Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 79 · 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 17 children, 7 like cricket, 8 like football and 6 like neither. How many like both? (a) 4 (b) 5 (c) 6 (d) 11
2. 2.What is the mode of 1, 15, 1, 10, 1, 10 and 8? (a) 1 (b) 8 (c) 15 (d) 10
3. 3.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 75° (b) 140° (c) 145° (d) 105°
4. 4.In a class of 28 children, 10 like dance, 16 like music and 2 like both. How many like at least one of the two? (a) 26 (b) 28 (c) 24 (d) 22
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 3 times (c) 27 times (d) 9 times
6. 6.Two angles of a triangle are 55° and 70°. What is the third angle? (a) 235° (b) 125° (c) 55° (d) 110°
7. 7.What is the mean of 20, 13, 11 and 16? (a) 12 (b) 20 (c) 16 (d) 15
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
9. 9.In a class of 40 children, 23 like mangoes, 14 like bananas and 6 like both. How many like at least one of the two? (a) 31 (b) 37 (c) 40 (d) 25
10. 10.In a class of 21 children, 10 like maths, 10 like science and 8 like neither. How many like both? (a) 8 (b) 7 (c) 13 (d) 6
11. 11.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 105 (c) 210 (d) 120
12. 12.In a league, 12 teams each play every other team once. How many matches are played? (a) 78 (b) 66 (c) 144 (d) 132
13. 13.A bag has 10 green balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 21 (c) 2 (d) 11
14. 14.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
15. 15.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 95° (c) 130° (d) 85°
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
17. 17.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/8 (d) 3/5
18. 18.What is the distance between the points (3, 10) and (15, 5)? (a) 13 (b) 17 (c) 169 (d) 14
19. 19.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 21 (c) 25 (d) 10
20. 20.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 84 (b) 20 (c) 75 (d) 150
21. 21.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 128 (c) 120 (d) 136
22. 22.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 456 (c) 376 (d) 457
23. 23.A bag has 9 blue 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) 10 (b) 4 (c) 12 (d) 2
24. 24.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
25. 25.A bag has 4 green 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) 2 (b) 5 (c) 4 (d) 7
26. 26.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
27. 27.In a class of 41 children, 18 like tea, 30 like coffee and 10 like both. How many like at least one of the two? (a) 41 (b) 48 (c) 38 (d) 28
28. 28.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 21 (c) 42 (d) 28
29. 29.In which quadrant does the point (3, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
30. 30.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
31. 31.What is the smallest prime factor of 133? (a) 1 (b) 7 (c) 2 (d) 19
32. 32.If a + b = 15 and ab = 56, what is a² + b²? (a) 113 (b) 225 (c) 337 (d) 169
33. 33.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
35. 35.In a class of 13 children, 8 like mangoes, 6 like bananas and 1 like neither. How many like both? (a) 3 (b) 1 (c) 12 (d) 2
36. 36.A bag has 3 green, 7 blue and 4 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 5/7 (c) 2/5 (d) 2/7
37. 37.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 80° (d) 160°
38. 38.A cuboid is 11 cm long, 3 cm wide and 6 cm high. What is its total surface area? (a) 234 sq cm (b) 198 sq cm (c) 468 sq cm (d) 117 sq cm
39. 39.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 14 (b) 15 (c) 7 (d) 8
40. 40.Two angles of a triangle are 70° and 65°. What is the third angle? (a) 45° (b) 135° (c) 110° (d) 115°

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