Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 364 · 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 circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
2. 2.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 100 (d) 55
3. 3.What is the mean of 12, 20, 16, 3 and 4? (a) 12 (b) 13 (c) 11 (d) 10
4. 4.A bag has 2 white, 7 blue and 9 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 8/9 (b) 1/8 (c) 1/3 (d) 1/9
5. 5.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 1 (d) 4
6. 6.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 30 (d) 15
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/6 (c) 5/36 (d) 1/11
8. 8.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
10. 10.What is the mean of 13, 19, 18, 11 and 9? (a) 15 (b) 16 (c) 13 (d) 14
11. 11.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 40° (b) 105° (c) 140° (d) 115°
12. 12.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 176 (c) 175 (d) 166
13. 13.What is the median of 15, 28, 9, 3, 16, 19 and 23? (a) 16 (b) 19 (c) 3 (d) 15
14. 14.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 100° (b) 260° (c) 160° (d) 80°
15. 15.What is the midpoint of the line joining (4, 1) and (10, 3)? (a) (2, 7) (b) (3, 1) (c) (14, 4) (d) (7, 2)
16. 16.A bag has 3 red, 4 green and 2 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 2/3 (b) 5/9 (c) 4/9 (d) 1/3
17. 17.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/4 (d) 1/8
18. 18.What are the roots of x² − 12x + 27 = 0? (a) 2 and 10 (b) 1 and 27 (c) 3 and 9 (d) 1 and 11
19. 19.How many factors does 47 have? (a) 3 (b) 4 (c) 1 (d) 2
20. 20.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 121 (c) 55 (d) 110
21. 21.The mean of 4 numbers is 35. When the number 40 is added to them, what is the new mean? (a) 36 (b) 35 (c) 38 (d) 37
22. 22.A bag has 7 white balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 8 (c) 19 (d) 9
23. 23.What is the 28th term of the AP 5, 9, 13, 17, …? (a) 113 (b) 108 (c) 117 (d) 112
24. 24.What is the mean of 8, 4, 17, 2 and 14? (a) 11 (b) 10 (c) 8 (d) 9
25. 25.A bag has 10 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 7 (c) 2 (d) 16
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/18 (c) 1/11 (d) 2/11
27. 27.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
28. 28.What is the median of 14, 33, 27, 28, 4, 37 and 29? (a) 29 (b) 27 (c) 28 (d) 30
29. 29.The mean of 8 numbers is 35. When the number 44 is added to them, what is the new mean? (a) 38 (b) 37 (c) 35 (d) 36
30. 30.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
31. 31.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
32. 32.A drawer has lots of white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 5 (d) 4
33. 33.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 65 (b) 70 (c) 130 (d) 11
34. 34.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 84 (b) 42 (c) 13 (d) 48
35. 35.In a class of 25 children, 14 like dance, 19 like music and 9 like both. How many like only dance? (a) 6 (b) 5 (c) 10 (d) 14
36. 36.A bag has 11 blue balls and 12 red 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) 13 (c) 23 (d) 2
37. 37.In a class of 19 children, 9 like tea, 5 like coffee and 2 like both. How many like neither? (a) 9 (b) 2 (c) 7 (d) 5
38. 38.A cube has edges of 12 cm. What is its total surface area? (a) 1728 sq cm (b) 144 sq cm (c) 864 sq cm (d) 576 sq cm
39. 39.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 60° (c) 150° (d) 30°
40. 40.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 2 (d) 29

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