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General Mathematics Paper 2,Nov/Dec. 2013  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
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Question 5

Question 5


  1.              Ceramic

                              72o      Textile
                Plywood              65o

The pie chart shows the result of a survey conducted on the maintenance of five small and medium scale industries in a state.  If the cost of maintenance of the plywood industry was N34,500.00, calculate the cost of maintenance of the textile industry.


  1.        T            Y



            X                                                                                                                                                                               42o        Z               
                 U              W
           In the diagram, TYZ and UWZ are tangents to the circle WXY, X 
= 100o, ∠YZW = 42o and ∠UWX = m.  Find the value of m.



This question was reported to be attempted by majority of the candidates.  According to the report, while the candidates performed well in part(a), their performance in part(b) was described as poor.  Candidates reportedly showed poor knowledge of circle geometry.

In part(a) candidates were reported to have obtained the value of x by:  +  + 82 + 68 + 72 = 360o which gave x = 69o.  Thus the value of the angle of the sector for plywood = 69o.  The total cost of maintenance of the industries was obtained as
 = N180,000.00.  Therefore the cost of maintenance of the textile industry =   = N34,000.00.

In part(b) candidates were expected to respond as follows:  In the diagram, triangle ZYW is an isosceles triangle and ∠ZYW = ∠YWZ (The length of the tangents drawn from the same external point are equal). XYW = m (angle in alternate segment to XWU).  This implied that ∠ZYW = 100 – m.  Therefore, (100 – m) + (100 – m) + 42 = 180o (sum of angles of a triangle).  Solving this equation gave m = 31o.



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