General Mathematics Paper 2, May/June. 2015

Question 9

(a)  The first term of an Arithmetic Progression (AP) is - 8.  If the ratio of the 7th term to the 9th term is 5 : 8, find the common difference of the AP.

(b)  A trader bought 30 baskets of pawpaw and 100 baskets of mangoes       forN2,450.00.  She sold the pawpaw at a profit of 40% and the mangoes at
a profit of 30%.  If her profit on the entire transaction was N855.00, find the:

(i)    cost price of a basket of pawpaw;

(ii)   selling price of the 100 baskets of mangoes.

Observation

It was reported that this question was popular among the candidates. In part (a), candidates’ performance was commended as majority of those who attempted it scored full marks. They were reportedly able to apply the appropriate formula, Tn = a + (n – 1)d, where Tn = nth term, a = first term and d = common difference, to obtain  = . By cross multiplying we obtain -64 + 48d = -40 + 40d. Simplifying this equation gave d = 3.

In part (b), candidates were reported to have performed poorly. According to the report, majority of them were not able to translate the word problem into Mathematical language correctly. Candidates were expected to show that if p = cost of a basket of paw-paw and m = cost of a basket of mangoes, then 30p + 100m = 2450 ----(1) and 12p + 30m = 855 ----(2). Solving these two equations simultaneously gave p = N 40.00. and m = N 12.50. This implied that the cost price of a bag of paw-paw = N 40.00 while the selling price of 100 baskets of mangoes= 100m = 100 × N 12.50 = N 1250.00.