Further Mathematics Past Questions and Answers

(a) The distribution of the lives (in days) of 40 transitor batteries is shown in the table:

Battery life(in days)	26-30	31-35	36-40	41-45	46-50	51-55
Frequency	4	7	13	8	6	2

(a) Draw a histogram for the distribution.
(b) Use your graph in (a) to determine the mode for the distribution.
(c) Using an assumed mean of 43 days, calculate the mean of the distribution.
(d) What percentage number of batteries will live for less than 31 days or more than 45 days?

The table below shows the corresponding values of two variables X and Y.

X	33	31	28	25	23	22	19	17	16	14
Y	4	6	4	10	12	10	14	15	18	22

(a) Plot a scatter diagram to represent the data.
(b) Calculate \(\bar{x}\), the mean of X and \(\bar{y}\), the mean of Y.
(c) Draw the line of best fit to pass through \((\bar{x}, \bar{y})\).
(d) From your graph in (c), determine the (i) relationship between X and Y ; (ii) value of Y when X is 24.

(a) The position vectors of points L and M are (5i + 6j) and (13i + 4j) respectively. If point K lies on LM such that LK : KM is 2 : 3, find the position vector of K.
(b) Three poles are situated at points A, B and C on the same horizontal plane such that \(AB = (8km, 060°)\) and \(BC = (12km, 130°)\). Calculate,
(i) |AC|, correct to three significant figures ; (ii) the bearing of C from A, correct to the nearest degree.

Coplanar force 4N, 8N, 6N, 4N and 5N act at a point as shown in the diagram. If the 6N force acts in the direction 090°, calculate the :
(a) magnitude of the resultant force;
(b) direction of the resultant force.

Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.