Further Mathematics 2009 Waec Past Questions and Answers

Question 6 :

• WAEC 2009

Given \(\sin \theta = \frac{\sqrt{3}}{2}, 0° \leq \theta \leq 90°\), find \(\tan 2\theta\) in surd form.

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

Question 7 :

• WAEC 2009

Find the coefficient of \(x^{4}\) in the binomial expansion of \((2 + x)^{6}\).

A. 120
B. 80
C. 60
D. 15

Question 8 :

• WAEC 2009

Which of the following binary operations is not commutative?

A. \(a * b = \frac{1}{a} + \frac{1}{b}\)
B. \(a * b = a + b - ab\)
C. \(a * b = 2a + 2b + ab\)
D. \(a * b = a - b + ab\)

Question 9 :

• WAEC 2009

Express \(\frac{2}{3 - \sqrt{7}} \text{ in the form} a + \sqrt{b}\), where a and b are integers.

A. \(6 + \sqrt{7}\)
B. \(3 + \sqrt{7}\)
C. \(3 - \sqrt{7}\)
D. \(6 - \sqrt{7}\)

Question 10 :

• WAEC 2009

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. \(\frac{25}{4} + 2m\)