Mathematics Past Questions and Answers

(a)
A segment of a circle is cut off from a rectangular board as shown in the diagram. If the radius of the circle is \(1\frac{1}{2}\) times the length of the chord; calculate, correct to 2 decimal places, the perimeter of the remaining portion. [Take \(\pi = \frac{22}{7}\)]
(b) Evaluate without using calculators or tables, \(\frac{3}{\sqrt{3}}(\frac{2}{\sqrt{3}} - \frac{\sqrt{12}}{6})\).

The frequency distribution table shows the marks obtained by 100 students in a Mathematics test.

Marks (%)	1-10	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90	91-100
Frequency	2	3	5	13	19	31	13	9	4	1

(a) Draw the cumulative curve for the distribution.
(b) Use the graph to find the : (i) 60th percentile ; (ii) probability that a student passed the test if the pass mark was fixed at 35%.

An aeroplane flies due North from a town T on the equator at a speed of 950km per hour for 4 hours to another town P. It then flies eastwards to town Q on longitude 65°E. If the longitude of T is 15°E,
(a) represent this information in a diagram ;
(b) calculate the : (i) latitude of P, correct to the nearest degree ; (ii) distance between P and Q, correct to four significant figures. [Take \(\pi = \frac{22}{7}\); Radius of the earth = 6400km].

Simplify 10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)

Simplify 10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)