Further Mathematics Past Questions and Answers

The roots of the quadratic equation \(2x^{2} - 5x + m = 0\) are \(\alpha\) and \(\beta\), where m is a constant. Find \(\alpha^{2} + \beta^{2}\) in terms of m.

A \(\frac{25}{4} - m\)
B \(\frac{25}{4} - 2m\)
C \(\frac{25}{4} + m\)
D \(\frac{25}{4} + 2m\)

Question 347:

Given that \(2^{x} = 0.125\), find the value of x.

B -1
C -2
D -3

Question 348:

The gradient of point P on the curve \(y = 3x^{2} - x + 3\) is 5. Find the coordinates of P.

A (1, 5)
B (1, 7)
C (1, 13)
D (1, 17)

Question 349:

An arc of length 10.8 cm subtends an angle of 1.2 radians at the centre of a circle. Calculate the radius of the circle.

A 12.6 cm
B 12.0 cm
C 9.6 cm
D 9.0 cm

Question 350:

The first term of a geometric progression is 350. If the sum to infinity is 250, find the common ratio.

A \(\frac{-5}{7}\)
B \(-\frac{2}{5}\)
C \(\frac{2}{5}\)
D \(\frac{5}{7}\)