Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 136 · 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 mode of 16, 16, 6, 6, 13, 5 and 6? (a) 6 (b) 5 (c) 13 (d) 16
2. 2.A bag has 11 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 13 (c) 2 (d) 20
3. 3.Two angles of a triangle are 25° and 110°. What is the exterior angle at the third corner? (a) 45° (b) 155° (c) 70° (d) 135°
4. 4.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 108 (d) 12
5. 5.In a class of 23 children, 14 like dance, 12 like music and 6 like both. How many like only dance? (a) 11 (b) 14 (c) 8 (d) 6
6. 6.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 6 (c) 18 (d) 54
7. 7.In a class of 31 children, 20 like mangoes, 11 like bananas and 6 like both. How many like only mangoes? (a) 20 (b) 6 (c) 5 (d) 14
8. 8.What is the mean of 7, 10, 16, 6, 15 and 12? (a) 13 (b) 11 (c) 12 (d) 10
9. 9.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 24 (c) 144 (d) 132
10. 10.A bag has 5 red, 7 yellow and 6 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/18 (b) 7/9 (c) 1/3 (d) 13/18
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
12. 12.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 100° (c) 260° (d) 80°
13. 13.In a class of 30 children, 11 like mangoes, 21 like bananas and 4 like both. How many like neither? (a) 6 (b) 3 (c) 2 (d) 4
14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
15. 15.What is the 20th term of the AP 5, 7, 9, 11, …? (a) 45 (b) 38 (c) 43 (d) 40
16. 16.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
17. 17.What is the distance between the points (0, 20) and (9, 8)? (a) 15 (b) 16 (c) 225 (d) 21
18. 18.A drawer has lots of red, blue, green, yellow 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) 5 (b) 10 (c) 6 (d) 2
19. 19.What is the 10th term of the AP 18, 23, 28, 33, …? (a) 63 (b) 45 (c) 50 (d) 68
20. 20.What is the mean of 19, 3, 9, 13, 6 and 22? (a) 14 (b) 13 (c) 12 (d) 11
21. 21.There are 6 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) 10 (b) 48 (c) 24 (d) 30
22. 22.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
23. 23.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 77 sq cm (d) 616 sq cm
25. 25.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 7225 (b) 8125 (c) 9025 (d) 9035
26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
27. 27.In a league, 10 teams each play every other team once. How many matches are played? (a) 45 (b) 90 (c) 55 (d) 100
28. 28.A drawer has lots of black, 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) 3 (c) 6 (d) 4
29. 29.In a class of 19 children, 12 like cricket, 14 like football and 9 like both. How many like at least one of the two? (a) 17 (b) 19 (c) 8 (d) 26
30. 30.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 80° (d) 100°
31. 31.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
32. 32.In a class of 14 children, 5 like tea, 10 like coffee and 2 like both. How many like neither? (a) 2 (b) 1 (c) 3 (d) 0
33. 33.A bag has 3 yellow, 4 green and 9 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/8 (b) 13/16 (c) 3/16 (d) 1/3
34. 34.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 72 (c) 81 (d) 36
35. 35.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
36. 36.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
37. 37.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 110° (c) 140° (d) 71°
38. 38.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 1331 cu cm (c) 33 cu cm (d) 484 cu cm
39. 39.In a class of 34 children, 11 like mangoes, 28 like bananas and 8 like both. How many like only mangoes? (a) 3 (b) 11 (c) 6 (d) 20
40. 40.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

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