(a) Find the value of X if X3five - 14five = 2Xfive•
(b)

The diagram is a circle passing through the points A, B, C and D such that AC and BD meet at a
point E inside the circle. If LDAC= 27°, LABD= 54° and LACB= 63°, find: (i) <CAB; (ii) <AEB.

Part (a) of this question was reported to be very popular among the candidates and majority of
them performed very well in it. However, it was observed that some candidates failed to
subtract correctly. They wrote -5 + 4 instead of -(5 + 4) when converting -14five to base 10.
Converting the given expression to base ten gave 5X + 3 - (5 + 4) = 10 + X. Simplifying this
given expression gave X = 4.
Part (b) was reported to be poorly attempted by majority of the candidates. Majority of the
candidates could not recall the appropriate theorems that would have enabled them to solve
the question correctly. Candidates were expected to recall that LDBC = 270 (angles in the same
segment as <CAD. Therefore, <CAB = 1800 - <ABD - <DBC - <BCA (sum of angles of a triangle), i.e.
1800 - 540 - 270 - 630 = 360• Angle AEB = 270 + 630 = 900•