Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 205 · 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.In a class of 35 children, 12 like tea, 21 like coffee and 2 like both. How many like neither? (a) 4 (b) 6 (c) 2 (d) 5
2. 2.What is the prime factorisation of 21? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
3. 3.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 49 (c) 42 (d) 13
4. 4.What is the mode of 4, 18, 4, 6, 8, 6 and 6? (a) 6 (b) 8 (c) 4 (d) 18
5. 5.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 400 sq cm (c) 1000 sq cm (d) 600 sq cm
6. 6.How many factors does 113 have? (a) 1 (b) 4 (c) 3 (d) 2
7. 7.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
8. 8.A bag has 4 red balls and 9 yellow 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) 10 (c) 2 (d) 5
9. 9.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 37 (c) 48 (d) 49
10. 10.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2² × 3
11. 11.How many factors does 70 have? (a) 6 (b) 9 (c) 8 (d) 7
12. 12.In a class of 32 children, 15 like mangoes, 16 like bananas and 7 like both. How many like at least one of the two? (a) 32 (b) 31 (c) 17 (d) 24
13. 13.The mean of 5 numbers is 25. When the number 49 is added to them, what is the new mean? (a) 37 (b) 25 (c) 29 (d) 30
14. 14.In a class of 39 children, 29 like cricket, 18 like football and 9 like both. How many like at least one of the two? (a) 29 (b) 38 (c) 39 (d) 47
15. 15.6 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) 9 (b) 36 (c) 24 (d) 18
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
17. 17.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 637 (b) 627 (c) 496 (d) 636
18. 18.What is the missing term in the AP 14, ?, 28, 35, 42? (a) 22 (b) 20 (c) 28 (d) 21
19. 19.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 39 (b) 270 (c) 540 (d) 288
20. 20.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
21. 21.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the missing term in the AP 20, 22, 24, ?, 28? (a) 26 (b) 28 (c) 25 (d) 27
23. 23.In a class of 29 children, 15 like tea, 14 like coffee and 5 like both. How many like neither? (a) 10 (b) 6 (c) 5 (d) 0
24. 24.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 5 (c) 18 (d) 45
25. 25.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
26. 26.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 120° (b) 80° (c) 100° (d) 160°
27. 27.What is the midpoint of the line joining (2, 2) and (12, 6)? (a) (4, 7) (b) (7, 4) (c) (14, 8) (d) (5, 2)
28. 28.A drawer has lots of black 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) 5 (b) 2 (c) 3 (d) 4
29. 29.What is the 15th term of the AP 11, 18, 25, 32, …? (a) 116 (b) 109 (c) 105 (d) 98
30. 30.What is the sum of all the whole numbers from 1 to 31? (a) 992 (b) 496 (c) 465 (d) 497
31. 31.In a class of 43 children, 30 like maths, 21 like science and 12 like both. How many like neither? (a) 4 (b) 12 (c) 16 (d) 5
32. 32.In a class of 43 children, 18 like tea, 21 like coffee and 4 like both. How many like at least one of the two? (a) 39 (b) 35 (c) 43 (d) 31
33. 33.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2 × 3 × 7
34. 34.What is the mean of 7, 11, 3 and 23? (a) 13 (b) 12 (c) 11 (d) 10
35. 35.What is the median of 25, 38, 8, 24 and 29? (a) 24 (b) 25 (c) 8 (d) 29
36. 36.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 9 (c) 5 (d) 6
37. 37.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 64 (c) 56 (d) 28
38. 38.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 76 (c) 75 (d) 84
39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
40. 40.A bag has 3 green, 8 red and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 6/7 (b) 11/14 (c) 1/3 (d) 3/14

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