O-LevelMathematicsNumber4024/12 · Oct/Nov 2021 · Q257 Marks

40 students can take part in three activities, Art (A), Dancing (D) and Gardening (G). • 5 do not take part in any of the activities • 12 do Art only • 4 do Dancing and Gardening but not Art • 1 student does all three activities

(a)Complete the Venn diagram. [Figure X.X][2]
(b)On the Venn diagram, the ratio x : y : z = 1 : 2 : 3. Find the value of each of x, y and z.[3]
(c)One subset in the Venn diagram in part (a) has no students. Use set notation to describe this subset.[1]
(d)Find n((D∪G)∩A).[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[2] Venn diagram with 12, 0, 1, 4, 5 correctly placed, and x, y, z in correct locations
B1 for 2 or 3 values correctly placed
[3] [x = ] 3 [y = ] 6 [z = ] 9
B2 for x=3 OR M2 for (40-12-1-4-5)/(1+2+3) soi or M1 for 40-12-1-4-5 soi or x + y + z +12 + 1 + 4 + 5 = 40 oe
[1] A ∩ G ∩ D' oe
[1] (their x) + 1 evaluated

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