Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 49 · 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 25 children, 15 like maths, 19 like science and 12 like both. How many like neither? (a) 4 (b) 12 (c) 15 (d) 3
2. 2.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 85° (c) 86° (d) 170°
3. 3.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) 5 (c) 4 (d) 3
4. 4.A drawer has lots of blue 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
5. 5.What is the distance between the points (9, 6) and (25, 18)? (a) 28 (b) 20 (c) 21 (d) 400
6. 6.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
7. 7.A bag has 4 red balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 2 (c) 14 (d) 6
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
9. 9.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
10. 10.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
11. 11.What is the 33rd term of the AP 8, 12, 16, 20, …? (a) 140 (b) 136 (c) 128 (d) 132
12. 12.What is the distance between the points (4, 11) and (8, 8)? (a) 7 (b) 25 (c) 5 (d) 6
13. 13.Two angles of a triangle are 45° and 20°. What is the exterior angle at the third corner? (a) 65° (b) 160° (c) 115° (d) 135°
14. 14.A bag has 7 yellow balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 8 (c) 17 (d) 2
15. 15.A bag has 4 black balls and 6 blue 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) 7 (c) 10 (d) 5
16. 16.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 207 (c) 217 (d) 324
17. 17.What is the 10th term of the AP 9, 11, 13, 15, …? (a) 20 (b) 27 (c) 29 (d) 18
18. 18.A cube has edges of 5 cm. What is its total surface area? (a) 150 sq cm (b) 25 sq cm (c) 100 sq cm (d) 125 sq cm
19. 19.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 289 (b) 539 (c) 409 (d) 529
20. 20.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
22. 22.A bag has 3 blue balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 4 (b) 5 (c) 2 (d) 8
23. 23.What is the mode of 8, 8, 8, 4, 1, 1 and 7? (a) 8 (b) 7 (c) 1 (d) 4
24. 24.What is the sum of the first 8 terms of the AP 10, 11, 12, …? (a) 112 (b) 108 (c) 17 (d) 216
25. 25.A bag has 4 green, 9 white and 9 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 13/22 (b) 1/3 (c) 9/13 (d) 9/22
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 19 (b) 20 (c) 21 (d) 9
27. 27.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
28. 28.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 325 (c) 288 (d) 324
29. 29.What is the median of 35, 16, 26, 1, 3, 32 and 23? (a) 23 (b) 26 (c) 16 (d) 1
30. 30.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
31. 31.What is the mode of 15, 15, 16, 15, 5, 13 and 16? (a) 16 (b) 5 (c) 15 (d) 13
32. 32.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 11 (c) 56 (d) 28
33. 33.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
34. 34.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 4 times (c) 16 times (d) 8 times
35. 35.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 28 (c) 11 (d) 35
36. 36.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
37. 37.What is the distance between the points (1, 20) and (10, 8)? (a) 225 (b) 16 (c) 15 (d) 21
38. 38.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
39. 39.A drawer has lots of black and red 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) 4 (c) 3 (d) 2
40. 40.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 95° (b) 135° (c) 140° (d) 85°

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