Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 744 · 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 6 red, 2 white and 5 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 8/13 (c) 5/13 (d) 9/13
2. 2.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
3. 3.What is the mode of 15, 8, 15, 17, 3, 8 and 15? (a) 15 (b) 17 (c) 8 (d) 3
4. 4.In a class of 36 children, 25 like mangoes, 13 like bananas and 7 like both. How many like at least one of the two? (a) 36 (b) 38 (c) 24 (d) 31
5. 5.What is the distance between the points (0, 2) and (24, 9)? (a) 25 (b) 625 (c) 26 (d) 31
6. 6.What is the sum of the first 12 terms of the AP 3, 4, 5, …? (a) 102 (b) 14 (c) 204 (d) 108
7. 7.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/8 (d) 3/4
8. 8.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 22 (d) 21
9. 9.A bag has 11 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 12 (c) 20 (d) 2
10. 10.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 130° (d) 80°
11. 11.Which term of the AP 2, 10, 18, 26, … is 82? (a) 13th (b) 10th (c) 12th (d) 11th
12. 12.A bag has 8 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 16 (d) 10
13. 13.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 7 (d) 5
14. 14.In a class of 22 children, 9 like cricket, 18 like football and 6 like both. How many like at least one of the two? (a) 22 (b) 27 (c) 21 (d) 15
15. 15.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 100° (d) 50°
16. 16.A drawer has lots of green, yellow, blue, black 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) 6 (b) 5 (c) 10 (d) 2
17. 17.A bag has 9 green balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 12 (c) 20 (d) 10
18. 18.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 6 cu cm (b) 82 cu cm (c) 12 cu cm (d) 42 cu cm
19. 19.Two angles of a triangle are 50° and 115°. What is the third angle? (a) 165° (b) 15° (c) 65° (d) 130°
20. 20.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
21. 21.In a class of 51 children, 24 like maths, 25 like science and 5 like both. How many like neither? (a) 12 (b) 2 (c) 5 (d) 7
22. 22.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 32 (c) 16 (d) 10
23. 23.A bag has 8 red, 2 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/6 (b) 1/3 (c) 11/12 (d) 5/6
24. 24.A bag has 4 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 6 (c) 2 (d) 12
25. 25.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
26. 26.A bag has 11 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 16 (c) 12 (d) 13
27. 27.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 28 (d) 16
28. 28.In a class of 26 children, 19 like tea, 8 like coffee and 2 like both. How many like neither? (a) 3 (b) 0 (c) 2 (d) 1
29. 29.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 225° (b) 135° (c) 90° (d) 45°
30. 30.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 160° (d) 125°
31. 31.What is the missing term in the AP 3, 6, ?, 12, 15? (a) 10 (b) 9 (c) 12 (d) 8
32. 32.A bag has 9 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 10 (c) 2 (d) 9
33. 33.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
34. 34.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
35. 35.How many factors does 61 have? (a) 1 (b) 3 (c) 2 (d) 4
36. 36.In a class of 34 children, 10 like cricket, 24 like football and 7 like both. How many like at least one of the two? (a) 27 (b) 28 (c) 20 (d) 34
37. 37.What is the midpoint of the line joining (0, 9) and (2, 21)? (a) (1, 6) (b) (15, 1) (c) (1, 15) (d) (2, 30)
38. 38.What is the prime factorisation of 35? (a) 5 × 7² (b) 5 × 7 (c) 5³ × 7 (d) 5² × 7
39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
40. 40.If a + b = 16 and ab = 55, what is a² + b²? (a) 201 (b) 366 (c) 146 (d) 256

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