UNN Mathematics 2012/2013 Past Questions

If p, q and r are in the ratio 6: 4: 5, find the value of (3p - q) ÷ (4q + r)

If log₁₀2 = x and log₁₀3 = y, express log₁₀10 + 2log₁₀6 in terms of x and y.

Simplify ${1 1/2}/{2 ÷ {1/4} of 16}$

If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.

Find the sum to infinity of the series 2 + 1/2 + 9/8 + 27/32 + ....

Evaluate $|\table;cos2θ,-2sinθ;2sinθ,2;|$

The point A has coordinates (5, 16) and the point B has coordinates (-4, 4). The variable point P has coordinates (x, y) and moves on a path such that AP = 2BP. Find the Cartesian equation of the path of P.

Simplify $4sinθsin(π/3 - θ)sin(π/3 + θ)$

The distance points P and Q with coordinates (ap², 2ap) and (aq², 2aq) respectively lie on the curve y² = 4ax. The tangents to the curve at P and Q meet at the point T. Find the coordinates of T if pq not equal to 0

If y = 2cos(3x - π), then dy/dx is

Find the coordinates of the turning points of the curve y = 27x³ - 27x² + 4

If y = (1 + 2x)³, find dy/dx at x = -1

An examiner has five envelopes labeled A to E for each of the five options of a question paper. In how many ways can the examiner place one option of the question in each envelope without getting every option in the envelope?

The distribution below shows the money received by a group of students who shared 12,000.00 with a teacher. How much did the teacher receive?

Amt. Received	200	350	700	1000
No. of students	1	2	3	5

Two numbers are removed at random from the numbers -1, 0, 1. What is the probability that the product of the numbers removed is zero?