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WAEC 2022 · Paper 2 · Q6

  1. (a)

    The sum of two numbers is 8 and their product is −33-33. Find the numbers.

    Separate values with commas, e.g. 3, −2

  2. (b)

    A truck, PP, travelling at 54 km h−154\text{ km h}^{-1} passes through a point at 10.30 am while another truck, QQ, travelling at 90 km h−190\text{ km h}^{-1} passes through this same point 30 minutes later. At what time will truck QQ overtake PP?

    Show the answer

    11.45 am

Worked solution (try it first)

(a)

  1. Let the numbers be aa and 8−a8 - a (so their sum is 8).
  2. Their product is −33-33: a(8−a)=−33a(8 - a) = -33.
  3. So 8a−a2=−338a - a^2 = -33, which rearranges to a2−8a−33=0a^2 - 8a - 33 = 0.
  4. Factorise: (a−11)(a+3)=0(a - 11)(a + 3) = 0.
  5. So a=11a = 11 or a=−3a = -3.
  6. The numbers are 11 and −3-3.

(b)

  1. Let QQ overtake PP at tt hours after 10.30 am.
  2. By then PP has travelled for tt hours, and QQ (which passed the point 30 minutes later) for t−12t - \frac12 hours.
  3. When QQ overtakes, they have gone the same distance from the point: 54t=90(t−12)54t = 90\left(t - \frac12\right).
  4. So 54t=90t−4554t = 90t - 45, 36t=4536t = 45 and t=114t = 1\frac14 hours =1= 1 hour 15 minutes.
  5. QQ overtakes PP at 11.45 am.

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