Further Mathematics Past Questions and Answers

An object is thrown vertically upwards from the top of a cliff with a velocity of \(25ms^{-1}\). Find the time, in seconds, when it is 20 metres above the cliff. \([g = 10ms^{-2}]\).

A 0 and 1
B 0 and 4
C 0 and 5
D 1 and 4

Question 587:

Evaluate \(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x\).

A \(-16\)
B \(\frac{-16}{3}\)
C \(\frac{16}{3}\)
D \(16\)

Question 588:

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.

A \((5\frac{2}{3}, \frac{2}{5})\)
B \((\frac{2}{5}, 5\frac{2}{5})\)
C \((\frac{2}{5}, 2\frac{2}{5})\)
D \((\frac{-2}{5}, 5\frac{2}{5})\)

Question 589:

The angle subtended by an arc of a circle at the centre is \(\frac{\pi}{3} radians\). If the radius of the circle is 12cm, calculate the perimeter of the major arc.

A \(4(6 + 5\pi)\)
B \(4(6 + 2\pi)\)
C \(4(3 + 3\pi)\)
D \(4(3 + 5\pi)\)

Question 590:

The function \(f : F \to R\)
= \(f(x) = \begin{cases} 3x + 2 : x > 4 \\ 3x - 2 : x = 4 \\ 5x - 3 : x < 4 \end{cases}\). Find f(4) - f(-3).

A 28
B 26
C -26
D -28