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WAEC 2020 · Paper 2 · Q9

  1. (a)

    An aeroplane flies 100 km100\text{ km} from point AA to point BB on a bearing of 330∘330^\circ. It then flies from point BB to point CC, 300 km300\text{ km} due west. (i) Illustrate this on a diagram. (ii) How far west, correct to the nearest km, is the aeroplane from the starting point?

  2. (b)

    A student added consecutive odd numbers starting from 11 and had a sum of 551. How many odd numbers were added?

Worked solution (try it first)

(a)(i)

  1. Draw north at AA and ABAB, 100 km on 330∘330^\circ (30∘30^\circ west of north).
  2. From BB, draw BCBC, 300 km due west.

(ii)

  1. On the first leg, the westward part is the side opposite the 30∘30^\circ angle between ABAB and north: 100sin⁡30∘=50100\sin 30^\circ = 50 km.
  2. The second leg adds 300 km more to the west.
  3. So CC is 50+300=35050 + 300 = 350 km west of AA.

(b)

  1. The odd numbers from 11 form an A.P. with a=11a = 11 and d=2d = 2.
  2. Sn=n2[2a+(n−1)d]S_n = \frac n2[2a + (n - 1)d]
    =n2[22+2(n−1)]= \frac n2[22 + 2(n - 1)]
    =n(n+10)= n(n + 10).
  3. So n2+10n=551n^2 + 10n = 551, which is n2+10n−551=0n^2 + 10n - 551 = 0.
  4. Factorise: (n−19)(n+29)=0(n - 19)(n + 29) = 0.
  5. The number of terms is positive, so n=19n = 19.

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