Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 651 · 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.What is the 21st term of the AP 11, 14, 17, 20, …? (a) 74 (b) 71 (c) 60 (d) 63
2. 2.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 115° (d) 50°
3. 3.In a class of 35 children, 9 like mangoes, 22 like bananas and 3 like both. How many like neither? (a) 10 (b) 4 (c) 3 (d) 7
4. 4.In a class of 41 children, 21 like tea, 25 like coffee and 12 like both. How many like neither? (a) 8 (b) 12 (c) 7 (d) 19
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 132 cm (c) 1386 cm (d) 264 cm
6. 6.A bag has 3 yellow, 4 green and 4 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/8 (b) 1/3 (c) 8/11 (d) 3/11
7. 7.A bag has 11 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 8 (c) 18 (d) 2
8. 8.In a class of 37 children, 23 like mangoes, 19 like bananas and 7 like both. How many like at least one of the two? (a) 35 (b) 42 (c) 28 (d) 37
9. 9.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 64 (d) 56
10. 10.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 900 (b) 930 (c) 59 (d) 465
11. 11.A drawer has lots of green, black, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 8 (d) 2
12. 12.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 2/3 (c) 1/4 (d) 5/6
13. 13.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 72 (d) 81
14. 14.In a class of 29 children, 17 like tea, 18 like coffee and 10 like both. How many like at least one of the two? (a) 29 (b) 35 (c) 25 (d) 15
15. 15.What is the distance between the points (1, 18) and (17, 6)? (a) 28 (b) 21 (c) 20 (d) 400
16. 16.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
17. 17.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2² × 3 × 7 (d) 2 × 3 × 7
18. 18.A drawer has lots of black, blue, green and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 4 (c) 8 (d) 2
19. 19.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
20. 20.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm
21. 21.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 70° (c) 100° (d) 110°
22. 22.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
23. 23.A bag has 9 blue, 4 white and 3 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/16 (b) 1/3 (c) 13/16 (d) 7/8
24. 24.Two angles of a triangle are 20° and 140°. What is the third angle? (a) 20° (b) 40° (c) 200° (d) 160°
25. 25.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
26. 26.A bag has 9 green, 6 red and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/4 (b) 1/3 (c) 1/4 (d) 19/24
27. 27.What are the roots of x² − 13x + 42 = 0? (a) 6 and 7 (b) 1 and 12 (c) 1 and 42 (d) 2 and 21
28. 28.In a class of 41 children, 19 like cricket, 29 like football and 10 like both. How many like neither? (a) 3 (b) 4 (c) 13 (d) 10
29. 29.What is the sum of all the whole numbers from 1 to 68? (a) 2278 (b) 4692 (c) 2312 (d) 2346
30. 30.In a class of 18 children, 12 like cricket, 11 like football and 8 like both. How many like neither? (a) 8 (b) 11 (c) 3 (d) 4
31. 31.Two angles of a triangle are 65° and 90°. What is the third angle? (a) 115° (b) 25° (c) 155° (d) 90°
32. 32.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 20° (c) 80° (d) 100°
33. 33.What is the midpoint of the line joining (7, 9) and (15, 17)? (a) (22, 26) (b) (11, 13) (c) (4, 4) (d) (13, 11)
34. 34.A bag has 5 red, 8 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 13/15 (c) 2/15 (d) 2/13
35. 35.What is the mean of 3, 19, 17 and 13? (a) 14 (b) 15 (c) 13 (d) 12
36. 36.A bag has 12 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 13 (b) 20 (c) 2 (d) 14
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
38. 38.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 160° (b) 20° (c) 200° (d) 100°
39. 39.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 1/2 (d) 2/3
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 7/36 (c) 1/11 (d) 1/6

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