Waec Further Mathematics 2009 Past Questions and Answers

Question 41:

• WAEC 2009

In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.

A. \(\frac{\sqrt{3} \tan x - 1}{\sqrt{3} + \tan x}\)
B. \(\frac{\sqrt{3} \tan x}{\sqrt{3} + \tan x}\)
C. \(\frac{\sqrt{3} \tan x + 1}{\sqrt{3} - \tan x}\)
D. \(\frac{3 \tan x - 1}{\sqrt{3} - \tan x}\)

Question 42:

• WAEC 2009

(a) Solve : \(2x^{2} + x - 6 < 0\)
(b) Express \(\frac{5 - 2\sqrt{10}}{3\sqrt{5} + \sqrt{2}}\) in the form \(m\sqrt{2} + n\sqrt{5}\) where m and n are rational numbers.

Question 43:

• WAEC 2009

Solve the simultaneous equations : \(\log_{2} x - \log_{2} y = 2 ; \log_{2} (x - 2y) = 3\)

Question 44:

• WAEC 2009

If the quadratic equation \((x + 1)(x + 2) = k(3x + 7)\) has equal roots, find the possible values of the constant k.

Question 45:

• WAEC 2009

Given that \(\tan 2A = \frac{2 \tan A}{1 - \tan^{2} A}\), evaluate \(\tan 15°\), leaving your answer in surd form.