Mathematics Past Questions and Answers

Using ruler and a pair of compasses only,
(a) construct, (i) triangle XYZ with |XY| = 8cm, < YXZ = 60° and < XYZ = 30° ; (ii) the perpendicular ZT to meet XY in T ; (iii) the locus \(l_{1}\) of points equidistant from ZY and XY.
(b) If \(l_{1}\) and ZT intersect at S, measure |ST|.

In the diagram, /PQ/ = 8m, /QR/ = 13m, the bearing of Q from P is 050° and the bearing of R from Q is 130°.
(a) Calculate, correct to 3 significant figures, (i) /PR/ ; (ii) the bearing of R from P.
(b) Calculate the shortest distance between Q and PR, hence the area of triangle PQR.

The following data gives the lengths, in cm, of 30 pieces of iron rods :
45 55 65 60 61 68 59 54 64 76 50 68 72 68 80 67 70 62 79 67 64 63 71 59 64 53 57 74 55 57
(a) Using class intervals of 45 - 49, 50 - 54, 55 - 59, ... construct a frequency table of the data.
(b) Draw the histogram for the distribution
(c) Calculate the mean of the distribution
(d) What is the probability of selecting an iron rod whose length is in the modal class?

Simplify \(\left(\frac{3}{4} - \frac{1}{3}\right)\times 4\frac{1}{3}\div 3\frac{1}{4}\)

Simplify \(\left(\frac{3}{4} - \frac{1}{3}\right)\times 4\frac{1}{3}\div 3\frac{1}{4}\)