Further Mathematics Past Questions and Answers

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 the relation between x and y.

A \(y = \frac{1}{2}x + 30\)
B \(y = \frac{1}{2}x + 30\)
C \(y = x + 30\)
D \(y = x - 30\)

Question 377:

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 378:

(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 379:

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

Question 380:

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