Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 266 · 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 33 children, 22 like tea, 15 like coffee and 12 like both. How many like neither? (a) 9 (b) 12 (c) 20 (d) 8
2. 2.A bag has 5 black balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 9 (c) 2 (d) 7
3. 3.There are 3 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) 18 (b) 9 (c) 6 (d) 12
4. 4.What is the smallest prime factor of 403? (a) 2 (b) 1 (c) 13 (d) 31
5. 5.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 30 (c) 18 (d) 8
6. 6.In a class of 38 children, 24 like mangoes, 16 like bananas and 12 like both. How many like at least one of the two? (a) 16 (b) 40 (c) 28 (d) 38
7. 7.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
8. 8.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
10. 10.What is the mean of 14, 12, 8 and 18? (a) 12 (b) 14 (c) 15 (d) 13
11. 11.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 55 (c) 22 (d) 110
12. 12.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 14 (d) 21
13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
14. 14.A bag has 2 green, 4 red and 6 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/12 (b) 1/12 (c) 1/2 (d) 1/3
15. 15.What is the mean of 2, 16, 15 and 7? (a) 11 (b) 10 (c) 9 (d) 8
16. 16.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 155° (d) 65°
17. 17.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 20 (c) 25 (d) 21
18. 18.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 54 (c) 55 (d) 15
19. 19.If a + b = 17 and ab = 66, what is a² + b²? (a) 223 (b) 421 (c) 289 (d) 157
20. 20.How many factors does 107 have? (a) 3 (b) 2 (c) 4 (d) 1
21. 21.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
22. 22.Two angles of a triangle are 20° and 70°. What is the exterior angle at the third corner? (a) 160° (b) 270° (c) 110° (d) 90°
23. 23.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) 49 (c) 48 (d) 37
24. 24.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 11 (d) 19
25. 25.A bag has 10 green balls and 11 red 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) 2 (c) 11 (d) 12
26. 26.What is the mode of 14, 11, 14, 5, 1, 11 and 14? (a) 14 (b) 1 (c) 5 (d) 11
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
28. 28.What is the sum of the first 10 terms of the AP 9, 10, 11, …? (a) 270 (b) 135 (c) 18 (d) 140
29. 29.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
30. 30.What is the smallest prime factor of 145? (a) 5 (b) 1 (c) 2 (d) 29
31. 31.In a class of 32 children, 16 like mangoes, 15 like bananas and 2 like both. How many like at least one of the two? (a) 31 (b) 29 (c) 32 (d) 27
32. 32.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 15 (d) 12
33. 33.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
34. 34.In a class of 26 children, 11 like maths, 11 like science and 8 like neither. How many like both? (a) 4 (b) 5 (c) 8 (d) 18
35. 35.If a + b = 10 and ab = 9, what is (a − b)²? (a) 8 (b) 82 (c) 64 (d) 100
36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
37. 37.A bag has 2 green, 8 red and 2 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/6 (b) 1/5 (c) 5/6 (d) 1/3
38. 38.Two angles of a triangle are 45° and 105°. What is the third angle? (a) 135° (b) 30° (c) 150° (d) 75°
39. 39.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
40. 40.A bag has 4 black 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) 5 (b) 16 (c) 2 (d) 13

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