PAST PAPER- 2019 Instructions: • This paper is 30 minutes long. • The maximum marks for this paper is 30. Questions 1. Two cyclists start from the middle of a 200m track and move in opposite directions towards the end of the track at 5m/s and 10m/s respectively. At the time when a cyclist first reaches the end, both cyclists turn around and start moving towards each other with their initial speeds. During this motion, a fly moves at a speed of 17 m/s, between the 2 cyclists, landing on one cyclist and then moving to the next continuously. How much distance has the fly covered when the two cyclists meet again? (3 marks) 2. A square of side n meters contains n circles of radius 1m. If the probability of hitting a circle is at least half, what is the minimum number of circles? (3 marks) 3. Two teams are playing a game. The format is best of 7 (first team to win four games wins). Each game can only be won or lost, not tied. Is a team more likely to win in 6 games, or 7? (4 marks) 4. An athlete takes a lap of a track with a speed v. At what speed must he cover the second lap, so that his average speed for the 2 laps is 2v? (4 marks) (A) v (B) 2v (C) 3v (D) 1.5 v 5. If m, n and p are positive integers with 𝑚 + (A) 3 (B) 4 (C) 1 (D) 17 ! ! !!! = (E) None of these !" ! , the value of n is: (E) 13 (3 marks) 6. Equilateral triangle ABC has side length 3, with vertices B and C on a circle of radius 3 as shown. The triangle is then rotated clockwise inside the circle: first about C until A reaches the circle, and then about A until B reaches the circles, and so on. Eventually the triangle returns to its original positions and stops. What is the total distance travelled by the point B? (5 marks) 7. A group of dragons and sheep are randomly divided into 2 equal rows. Each animal in one row is directly opposite an animal in the other row. If 75 of the animals are dragons, and the number of sheep opposite sheep is 10 more than the number of dragons, find the total number of animals in the group. (4 marks) 8. If 200 is added to a positive integer I, the result is a square number. If 276 is added to the same integer I, another square number is obtained. Find I. (4 marks)