Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 285 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 5 (d) 3
2. 2.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
3. 3.A bag has 5 white, 6 yellow and 2 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 2/13 (b) 12/13 (c) 11/13 (d) 1/3
4. 4.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/5 (d) 3/8
5. 5.A drawer has lots of black, blue, 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) 8 (b) 4 (c) 2 (d) 5
6. 6.A drawer has lots of red, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 6
7. 7.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 3/8 (d) 1/8
8. 8.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) 25 (b) 13 (c) 24 (d) 12
9. 9.A bag has 5 blue balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 17 (c) 6 (d) 7
10. 10.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 80° (c) 260° (d) 100°
11. 11.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/4 (d) 1/7
12. 12.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/4 (d) 1/8
13. 13.A bag has 3 green balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 11 (c) 2 (d) 4
14. 14.How many factors does 70 have? (a) 7 (b) 8 (c) 6 (d) 9
15. 15.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
16. 16.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 100 (d) 45
17. 17.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 30 (d) 15
18. 18.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
19. 19.What is the 12th term of the AP 8, 17, 26, 35, …? (a) 99 (b) 116 (c) 107 (d) 108
20. 20.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
21. 21.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 80° (b) 100° (c) 120° (d) 140°
22. 22.8 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 32 (c) 12 (d) 64
23. 23.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 220° (b) 40° (c) 110° (d) 70°
24. 24.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
25. 25.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 25° (b) 15° (c) 30° (d) 150°
26. 26.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
27. 27.What is the sum of the first 7 terms of the AP 9, 11, 13, …? (a) 21 (b) 112 (c) 210 (d) 105
28. 28.What is the median of 6, 7, 30, 29, 26, 9 and 19? (a) 18 (b) 29 (c) 19 (d) 26
29. 29.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 130° (b) 40° (c) 50° (d) 310°
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/9 (c) 1/11 (d) 3/11
31. 31.A drawer has lots of blue, red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 6 (d) 4
32. 32.What is the 35th term of the AP 20, 23, 26, 29, …? (a) 125 (b) 105 (c) 102 (d) 122
33. 33.How many factors does 90 have? (a) 10 (b) 13 (c) 12 (d) 11
34. 34.The mean of 3 numbers is 31. When the number 15 is added to them, what is the new mean? (a) 31 (b) 28 (c) 23 (d) 27
35. 35.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 21 (c) 28 (d) 42
36. 36.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 4 (d) 5
37. 37.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
38. 38.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 1 (d) 17
39. 39.What is the distance between the points (6, 8) and (14, 2)? (a) 11 (b) 14 (c) 10 (d) 100
40. 40.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2

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