WAEC - May/June. 2010 General Mathematics Past Questions

General Mathematics May/June 2010 Past Questions

The resources below on Mathematics have been provided by WAEC to assist you understand the required standards expected in Mathematics final Examination.

Students performance in examination under review was done by the Chief examiner.

Question 1
A = {2, 4, 6, 8}, B = {2, 3, 7, 9} and C = {x: 3 < x < 9} are subsets of the universal-set
U = {2, 3, 4, 5, 6, 7, 8, 9}. Find
(a)   A n(B'nC');
(b) (AuB) n(BuC).

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Observation
This question was reportedly attempted by majority of the candidates and their performance was described as satisfactory. Many of them lost some marks because they failed to use curly brackets to enclose the elements of the sets. A good number of the candidates were also reported not to have listed the elements of set C hence, were not able to find its complement while others did not separate the elements of a set with comas.

Candidates were expected to list the elements of C i.e. C = {4, 5,6, 7, 8}, obtain the compliments of the sets Band C thus B' = {4,5,6, 8}, C' = {2, 3, 9,}. Using these sets, the following procedures were to be followed:
(a)(B' nC') = { } Hence An (B' n C') = { }. Some candidates were reported to have written { 0 } instead of { } or 0.
(b) (A u B) = { 2, 3,4,6, 7, 8, 9 }, (BuC) = {2, 3, 4,5,6, 7, 8, 9 } Therefore { Au B } n (BuC) = { 2, 3, 4, 6, 7, 8, 9 }.


Question 2
(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

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Observation
This question was also reported to have been attempted by majority of the candidates. Furthermore, the report stated that in part (a), majority of the candidates could not draw the diagram correctly and this affected their performance significantly. A few others were unable to apply the trigonometric ratios correctly. Candidates were expected to draw the diagram.
From the diagram, I FMI :: 120 tan 35° = 84.02m. Therefore the height of the cliff:: 2 x 84.02 = 168.04.
In part (b), the most observed weakness was their inability to convert from minutes to hours. They were expected to recall that time :: distance (i.e. t:: ~) and apply this to the problem.
                                                         speed         v
Time taken by faster motorist « ~ while that of the other motorist = ~ where x is the distance
                                                             60                                                                   80
                     X x
from P to Q. - - - = Y2 (30 rnlnutes « Y2 hr). Simplifying this expression gave x = 120km.
                       60 80
Candidates' responses to this question were reported to be generally below average.



Question 3
(a) In the diagram, L PQR = 125°, LQRS = r, LRST = 800 and LSTU = 44°. Calculate the value of r

b) .

In the diagram, TS is a tangent to the circle at A. ABI ICE, LAEC = sx", LADB = 60° and LTAE = xo. Find the value of x",

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Observation
Part (a) of this question required that candidates drew straight lines, one each passing through points Sand R and parallel to PQ and UT as shown in the diagram below but the report stated that majority of the candidates did not.From the diagram, LMQR = LQRN = 180 -125 = 55° ( alternate angles), LVST = 44° (alternate angle to LSTU). Therefore LNRS = LVSR = 80 - 44° = 360• Hence, r = 55 + 36 = 91°

In part (b), candidates' performance was reported to be worse than part (a). Candidates were reported to have exhibited poor understanding of circle theorems. Teachers were encouraged to do a lot of work in this area.

From the diagram, LBDA = LBAS = 600 (angles in the alternate segment). LBAE = 180° - 5x (adjacent angles on a transversal). Therefore LBAS + LBAE + LEAT = 60 + 180 - 5x + x = 180 (angles on a straight line). Solving this simple equation gave x = 150. Candidates' performance this question was described as poor.

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