FUTA Mathematics 2012/2013 Past Questions

Determine x + y if $$\begin{vmatrix}2 & -3 \\ -1 & 4 \end{vmatrix}\begin{vmatrix}x \\ y \end{vmatrix} = \begin{vmatrix}-1\\ 8\end{vmatrix}$$

Find the minimum value of x² - 3x+2 for all real values of x

If the function f(x) = x³ + 2x² + qx - 6 is divisible by x + 1. find q.

Find the gradient of the curve y= 2x(x-3) at x = 1

Integrate 1/x + cos x with respect to x

Find the value of K if $${\frac k{\sqrt3} = \sqrt3}$$

If 6Cr/ 6Pr= 1/6. find the value of r.

How many two-digits numbers can be formed from the digits 0, 1, 2, 3, if a digit can be repeated and no number may begin with 0?

The length of the sides of a right-angled triangle are xcm, (3x - 1) cm and (3x + 1). Find x.

If y = x sin x, find dy/dx when x = π/2

9(-6, 1) and A(6, 6) are the two ends of the diameter of a given circle. Calculate the radius

Find the rate of change of the volurne, v of a sphere with respect to its radius r when r = 1.

IF 6_pr = 6, find the value of 6_pr+2*

Teams A and B are involved in a game of football. What is the probability that the game ends in a draw?

The range of the data k -2. k - 3, k + 4, k - 2, k-5, k +3, .k-1 and k + 6 is

If A = $|\table 2, 1; -3, 0|$ and I is a 2x2 unit matrix. Evaluate A² - 2A + 4I

If the 9th term of an A.P. is five times the 5th term, find the relationship between a and d.

Find the maximum value of y in the equation y = 1- 2x - 3x²

The binary operation * is defined on the set of integers P and q by p* q = pq + + q. Find 2*(3*4).

Given that Q = $$\begin{vmatrix}6 & 0 \\ 4 & 5 \end{vmatrix}$$ and Q + 2P = $$\begin{vmatrix}7 & -2 \\ 6 & 8 \end{vmatrix}$$ Evaluate the determinant of (Q + 2P)