Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 691 · 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 41 children, 23 like dance, 19 like music and 3 like neither. How many like both? (a) 1 (b) 3 (c) 4 (d) 38
2. 2.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/8 (c) 1/4 (d) 3/8
3. 3.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
4. 4.In a class of 28 children, 15 like dance, 12 like music and 4 like both. How many like neither? (a) 9 (b) 5 (c) 1 (d) 4
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 1/11 (c) 5/36 (d) 5/11
6. 6.A cuboid is 10 cm long, 8 cm wide and 3 cm high. What is its total surface area? (a) 240 sq cm (b) 536 sq cm (c) 268 sq cm (d) 134 sq cm
7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
8. 8.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 36 (c) 24 (d) 37
9. 9.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 45° (d) 125°
10. 10.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
11. 11.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 105 (d) 91
12. 12.Two angles of a triangle are 50° and 90°. What is the exterior angle at the third corner? (a) 40° (b) 90° (c) 140° (d) 130°
13. 13.What is the mean of 7, 3, 6 and 4? (a) 6 (b) 7 (c) 4 (d) 5
14. 14.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 3 (b) 2 (c) 4 (d) 5
16. 16.What is the midpoint of the line joining (10, 8) and (20, 2)? (a) (5, 3) (b) (15, 5) (c) (30, 10) (d) (5, 15)
17. 17.A bag has 8 white, 5 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 4/17 (b) 13/17 (c) 1/3 (d) 14/17
18. 18.How many factors does 40 have? (a) 9 (b) 6 (c) 7 (d) 8
19. 19.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
21. 21.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 86° (c) 85° (d) 265°
22. 22.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) 15 (b) 14 (c) 8 (d) 7
23. 23.In a class of 26 children, 13 like dance, 13 like music and 2 like both. How many like neither? (a) 2 (b) 0 (c) 4 (d) 3
24. 24.A drawer has lots of green, white 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) 6 (b) 3 (c) 4 (d) 2
25. 25.What is the mean of 8, 3, 3 and 10? (a) 5 (b) 7 (c) 8 (d) 6
26. 26.A bag has 11 white balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 13 (c) 2 (d) 15
27. 27.What is the sum of the first 6 terms of the AP 9, 11, 13, …? (a) 168 (b) 19 (c) 84 (d) 90
28. 28.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 95° (b) 85° (c) 160° (d) 105°
29. 29.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 110° (b) 165° (c) 85° (d) 15°
30. 30.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 104 (c) 114 (d) 113
31. 31.What is the 10th term of the AP 4, 8, 12, 16, …? (a) 36 (b) 41 (c) 44 (d) 40
32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
33. 33.What is the mode of 15, 19, 17, 15, 9, 9 and 9? (a) 19 (b) 15 (c) 9 (d) 17
34. 34.In a class of 28 children, 14 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 21 (b) 25 (c) 28 (d) 17
35. 35.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 64 (d) 36
36. 36.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
37. 37.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 160° (b) 150° (c) 50° (d) 130°
38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
40. 40.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4

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