April 2021

The Department of Health encourages elderly people to have a flu vaccination each year. The vaccination reduces the likelihood of getting a flu from 40% to 10%. If 45% of the elderly people visiting the doctor have the vaccination, find the probability that an elderly person chosen at random had the vaccination, given that they get flu.

Five men and three women are arranged randomly in a row. What is the probability that there are not two women standing together anywhere in the row?

There are four red, three green and five blue discs in a bag. Find the probability that two discs of the same color are drawn.

A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early. A screening test for the disease shows a positive result for 99% of the people with the disease. The test also shows positive for 2% of people who do not have the disease. For a population of one million people how many would you expect to test positive but do not have the disease?

Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a cylindrical swimming pool full of water with 6 m in diameter and 2 m depth?

A strip of 640 m² is sold from a triangular field whose sides are 96 m, 72 m, and 80 m. The strip is of uniform width h and has one of its sides parallel to the longest side of the field. Find the width of the strip.

Stations A and B are placed 1000 m apart on a straight road running East and West. From A, the bearing of the tower C is 32° West of North and from B the bearing of C is 26° North of East. Find the shortest distance of the tower from the road.

A man drives from station A to station B 60 km away at an average speed of 30 kph and return to A at an average speed of 20 kph. What was the average speed of the man in the whole journey?

At what time between 7 and 8 o’clock will the hands of the clock be directly opposite each other?

Mary was 4 times as old as Ann 4 years ago and if Mary will be twice as old as Ann 4 years hence, how old is Ann?