O-LevelAdditional MathematicsEquations, inequalities and graphs4037/11 · May/June 2010 · Q46 Marks

Copy the Venn diagram [Figure 4(a)] above and shade the region that represents (A ∩ B) U C.

(a)(i)Copy the Venn diagram [Figure 4(a)] above and shade the region that represents (A ∩ B) U C.[1]
(a)(ii)Copy the Venn diagram [Figure 4(a)] above and shade the region that represents A' ∩ Β'.[1]
(a)(iii)Copy the Venn diagram [Figure 4(a)] above and shade the region that represents (A ∪ B) ∩ C.[1]
(b)It is given that the universal set E = {x : 2 ≤ x ≤ 20, x is an integer}, X = {x : 4 < x < 15, x is an integer}, Y = {x : x = 9, x is an integer}, Z = {x: x is a multiple of 5}.
(b)(i)List the elements of X ∩ Y.[1]
(b)(ii)List the elements of XU Y.[1]
(b)(iii)Find (XU Y)' ∩ Z.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

[1] (a)(i) B1 for correct Venn diagram for (A ∩ B) U C (Shade the intersection of A and B, and also shade C entirely)
[1] (a)(ii) B1 for correct Venn diagram for A' ∩ B' (Shade the region outside both A and B)
[1] (a)(iii) B1 for correct Venn diagram for (A U B) ∩ C (Shade the intersection of C with the union of A and B)
[1] (b)(i) B1 for {9,10,11,12,13,14} (Or equivalent)
[1] (b)(ii) B1 for {5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} (Or equivalent)
[1] (b)(iii) B1 for ∅ or { }

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