O-LevelAdditional MathematicsFunctions4037/22 · Oct/Nov 2014 · Q15 Marks
On each of the Venn diagrams below shade the region which represents the given set. (A∩B) ∪ C' A' ∩ (B∪C)
- (a)On each of the Venn diagrams below shade the region which represents the given set. (A∩B) ∪ C' A' ∩ (B∪C)[2]
- (b)In a year group of 98 pupils, F is the set of pupils who play football and H is the set of pupils who play hockey. There are 60 pupils who play football and 50 pupils who play hockey. The number that play both sports is x and the number that play neither is 30 - 2x. Find the value of x.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [B1] (a) Shading for (A ∩ B) ∪ C'
- [B1] (a) Shading for A' ∩ (B ∪ C)
- [B1] (b) No. in H only = 50 − x ; No in F only = 60 - x. Both written or on diagram.
- [M1] (b) Sum: 50-x+60-x+x+30-2x=98. Add at least 3 terms each with x involved and equate to 98 soi.
- [A1] (b) x = 14
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