Mathematics Past Questions and Answers

An aeroplane flies due west for 3 hours from P (lat. 50°N, long. 60°W) to a point Q at an average speed of 600km/h. The aeroplane then flies due south from Q to a point Y 500km away. Calculate, correct to 3 significant figures,
(a) the longitude of Q ;
(b) the latitude of Y . [Take the radius of the earth = 6400km and \(\pi = \frac{22}{7}\)].

Using ruler and a pair of compasses only,
(a) construct a quadrilateral PXYQ such that /PX/ = 9.9 cm, /QX/ = 10.2 cm, < QPZ = 75°, /QY/ = 10.4 cm and PQ // XY.
(b) Construct the (i) locus \(l_{1}\) of points equidistant from X and Y ; (ii) locus \(l_{2}\) of points equidistant from QY and YX.
(c) Locate M, the point of intersection of \(l_{1}\) and \(l_{2}\).
(d) Measure /PM/.

1. Evaluate \( 202^2_{three} - 112^2_{three}\)

1. Evaluate \( 202^2_{three} - 112^2_{three}\)

If \(y = 23_{five} + 101_{three}\), find y, leaving your answer in base two