Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 119 · 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.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
3. 3.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
5. 5.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/5 (d) 3/8
6. 6.What is the distance between the points (2, 4) and (6, 1)? (a) 25 (b) 6 (c) 5 (d) 7
7. 7.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 105 (c) 120 (d) 225
8. 8.A bag has 3 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 4 (c) 5 (d) 2
9. 9.A bag has 8 green, 4 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 1/6 (c) 6/7 (d) 1/7
10. 10.In a class of 31 children, 17 like mangoes, 17 like bananas and 5 like both. How many like neither? (a) 2 (b) 7 (c) 5 (d) 3
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
12. 12.A bag has 11 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 23 (c) 12 (d) 2
13. 13.A cuboid is 12 cm long, 10 cm wide and 3 cm high. What is its total surface area? (a) 744 sq cm (b) 360 sq cm (c) 186 sq cm (d) 372 sq cm
14. 14.What is the sum of the roots of x² − 10x + 16 = 0? (a) 9 (b) 10 (c) 16 (d) 11
15. 15.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 40° (c) 70° (d) 110°
16. 16.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 1)(x + 15) (c) (x + 7)(x + 9) (d) (x − 7)(x − 9)
17. 17.Using (a − b)² = a² − 2ab + b², what is 97²? (a) 9409 (b) 9419 (c) 10609 (d) 9991
18. 18.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 6 (d) 4
20. 20.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 60 (c) 20 (d) 180
21. 21.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 418 (c) 350 (d) 408
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/18 (c) 1/11 (d) 1/36
23. 23.In a class of 35 children, 14 like cricket, 29 like football and 9 like both. How many like neither? (a) 9 (b) 2 (c) 1 (d) 10
24. 24.A bag has 9 black balls and 10 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) 11 (c) 19 (d) 10
25. 25.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
27. 27.A bag has 7 red, 9 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 1/5 (c) 17/20 (d) 4/5
28. 28.Which term of the AP 3, 12, 21, 30, … is 255? (a) 28th (b) 30th (c) 29th (d) 31st
29. 29.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 63 (d) 66
30. 30.What is the mode of 11, 11, 11, 18, 14, 14 and 2? (a) 18 (b) 14 (c) 11 (d) 2
31. 31.What is the smallest prime factor of 87? (a) 2 (b) 29 (c) 1 (d) 3
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
33. 33.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 30° (c) 60° (d) 150°
34. 34.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 6 (d) 8
35. 35.In a class of 25 children, 12 like mangoes, 16 like bananas and 2 like neither. How many like both? (a) 2 (b) 23 (c) 5 (d) 3
36. 36.What is the distance between the points (1, 7) and (25, 14)? (a) 25 (b) 625 (c) 26 (d) 31
37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 110° (c) 45° (d) 70°
38. 38.A drawer has lots of yellow, white, green, black 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) 2 (b) 5 (c) 6 (d) 10
39. 39.A bag has 12 black balls and 3 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) 15 (c) 2 (d) 13
40. 40.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 145° (b) 55° (c) 90° (d) 125°

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