General Mathematics Paper 2, May/June. 2015

Question 6

(a)  (i)  Illustrate the following statement in a Venn diagram:
                              All good Literature students in a school are in the General Arts class

  (ii)  Use the diagram to determine whether or not the following are valid
conclusions from the given statement:

(I)       Vivian is in the General Arts class therefore she is a good
Literature student;

(II)        Audu is not a good Literature student therefore he is not in the General Arts class;

(III)      Kweku is not in the General Arts class therefore he is not a good Literature student.

(b)  The cost (c) of producing n bricks is the sum of a fixed amount, h, and a
variable amount y, where y varies directly as n.  If it costs GH¢ 1,030.00 to   
produce 1000 bricks;

           (i)         find the relationship between c, h and n;

              (ii)         calculate the cost of producing 500 bricks.

Observation

The Chief Examiner reported that this question was attempted by majority of the candidates. The report further stated that majority of the candidates performed better in part (b) than in part (a).

In part (a), Candidates were reported not to draw the correct Venn diagram and so, could not answer part (a)(ii) of the question. Candidates were expected to represent the information in a Venn diagram thus:
 

Where µ = students in the school, GL = Good Literature students, GA = General Arts Students. From the diagram, the first statement is not valid since not all members of the General Arts class are Literature students. The second statement was not also valid since the General Arts class may contain students who are not good Literature students but the third statement was valid. In part (b), candidates were expected to show that since y  n, then y = kn, where k is the constant of variation. In the same way, since c = h + y, it implied that the required equation was c = h + kn. Substituting the given values into the equation gave two equations 950 = h + 600k and 1030 = h + 1000k. Solving these equations simultaneously gave h = 830 and k = . Thus c = 830 + . When n = 500, c = 830 +  = GH¢ 930.00. It was also observed that candidates did not write their final answer in currency format. Money is usually written to 2 decimal places.