Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 44 · 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.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 160° (b) 105° (c) 95° (d) 85°
2. 2.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 65° (b) 125° (c) 120° (d) 115°
3. 3.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 176 (c) 194 (d) 186
4. 4.How many prime numbers are there between 50 and 60? (a) 1 (b) 2 (c) 3 (d) 4
5. 5.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
6. 6.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 105 (c) 182 (d) 91
7. 7.What is the distance between the points (0, 5) and (12, 21)? (a) 21 (b) 400 (c) 20 (d) 28
8. 8.In a class of 30 children, 10 like maths, 22 like science and 5 like both. How many like at least one of the two? (a) 32 (b) 30 (c) 22 (d) 27
9. 9.In a class of 31 children, 22 like cricket, 12 like football and 9 like both. How many like only cricket? (a) 13 (b) 22 (c) 3 (d) 19
10. 10.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 30 (c) 10 (d) 33
11. 11.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
12. 12.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 86° (c) 85° (d) 95°
13. 13.What is the smallest prime factor of 403? (a) 13 (b) 2 (c) 31 (d) 1
14. 14.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 1/4 (d) 3/8
15. 15.What is the sum of all the whole numbers from 1 to 21? (a) 210 (b) 462 (c) 232 (d) 231
16. 16.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
17. 17.What is the 11th term of the AP 19, 24, 29, 34, …? (a) 74 (b) 55 (c) 69 (d) 50
18. 18.What is the mode of 20, 19, 19, 6, 6, 12 and 19? (a) 19 (b) 12 (c) 20 (d) 6
19. 19.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 0 (d) 2
20. 20.How many factors does 75 have? (a) 7 (b) 6 (c) 5 (d) 4
21. 21.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 3/8 (d) 5/8
22. 22.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 262 (d) 252
23. 23.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
24. 24.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) 25 (c) 24 (d) 37
25. 25.What is the 36th term of the AP 7, 10, 13, 16, …? (a) 105 (b) 108 (c) 115 (d) 112
26. 26.A drawer has lots of yellow and white 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) 5
27. 27.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 20 (c) 30 (d) 15
28. 28.What is the mode of 8, 8, 4, 8, 9, 16 and 4? (a) 16 (b) 4 (c) 9 (d) 8
29. 29.What is the sum of the first 6 terms of the AP 10, 16, 22, …? (a) 40 (b) 168 (c) 150 (d) 300
30. 30.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 20 (c) 25 (d) 240
31. 31.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 62 (d) 71
32. 32.What is the sum of the first 6 terms of the AP 4, 10, 16, …? (a) 228 (b) 114 (c) 132 (d) 34
33. 33.Two angles of a triangle are 40° and 55°. What is the third angle? (a) 95° (b) 125° (c) 140° (d) 85°
34. 34.How many factors does 35 have? (a) 5 (b) 2 (c) 4 (d) 3
35. 35.A cuboid is 5 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 90 sq cm (b) 252 sq cm (c) 63 sq cm (d) 126 sq cm
36. 36.What is the sum of the first 9 terms of the AP 3, 4, 5, …? (a) 64 (b) 63 (c) 11 (d) 126
37. 37.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 1/6 (d) 5/6
38. 38.How many factors does 32 have? (a) 4 (b) 5 (c) 7 (d) 6
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
40. 40.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 5 (d) 31

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