O-LevelAdditional MathematicsEquations, inequalities and graphs4037/21 · May/June 2015 · Q117 Marks
The Venn diagram above shows the sets A, B and C. It is given that n(A ∪ B ∪ C) = 48, n(A) = 30, n(B) = 25, n(C) = 15, n(A ∩ B) = 7, n(B ∩ C) = 6, n(A' ∩ B ∩ C') = 16. [Figure 11.1]
- (i)Find the value of x, where x = n(A ∩ B ∩ C).[3]
- (ii)Find the value of y, where y = n(A ∩ B' ∩ C).[3]
- (iii)Hence show that A' ∩ B' ∩ C = Ø.[1]
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Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [B1] 7-x, x, 6-x oe
- [M1] their attempt at 7-x+x+6-x+16=25 oe
- [A1] x = 4 Condone x = 4 for all 3 marks
- [B1] 23-y, y, 9 - y oe or n(A ∪ C) = 48-16 = 32
- [M1] 48 = 30 + 25 + 15 – 7 – 6 – (their 4 + y) + their 4 oe soi or 32 = 30 + 15 – (their 4 + y) or 48 = (23 - y) + 3 + 16 + y +4 + 2 + (9-y)
- [A1] y = 9 Condone y = 9 for all 3 marks
- [B1] n(C) = 15 and y + n(B∩C) = 9+ 6 = 15 [and so A'B'∩C = Ø]. or equivalent deduction
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