Mathematics Past Questions and Answers

Two towns K and Q are on the parallel of latitude 46°N. The longitude of town K is 130°W and that of town Q is 103°W. A third town P also on latitude 46°N is on longitude 23°E, Calculate:
(i) the length of the parallel of latitude 46°N, to the nearest 100km;
(ii) the distance between K and Q, correct to the nearest 100km;
(iii) the distance between Q and P measured along the parallel of latitude, to the nearest 10km.
[Take \(\pi = 3.142\); Radius of the earth = 6400km]

(a) Prove that the sum of the angles in a triangle is two right angles.
(b) In a triangle LMN, the side NM is produced to P and the bisector of < LNP meets ML produced at Q. If < LMN = 46°, and < MLN = 80°, calculate < LQN, stating clearly your reasins.

Using a ruler and a pair of compasses only,
(a) construct (i) a triangle ABC such that |AB| = 5cm, |AC| = 7.5cm and < CAB = 120° ; (ii) the locus \(L_{1}\) of points equidistant from A and B ; (iii) the locus \(L_{2}\) of points equidistant from Ab and AC, which passes through the triangle ABC.
(b) Label the point P where \(L_{1}\) and \(L_{2}\) intersect;
(c) Measure |CP|.

If 3loga + 5loga - 6loga = log64, what is a?

If 3loga + 5loga - 6loga = log64, what is a?