Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 940 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.A bag has 8 yellow, 4 green and 9 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/7 (b) 1/3 (c) 3/7 (d) 3/4
2. 2.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
3. 3.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 12 (d) 25
4. 4.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 50° (d) 40°
5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
6. 6.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 12 (c) 16 (d) 8
7. 7.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
8. 8.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 3/8 (c) 5/8 (d) 1/4
9. 9.What is the sum of the first 5 terms of the AP 2, 6, 10, …? (a) 50 (b) 18 (c) 100 (d) 60
10. 10.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 55° (b) 35° (c) 160° (d) 145°
11. 11.What are the roots of x² − 14x + 48 = 0? (a) 2 and 24 (b) 6 and 8 (c) 1 and 13 (d) 1 and 48
12. 12.How many factors does 104 have? (a) 9 (b) 7 (c) 8 (d) 6
13. 13.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 110° (b) 40° (c) 220° (d) 70°
14. 14.What is the 15th term of the AP 12, 21, 30, 39, …? (a) 138 (b) 147 (c) 135 (d) 126
15. 15.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 320° (b) 140° (c) 50° (d) 40°
16. 16.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 50° (d) 40°
17. 17.What is the smallest prime factor of 57? (a) 1 (b) 3 (c) 19 (d) 2
18. 18.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 55 (d) 110
19. 19.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 4235 (b) 3625 (c) 3025 (d) 4225
20. 20.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 9 sq cm (c) 36 sq cm (d) 27 sq cm
21. 21.In a class of 41 children, 20 like cricket, 19 like football and 2 like both. How many like neither? (a) 4 (b) 6 (c) 5 (d) 2
22. 22.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
23. 23.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
24. 24.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 110° (b) 290° (c) 145° (d) 70°
25. 25.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 145° (b) 115° (c) 100° (d) 35°
26. 26.What is the mean of 17, 20, 15 and 8? (a) 15 (b) 12 (c) 16 (d) 20
27. 27.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
28. 28.In a class of 14 children, 9 like dance, 5 like music and 2 like both. How many like neither? (a) 0 (b) 3 (c) 2 (d) 4
29. 29.The mean of 9 numbers is 28. When the number 18 is added to them, what is the new mean? (a) 23 (b) 27 (c) 28 (d) 26
30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
31. 31.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
32. 32.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
33. 33.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
34. 34.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 1 (c) 3 (d) 4
36. 36.In which quadrant does the point (4, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
37. 37.Two angles of a triangle are 30° and 125°. What is the third angle? (a) 155° (b) 55° (c) 25° (d) 150°
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
39. 39.A cuboid is 5 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 296 sq cm (b) 74 sq cm (c) 120 sq cm (d) 148 sq cm
40. 40.A bag has 3 green, 5 blue and 8 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 9/16 (b) 1/2 (c) 1/3 (d) 1/16

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