Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 694 · 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 an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 110° (d) 55°
2. 2.The mean of 3 numbers is 33. When the number 21 is added to them, what is the new mean? (a) 27 (b) 31 (c) 30 (d) 33
3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 15 (d) 16
5. 5.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 21 (c) 42 (d) 28
6. 6.What is the distance between the points (2, 6) and (7, 18)? (a) 13 (b) 17 (c) 14 (d) 169
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
8. 8.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 56) (c) (x − 7)(x − 8) (d) (x + 1)(x + 14)
9. 9.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) 29 (b) 21 (c) 22 (d) 28
10. 10.A drawer has lots of white, yellow, red, green 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) 5 (b) 10 (c) 2 (d) 6
11. 11.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
12. 12.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 260° (c) 130° (d) 80°
13. 13.In a class of 37 children, 19 like mangoes, 23 like bananas and 6 like both. How many like at least one of the two? (a) 37 (b) 42 (c) 30 (d) 36
14. 14.In a class of 41 children, 17 like mangoes, 24 like bananas and 9 like both. How many like neither? (a) 10 (b) 9 (c) 0 (d) 18
15. 15.A bag has 2 red, 5 blue and 4 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 5/11 (c) 6/11 (d) 5/6
16. 16.What is the sum of the first 10 terms of the AP 9, 15, 21, …? (a) 720 (b) 360 (c) 390 (d) 63
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
18. 18.What is the distance between the points (0, 0) and (6, 8)? (a) 10 (b) 100 (c) 11 (d) 14
19. 19.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 18 (c) 12 (d) 6
20. 20.Two angles of a triangle are 40° and 120°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 20°
21. 21.In which quadrant does the point (6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
22. 22.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 156 (d) 78
23. 23.A bag has 9 blue balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 10 (c) 11 (d) 13
24. 24.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 115° (b) 100° (c) 145° (d) 80°
25. 25.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 12 (d) 15
26. 26.A bag has 6 blue, 5 green and 4 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/3 (b) 3/5 (c) 1/3 (d) 2/5
27. 27.In a class of 34 children, 11 like cricket, 23 like football and 5 like both. How many like at least one of the two? (a) 24 (b) 29 (c) 34 (d) 30
28. 28.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 125° (d) 55°
29. 29.What is the midpoint of the line joining (4, 16) and (12, 10)? (a) (16, 26) (b) (4, 3) (c) (8, 13) (d) (13, 8)
30. 30.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
31. 31.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
33. 33.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 140° (d) 90°
34. 34.What is the distance between the points (8, 7) and (11, 3)? (a) 5 (b) 25 (c) 6 (d) 7
35. 35.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
36. 36.How many factors does 101 have? (a) 2 (b) 1 (c) 3 (d) 4
37. 37.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 12 (c) 70 (d) 35
38. 38.A drawer has lots of yellow, green, white, 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) 10 (b) 2 (c) 5 (d) 6
39. 39.A drawer has lots of white 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) 4 (c) 5 (d) 3
40. 40.A bag has 7 green, 6 red and 3 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/9 (b) 9/16 (c) 1/3 (d) 7/16

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad