Question

5(a) Given that m=tan30°, n=tan45°, simplify (m−n)/mn without using calculator, leaving the answer in the form p+√q.
(b) There are 20 women in a bus. 15 of them wear glasses and 10 wear watches. If a woman is chosen at random from the bus, find the probability that she wears both glasses and watch.

Accepted Answer

(a) tan30°=√3/3, tan45°=1. (m−n)/mn = (√3/3 − 1)/(√3/3 × 1) = (√3−3)/3 ÷ √3/3 = (√3−3)/√3.
Multiplying by conjugate √3/√3: = (3−3√3)/3 = 1−√3 = 1+(−√3). So p=1, q=3.

(b) n(G)=15, n(W)=10, n(U)=20 (total).
Using a Venn diagram: let x = number wearing both glasses and watches.
(15−x)+x+(10−x)=20
25−x=20
x=5
P(both) = 5/20 = 1/4.

WAEC Mathematics 2022 Theory — Question 5

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