Further Mathematics Past Questions

Point X and Y are on the same horizontal base as the foot of a building such that X is 96m due east of the building and Y is due west. If the angle of elevation of the top of that building from X is 30\(^o\) and that of Y is 50\(^o\), calculate the distance of Y from the base of the building.

The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively. Find the sixth term of the sequence 

If P = \(\begin {pmatrix} 2 & 3\\  -4 & 1 \end {pmatrix}\), Q = \(\begin{pmatrix} 6 \\ 8 \end {pmatrix}\) and PQ = k \(\begin {pmatrix} 45\\ -20 \end {pmatrix}\). Find the value of k.

Calculate the distance between points (-2, -5) and (-1, 3) 

Find the value of x for which 6\(\sqrt{4x^2 + 1}\) = 13x, where x > 0

Find the sum of the first 20 terms of the sequence -7-3, 1, ......

Given that \(\frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \frac{Q}{(x - 2})\)

x \(\neq \pm 2\)

Find the value of (P + Q)

Consider the following statements:

p: Birds fly

q: The sky is blue

r: The grass is green
What is the symbolic representation of "If the grass is green and the sky is not blue, then the birds do not fly"?

If g : r \(\to\) 5 - 2r, r is a real number, find the image of -3

A linear transformation is defined by T: (x, y) \(\to\) (-x + y, -4y). Find the image, Q`, of Q(-3, 2) under T

Given that g ; x \(\to\) 3x and f ; x \(\to\) cos x. Find the value of g\(^o\) f(20\(^o\)) 

An operation (*) is defined on the set T = {-1, 0, ...., 5} by x * y = x + y - xy. Which of the following operation(s) will give an image that is an element of T?

I. 2(*)5 II. 3(*)2 III. 3(*)4 

If \(^nC_2\) = 15, find the value of n

Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)

Evaluate tan 75\(^o\); leaving the answer in surd form (radicals) 

Solve; \(\frac{P}{2} + \frac{k}{3}\) = 5 and 2p = k = 6 simultaneously

Solve: 8\(^{x - 2}\) = 4\(^{3x}\)

Two functions f and g are defined on the set of real numbers by \(f : x \to x^{2} + 1\) and \(g : x \to x - 2\). Find f o g.

A car is moving at 120\(kmh^{-1}\). Find its speed in \(ms^{-1}\).