Mathematics Past Questions and Answers

If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).

If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.

A binary operation Δ is defined by a Δ b = a + 3b + 2.
Find (3 Δ 2) Δ 5

This table below gives the scores of a group of students in a Further Mathematics Test.

Score	1	2	3	4	5	6	7
Frequency	4	6	8	4	10	6	2

Find the mode of the distribution.

This table below gives the scores of a group of students in a Further Mathematics Test.

Score	1	2	3	4	5	6	7
Frequency	4	6	8	4	10	6	2

Calculate the mean deviation for the distribution