Mathematics Past Questions and Answers

In the diagram, O is the center of the circle, If ∠POQ = 80^o and ∠PRQ = 5x, find the value of x.

In an A.P the first term is 2, and the sum of the 1st and the 6th term is 161/2. What is the 4th term

(a) Without using Mathematical tables, find x, given that \(6 \log (x + 4) = \log 64\)
(b) If \(U = {1, 2, 3,4, 5, 6, 7, 8, 9, 10}, X = {1, 2, 4, 6, 7, 8, 9}, Y = {1, 2, 3, 4, 7, 9}\) and \(Z = {2, 3, 4, 7, 9}\). What is \(X \cap Y \cap Z' \)?

The table shows the weights, to the nearest kilogram, of twelve students in a Further Mathematics class

Weight in kg	55	57	59	61	63
No of students	2	1	2	4	3

(a) Draw a bar chart to illustrate the above information;
(b) What is (i) the mode; (ii) the median of the distribution?
(c) Calculate the mean weight correct to the nearest kilogram.

The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 24cm and the base height 7cm. Calculate, correct to three significant figures, the surface area of the structure. [Take \(\pi = \frac{22}{7}\)].