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WAEC 2017 · Paper 2 · Q1

  1. (a)

    If (y−1)log⁡104=ylog⁡1016(y - 1)\log_{10} 4 = y\log_{10} 16, without using mathematical tables or a calculator, find the value of yy.

  2. (b)

    When I walk from my house at 4 km/h4\text{ km/h}, I get to the office 30 minutes later than when I walk at 5 km/h5\text{ km/h}. Calculate the distance between my house and the office.

Worked solution (try it first)

(a)

  1. Write 16 as a power of 4: 16=4216 = 4^2, so log⁡1016=2log⁡104\log_{10} 16 = 2\log_{10} 4.
  2. The equation becomes (y−1)log⁡104=2ylog⁡104(y - 1)\log_{10} 4 = 2y\log_{10} 4.
  3. Divide both sides by log⁡104\log_{10} 4: y−1=2yy - 1 = 2y.
  4. So y=−1y = -1.

(b)

  1. Let the distance be xx km.
  2. Time =distancespeed= \frac{\text{distance}}{\text{speed}}, so walking at 4 km/h takes x4\frac x4 hours and at 5 km/h takes x5\frac x5 hours.
  3. The slower walk takes 30 minutes =12= \frac12 hour longer: x4−x5=12\frac x4 - \frac x5 = \frac12.
  4. Multiply by 20: 5x−4x=105x - 4x = 10, so x=10x = 10.
  5. The office is 10 km from the house.

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