Further Mathematics Past Questions and Answers

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 7x + 4 = 0\), find the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\).

(a) Write down the binomial expansion of \((2 - x)^{5}\) in ascending powers of x.
(b) Use your expansion in (a) to evaluate \((1.98)^{5}\) correct to four decimal places.

Solve \(2^{(2y + 2)} - 9(2^{y}) = -2\).

(a) Write the following as column vectors: \(r = (10N, 090°) ; q = (8N, 135°)\).
(b) Use your answer in (a) to find \((r + q)\).

(a) Evaluate \(\frac{^{9}P_{3}}{^{15}C_{3}} + \frac{^{5}C_{3}}{^{3}P_{2}}\) correct to two decimal places.
(b) A committee of 2 tutors and 5 pupils is to be formed among 6 tutors and 10 pupils. In how many ways can this be done if one particular tutor must be on the committee and two particular pupils must not be on the committee?