O-LevelMathematicsNumber4024/22 · May/June 2018 · Q48 Marks

& = {x : x is an integer 1 ≤ x ≤ 18}, A = {x : x is a prime number}, B = {1, 2, 3, 4, 6, 9, 12, 18}.

(a)(i)Complete the Venn diagram to illustrate this information. [Figure: incomplete Venn diagram with elements 1, 4, 9, 12, 18, 2, 3, 6 inside circles A and B or their intersection.][1]
(a)(ii)Complete the description of the set B. Answer B = { x : x is a factor of ............}[1]
(a)(iii)Find n(A U B).[1]
(a)(iv)List the elements of A' ∩ B.[1]
(b)Find the lowest common multiple (LCM) of 140 and 770.[2]
(c)A rectangular field measures 450m by 306 m. The whole field is divided into identical square plots with no land remaining. Find the largest possible side length for the squares.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[1] Correctly completed Venn diagram
[1] 36
[1] FT n(A U B) from their Venn diagram provided no repeated elements in sets A and B
[1] FT provided no repeated elements in sets A and B
[2] B1 for answer 1540k, where k is an integer or for 2 × 2 × 5 × 7 and 2×5×7× 11 seen or 2, 2, 5, 7, 11
[2] B1 for answer 2, 3, 6 or 9 or for 2 x 3×3×5×5 and 2 × 3 × 3 × 17 seen or 2, 3, 3 with 25 and 17

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