Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 358 · 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.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
2. 2.What is the mode of 18, 1, 11, 1, 16, 1 and 11? (a) 18 (b) 11 (c) 16 (d) 1
3. 3.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
4. 4.What is the distance between the points (1, 32) and (8, 8)? (a) 26 (b) 625 (c) 25 (d) 31
5. 5.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 10 (c) 20 (d) 11
6. 6.The mean of 8 numbers is 28. When the number 37 is added to them, what is the new mean? (a) 29 (b) 31 (c) 28 (d) 30
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 6 (b) 16 (c) 17 (d) 18
8. 8.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 140° (b) 160° (c) 40° (d) 60°
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
10. 10.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
12. 12.In a class of 29 children, 12 like cricket, 20 like football and 8 like both. How many like at least one of the two? (a) 32 (b) 16 (c) 24 (d) 29
13. 13.A drawer has lots of white, blue, red 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) 8 (c) 2 (d) 4
14. 14.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
15. 15.What is the distance between the points (4, 16) and (9, 4)? (a) 14 (b) 169 (c) 17 (d) 13
16. 16.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 29 (d) 13
17. 17.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
18. 18.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 145° (b) 150° (c) 65° (d) 115°
19. 19.How many factors does 43 have? (a) 2 (b) 3 (c) 4 (d) 1
20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 36 (d) 81
21. 21.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
22. 22.In a class of 38 children, 27 like cricket, 17 like football and 11 like both. How many like at least one of the two? (a) 44 (b) 38 (c) 22 (d) 33
23. 23.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 35° (c) 145° (d) 110°
24. 24.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
25. 25.In a class of 31 children, 10 like tea, 16 like coffee and 9 like neither. How many like both? (a) 5 (b) 9 (c) 22 (d) 4
26. 26.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 55 (d) 121
27. 27.If a + b = 6 and ab = 5, what is (a − b)²? (a) 36 (b) 26 (c) 4 (d) 16
28. 28.What is the 19th term of the AP 19, 26, 33, 40, …? (a) 152 (b) 133 (c) 145 (d) 126
29. 29.A cuboid is 3 cm long, 2 cm wide and 8 cm high. What is its volume? (a) 13 cu cm (b) 92 cu cm (c) 6 cu cm (d) 48 cu cm
30. 30.A bag has 11 black balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 12 (c) 2 (d) 13
31. 31.How many factors does 31 have? (a) 1 (b) 3 (c) 4 (d) 2
32. 32.A bag has 10 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 17 (b) 11 (c) 2 (d) 12
33. 33.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
34. 34.What is the distance between the points (8, 9) and (11, 13)? (a) 6 (b) 25 (c) 5 (d) 7
35. 35.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 156 (d) 169
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 1 (c) 3 (d) 2
38. 38.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
39. 39.In a class of 32 children, 11 like mangoes, 19 like bananas and 3 like both. How many like at least one of the two? (a) 24 (b) 30 (c) 27 (d) 32
40. 40.What is the 39th term of the AP 16, 24, 32, 40, …? (a) 312 (b) 320 (c) 328 (d) 304

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