General Mathematics Paper 2,Nov/Dec. 2014  
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General Comments

Question 7

A spherical tank of diameter 3 m is filled with water from a pipe of radius 30 cm at 0.2 m per second. Calculate, correct to 3 significant figures, the time, in minutes, it takes to fill the tank. [Take = ].
  1. When k is added to the expression y2 – 12y, the expression becomes

(y + p)2. Find the values of p and k.



The Chief Examiner reported that this question was quite unpopular with the candidates as majority of them did not attempt it. The performance of those who attempted it was also reported to be poor.
In part (a), the Chief Examiner observed that some candidates did not take note of the different units involved and this affected the accuracy of their answers.
Candidates were expected to recall that radius was half of the diameter. This will enable them to obtain the volume of the spherical tank as  =  m3.
Candidates were then expected to obtain the volume of water from the pipe per second by first converting the radius of the pipe from centimetres to metres. The volume of water was r2h =  =   m3. Time it takes to fill the tank =  =  = 250 seconds. Converting to minutes gave  = 4 minutes.
In part (b), candidates were expected to expand (y + p)2 and compare the coefficients with y2 – 12y + k. Expanding (y + p)2 gave y2 +2yp + p2. By comparing the coefficients we have 2p = -12 ----- eqn(1) and p2 = k ---- eqn(2).
Solving these equations simultaneously gave p = -6 and k = 36.

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