Further Mathematics Past Questions and Answers

The radius of a circle increases at a rate of 0.5\(cms^{-1}\). Find the rate of change in the area of the circle with radius 7cm. \([\pi = \frac{22}{7}]\)

A 11\(cm^{2}s^{-1}\)
B 22\(cm^{2}s^{-1}\)
C 33\(cm^{2}s^{-1}\)
D 44\(cm^{2}s^{-1}\)

Question 92:

Find an expression for y given that \(\frac{\mathrm d y}{\mathrm d x} = x^{2}\sqrt{x}\)

A \(\frac{1x^{\frac{2}{7}}}{7} + c\)
B \(\frac{2x^{\frac{3}{2}}}{7} + c\)
C \(\frac{2x^{\frac{7}{2}}}{7} + c\)
D \(\frac{1x^{\frac{7}{2}}}{7} + c\)

Question 93:

Evaluate \(\cos leaving the answer in surd form.

A \(\frac{\sqrt{2}}{2}(\sqrt{3} + 1)\)
B \(\frac{\sqrt{2}}{4}(\sqrt{3} - 1)\)
C \(\frac{\sqrt{2}}{4}(\sqrt{3} + 1)\)
D \(\frac{\sqrt{2}}{2}(\sqrt{3} - 1)\)

Question 94:

Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\).

A \(\frac{16}{33}\)
B \(\frac{33}{56}\)
C \(\frac{33}{16}\)
D \(\frac{56}{33}\)

Question 95:

Find the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5.

A Y = 2x + 11
B Y = 3x + 11
C Y = 3x - 5
D Y = 2x - 11