O-LevelAdditional MathematicsEquations, inequalities and graphs4037/22 · Oct/Nov 2018 · Q25 Marks
E [Figure: Venn Diagram with F and C circles, overlapping] There are 105 boys in a year group at a school. Some boys play football (F) and some play cricket (C). • x boys play both football and cricket. • The number of boys that play neither game is the same as the number of boys that play both. • 40 boys play cricket. • The number of boys that only play football is twice the number of boys that only play cricket. Complete the Venn diagram and find the value of x.
- Complete the Venn diagram and find the value of x.[5]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] n(F∩C)=n(F∪C)' = x
- [B1] n(C∩F') = 40-x
- [B1] n(F∩C')=80-2x or 2(40-x)
- [M1] x+x+40-x+80-2x = 105
- [A1] x=15 cao
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