Further Mathematics Past Questions and Answers

Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)

A \(3\sqrt{2}\)
B \(2\sqrt{3}\)
C \(\sqrt{3}\)
D \(\sqrt{2}\)

Question 207:

The binary operation * is defined on the set of R, of real numbers by \(x * y = 3x + 3y - xy, \forall x, y \in R\). Determine, in terms of x, the identity element of the operation.

A \(\frac{2x}{x - 3}, x \neq 3\)
B \(\frac{2x}{x + 3}, x \neq -3\)
C \(\frac{3x}{x - 3}, x \neq 3\)
D \(\frac{3x}{x + 3}, x \neq -3\)

Question 208:

Find the fourth term of the binomial expansion of \((x - k)^{5}\) in descending powers of x.

A \(10x^{3}k^{2}\)
B \(5x^{3}k^{2}\)
C \(-5x^{2}k^{3}\)
D \(-10x^{2}k^{3}\)

Question 209:

The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Find the value of k.

A 3
B 2
C -3
D -2

Question 210:

The tangent to the curve \(y = 4x^{3} + kx^{2} - 6x + 4\) at the point P(1, m) is parallel to the x- axis, where k and m are constants. Determine the coordinates of P.

A (1, 2)
B (1, 1)
C (1, -1)
D (1, -2)