ECZ 2018 · GCE Paper 2 · Question 3 — Sets

Learners in a Grade 12 class at Twaenda School travel by buses (B), cars (C) or walk (W). Venn diagram regions: B only = 14, B∩C only = 2, C only = 7, B∩W only = 4, all three = x, C∩W only = 3, W only = 7.

(a(i)) If 22 learners walk to school, find the value of x.[2]

Verified working — step 1

Walkers = W only + B∩W only + C∩W only + all three

(a(ii)(a)) How many learners use only one mode of transport?[1]

Verified working — step 1

Only one mode = B only + C only + W only

(a(ii)(b)) How many learners use two different modes of transport?[1]

Verified working — step 1

Two modes = B∩C only + B∩W only + C∩W only

(b) Show that the points L(-2,-10), M(2,2) and N(5,11) are collinear.[5]

Verified working — step 1

Gradient LM = (2-(-10))/(2-(-2)) = 124= 3

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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