Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 836 · 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.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 1/8 (d) 3/8
2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 21 (b) 9 (c) 20 (d) 19
3. 3.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
4. 4.4 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) 7 (b) 24 (c) 16 (d) 12
5. 5.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 155° (c) 75° (d) 100°
6. 6.How many factors does 36 have? (a) 10 (b) 7 (c) 8 (d) 9
7. 7.In a class of 36 children, 20 like maths, 19 like science and 12 like both. How many like at least one of the two? (a) 39 (b) 36 (c) 27 (d) 15
8. 8.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
9. 9.What is the mode of 10, 18, 7, 19, 7, 10 and 10? (a) 7 (b) 10 (c) 18 (d) 19
10. 10.In a class of 36 children, 17 like dance, 18 like music and 9 like neither. How many like both? (a) 27 (b) 7 (c) 8 (d) 9
11. 11.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) 49 (b) 37 (c) 36 (d) 48
12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 8 (d) 20
13. 13.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 33 (d) 36
14. 14.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 93 (c) 84 (d) 94
15. 15.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 96 (c) 14 (d) 56
16. 16.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3
17. 17.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 18 (b) 180 (c) 99 (d) 90
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 4 (d) 5
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 24 (d) 25
20. 20.Which term of the AP 20, 29, 38, 47, … is 128? (a) 12th (b) 15th (c) 14th (d) 13th
21. 21.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 216 cu cm (d) 144 cu cm
22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 24 (d) 48
23. 23.What is the product of the roots of x² − 12x + 27 = 0? (a) 27 (b) 26 (c) 12 (d) 28
24. 24.What are the roots of x² − 5x + 6 = 0? (a) 1 and 4 (b) 1 and 6 (c) 2 and 3 (d) 2 and 4
25. 25.3 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) 15 (b) 12 (c) 24 (d) 7
26. 26.What is the sum of the first 6 terms of the AP 4, 5, 6, …? (a) 39 (b) 78 (c) 42 (d) 9
27. 27.A drawer has lots of red 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) 3 (b) 4 (c) 5 (d) 2
28. 28.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) 18 (b) 5 (c) 45 (d) 15
29. 29.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
30. 30.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) 21 (b) 29 (c) 28 (d) 22
31. 31.What is the missing term in the AP 5, 14, ?, 32, 41? (a) 23 (b) 22 (c) 32 (d) 24
32. 32.A bag has 12 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 15 (d) 14
33. 33.What is the sum of all the whole numbers from 1 to 20? (a) 420 (b) 200 (c) 190 (d) 210
34. 34.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
35. 35.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 155° (b) 100° (c) 80° (d) 125°
36. 36.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 70° (b) 30° (c) 60° (d) 120°
37. 37.In a class of 38 children, 22 like mangoes, 17 like bananas and 2 like both. How many like at least one of the two? (a) 35 (b) 37 (c) 38 (d) 39
38. 38.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 135° (d) 85°
39. 39.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 72 (d) 36
40. 40.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 210 (d) 105

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