Further Mathematics Past Questions and Answers

If \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{15}{17}\), where A is an obtuse angle and B is acute, find the value of \(\cos (A + B)\).

Differentiate, with respect to x, \(x^{3} + 2x\) from the first principle.

A straight line passes through the point P(-1, 3). Another line which passes through Q(-4, 4) intersects the first line at the point R(k, 5), where k is a constant. If \(<PRQ = 90°\), find the values of k.

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both. The Venn diagram shows the choices made by 25 guests of the hotel.
(a) Find the value of x;
(b) What is the probability that a guest chosen at random chose only one of the two?

The table shows the distribution of marks obtained by some candidates in a test.

Marks	10-14	15-24	25-29	30-39	40-44	45-49
No of candidates	14	30	22	18	12	4

Draw a histogram for the distribution.