Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 684 · 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.If a + b = 12 and ab = 27, what is (a − b)²? (a) 144 (b) 36 (c) 6 (d) 90
2. 2.In a class of 23 children, 9 like cricket, 17 like football and 2 like neither. How many like both? (a) 2 (b) 21 (c) 3 (d) 5
3. 3.A bag has 8 red, 3 blue and 3 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/7 (b) 3/7 (c) 9/14 (d) 1/3
4. 4.What is the mean of 2, 17, 5, 2 and 9? (a) 9 (b) 8 (c) 7 (d) 6
5. 5.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) 36 (c) 48 (d) 37
6. 6.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 20° (b) 160° (c) 340° (d) 70°
7. 7.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 543 (c) 534 (d) 544
8. 8.A drawer has lots of white, red and yellow 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) 6 (c) 3 (d) 4
9. 9.There are 4 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) 20 (b) 9 (c) 40 (d) 24
10. 10.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 100 (d) 20
11. 11.What is the missing term in the AP 19, 23, ?, 31, 35? (a) 28 (b) 27 (c) 26 (d) 31
12. 12.In a class of 39 children, 17 like dance, 30 like music and 3 like neither. How many like both? (a) 36 (b) 11 (c) 8 (d) 3
13. 13.What is the sum of the roots of x² − 8x + 15 = 0? (a) 15 (b) 7 (c) 9 (d) 8
14. 14.In a class of 29 children, 16 like mangoes, 19 like bananas and 2 like neither. How many like both? (a) 6 (b) 27 (c) 2 (d) 8
15. 15.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 163 (d) 164
16. 16.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
17. 17.A bag has 3 green balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 12 (c) 2 (d) 14
18. 18.A cuboid is 10 cm long, 7 cm wide and 7 cm high. What is its total surface area? (a) 490 sq cm (b) 189 sq cm (c) 756 sq cm (d) 378 sq cm
19. 19.What is the mean of 17, 12, 11, 10, 4 and 6? (a) 12 (b) 9 (c) 11 (d) 10
20. 20.What is the distance between the points (0, 24) and (7, 0)? (a) 25 (b) 625 (c) 26 (d) 31
21. 21.How many factors does 27 have? (a) 5 (b) 3 (c) 4 (d) 2
22. 22.What is the smallest prime factor of 169? (a) 13 (b) 2 (c) 3 (d) 1
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/18 (c) 1/11 (d) 2/11
25. 25.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 5 times (c) 25 times (d) 10 times
26. 26.A bag has 7 red 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) 9 (c) 8 (d) 14
27. 27.A bag has 11 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 15 (c) 12 (d) 5
28. 28.A bag has 2 white, 8 red and 3 green balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 12/13 (c) 11/13 (d) 2/13
29. 29.If a + b = 7 and ab = 12, what is (a − b)²? (a) 49 (b) 25 (c) 37 (d) 1
30. 30.A bag has 10 black balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 4 (c) 2 (d) 13
31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 6 (c) 4 (d) 5
32. 32.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 23 (b) 30 (c) 25 (d) 24
33. 33.What is the sum of the first 5 terms of the AP 3, 5, 7, …? (a) 35 (b) 70 (c) 40 (d) 11
34. 34.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 16 (c) 64 (d) 28
35. 35.A bag has 9 blue, 6 white and 7 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/8 (b) 8/11 (c) 1/3 (d) 3/11
36. 36.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 110 (d) 22
37. 37.What is the mode of 6, 9, 14, 14, 17, 6 and 6? (a) 6 (b) 17 (c) 14 (d) 9
38. 38.If a + b = 5 and ab = 6, what is (a − b)²? (a) 1 (b) 25 (c) 19 (d) 13
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/18 (d) 1/11
40. 40.What is the distance between the points (3, 9) and (9, 1)? (a) 14 (b) 100 (c) 11 (d) 10

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