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WAEC 2020 · Paper 2 · Q8

  1. (a)

    In a class, students were taught French, Mathematics and Economics. The teachers observed that 5 liked all the 3 subjects, 9 French and Mathematics, 8 Mathematics and Economics and 7 French and Economics. If 17 liked Economics, 18 Mathematics, 16 French and 4 none of the subjects: (i) illustrate the information on a Venn diagram; (ii) how many students were in the class?

  2. (b)

    The length of the shadow of a pole on level ground increases by 90 metres when the angle of elevation of the sun changes from 58∘58^\circ to 36∘36^\circ. Calculate, correct to three significant figures, the height of the pole.

Worked solution (try it first)

(a)(i)

  1. Fill the Venn diagram from the middle outwards.
  2. All three: 5.
  3. French and Mathematics only: 9−5=49 - 5 = 4.
  4. Mathematics and Economics only: 8−5=38 - 5 = 3.
  5. French and Economics only: 7−5=27 - 5 = 2.
  6. Mathematics only: 18−5−4−3=618 - 5 - 4 - 3 = 6.
  7. French only: 16−5−4−2=516 - 5 - 4 - 2 = 5.
  8. Economics only: 17−5−3−2=717 - 5 - 3 - 2 = 7.
  9. Outside the circles: 4.

(ii)

  1. Total: 5+4+3+2+6+5+7+4=365 + 4 + 3 + 2 + 6 + 5 + 7 + 4 = 36 students.

(b)

  1. Let the pole be hh m high and its first shadow xx m long.
  2. With the sun at 58∘58^\circ: h=xtan⁡58∘h = x\tan 58^\circ.
  3. With the sun at 36∘36^\circ the shadow is x+90x + 90: h=(x+90)tan⁡36∘h = (x + 90)\tan 36^\circ.
  4. Set them equal: xtan⁡58∘=xtan⁡36∘+90tan⁡36∘x\tan 58^\circ = x\tan 36^\circ + 90\tan 36^\circ, so x=90tan⁡36∘tan⁡58∘−tan⁡36∘x = \frac{90\tan 36^\circ}{\tan 58^\circ - \tan 36^\circ}
    =65.390.8738= \frac{65.39}{0.8738}
    ≈74.83\approx 74.83 m.
  5. Then h=74.83tan⁡58∘≈119.7h = 74.83\tan 58^\circ \approx 119.7 m, which is 120 m to three significant figures.

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