Mathematics Past Questions and Answers

(a) A man travels from a village X on a bearing of 060° to a village Y which is 20km away. From Y, he travels to a village Z, on a bearing of 195°. If Z is directly east of X, calculate, correct to three significant figures, the distance of :
(i) Y from Z ; (ii) Z from X .
(b) An aircraft flies due South from an airfield on latitude 36°N, longitude 138°E to an airfield on latitude 36°S, longitude 138°E.
(i) Calculate the distance travelled, correct to three significant figures ; (ii) if the speed of the aircraft is 800km per hour, calculate the time taken, correct to the nearest hour.
[Take \(\pi = \frac{22}{7}\), R = 6400km].

The table shows the scores of 2000 candidates in an entrance examination into a private secondary school.

% Mark	11-20	21-30	31-40	41-50	51-60	61-70	71-80	81-90
No of pupils	68	184	294	402	480	310	164	98

(a) Prepare a cumulative frequency table and draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the : (i) cut off mark, if 300 candidates are to be offered admission ; (ii) probability that a candidate picked at random, scored at least 45%.

Express (0.0425 / 2.5) as a fraction

Express (0.0425 / 2.5) as a fraction

If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals