Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 90 · 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 30° and 85°. What is the third angle? (a) 95° (b) 115° (c) 150° (d) 65°
2. 2.What is the 23rd term of the AP 6, 10, 14, 18, …? (a) 98 (b) 88 (c) 92 (d) 94
3. 3.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 78 (d) 144
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
5. 5.What is the median of 12, 7, 6, 4 and 10? (a) 10 (b) 6 (c) 8 (d) 7
6. 6.What is the smallest prime factor of 377? (a) 29 (b) 2 (c) 1 (d) 13
7. 7.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 36 (c) 81 (d) 72
8. 8.What is the smallest prime factor of 221? (a) 17 (b) 2 (c) 13 (d) 1
9. 9.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) 37 (b) 25 (c) 24 (d) 36
10. 10.How many factors does 62 have? (a) 2 (b) 5 (c) 4 (d) 3
11. 11.If a + b = 14 and ab = 48, what is (a − b)²? (a) 2 (b) 100 (c) 196 (d) 4
12. 12.In a class of 37 children, 24 like cricket, 12 like football and 5 like both. How many like at least one of the two? (a) 37 (b) 31 (c) 36 (d) 26
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/11 (c) 6/11 (d) 1/6
14. 14.7 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
15. 15.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) 24 (b) 25 (c) 13 (d) 12
16. 16.If a + b = 15 and ab = 50, what is a² + b²? (a) 325 (b) 225 (c) 175 (d) 125
17. 17.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 100° (b) 145° (c) 135° (d) 80°
18. 18.How many factors does 117 have? (a) 5 (b) 4 (c) 6 (d) 7
19. 19.A bag has 9 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 10 (c) 2 (d) 13
20. 20.A bag has 3 red, 3 blue and 7 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 11/13 (b) 1/3 (c) 10/13 (d) 3/13
21. 21.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
22. 22.What is the sum of the first 8 terms of the AP 4, 10, 16, …? (a) 224 (b) 46 (c) 400 (d) 200
23. 23.How many factors does 64 have? (a) 8 (b) 5 (c) 6 (d) 7
24. 24.A bag has 11 black balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 11 (c) 2 (d) 21
25. 25.In which quadrant does the point (4, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
26. 26.What is the product of the roots of x² − 14x + 45 = 0? (a) 44 (b) 14 (c) 45 (d) 46
27. 27.The mean of 3 numbers is 37. When the number 29 is added to them, what is the new mean? (a) 36 (b) 37 (c) 35 (d) 33
28. 28.What is the sum of all the whole numbers from 1 to 98? (a) 4753 (b) 4802 (c) 4851 (d) 9702
29. 29.Two angles of a triangle are 80° and 65°. What is the third angle? (a) 145° (b) 35° (c) 115° (d) 100°
30. 30.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 277 (b) 256 (c) 276 (d) 267
32. 32.Two angles of a triangle are 25° and 110°. What is the third angle? (a) 135° (b) 70° (c) 155° (d) 45°
33. 33.A drawer has lots of red 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) 2 (b) 3 (c) 4 (d) 5
34. 34.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 48 (c) 24 (d) 30
35. 35.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 45 (b) 300 (c) 276 (d) 552
36. 36.A bag has 4 white balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 5 (c) 6 (d) 11
37. 37.A drawer has lots of yellow, black, green, 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) 5 (b) 2 (c) 10 (d) 6
38. 38.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
39. 39.In a class of 37 children, 21 like mangoes, 13 like bananas and 2 like both. How many like at least one of the two? (a) 30 (b) 37 (c) 34 (d) 32
40. 40.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 70° (d) 50°

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