WAEC GCE Mathematics Questions
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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).
Mathematics waec gce 2017 ObservationPlease ensure to use curly brackets to enclose the elements of the sets.
Furthermore always list the elements of set C hence, this is for you to be able to find its complement.
Do it this way 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’) = { }. Don’t be like Some candidates know to write like this { 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.
WAEC GCE 2017 Observation.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”,
WAEC GCE 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 – . 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.
