)
| Scheme | Marks |
|---|---|
| \(7 - x\) | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(8 - x\) seen or 9, 13, 6 marked correctly on diagram or 50 − (10 + 9 + 13 + 6) = 50 − 38 = 12 and 8 + 7 = 15 | M1 |
| \(10 + 13 + 9 + 6 + (7 - x) + (8 - x) + x = 50\) oe inc \(7 - x + 8 - x + x = 12\) or 15 − 12 | M1 |
| 3 | A1 |
| (3) | |
| (4 marks) |
Notes
M1: equation must be correct