Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 820 · 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.A bag has 6 black balls and 9 red 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) 7 (c) 15 (d) 10
2. 2.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 136 (b) 31 (c) 272 (d) 256
3. 3.In a class of 24 children, 13 like tea, 14 like coffee and 5 like both. How many like at least one of the two? (a) 27 (b) 22 (c) 17 (d) 24
4. 4.In a class of 26 children, 11 like tea, 13 like coffee and 7 like both. How many like only tea? (a) 11 (b) 6 (c) 4 (d) 13
5. 5.Which term of the AP 1, 5, 9, 13, … is 109? (a) 29th (b) 28th (c) 30th (d) 27th
6. 6.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) 24 (b) 36 (c) 25 (d) 37
7. 7.What is the sum of all the whole numbers from 1 to 60? (a) 1770 (b) 1800 (c) 3660 (d) 1830
8. 8.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
9. 9.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
10. 10.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 14 (c) 9 (d) 21
11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
12. 12.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 31 (b) 60 (c) 30 (d) 8
13. 13.What is the 36th term of the AP 11, 18, 25, 32, …? (a) 245 (b) 252 (c) 263 (d) 256
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/11 (c) 1/18 (d) 1/12
16. 16.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 8 (c) 7 (d) 6
18. 18.The mean of 8 numbers is 21. When the number 30 is added to them, what is the new mean? (a) 23 (b) 21 (c) 22 (d) 24
19. 19.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 3/4 (d) 1/2
20. 20.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 78 (c) 169 (d) 156
21. 21.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 100° (b) 50° (c) 140° (d) 40°
22. 22.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 2 (d) 1
23. 23.In a class of 24 children, 5 like maths, 17 like science and 2 like both. How many like at least one of the two? (a) 22 (b) 18 (c) 20 (d) 24
24. 24.What is the distance between the points (9, 5) and (13, 8)? (a) 7 (b) 6 (c) 25 (d) 5
25. 25.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
26. 26.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 100 (d) 20
27. 27.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
28. 28.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 504 (c) 505 (d) 495
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 7/36 (d) 1/11
30. 30.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 60° (b) 120° (c) 61° (d) 30°
31. 31.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 66 (d) 69
32. 32.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 24 (d) 144
33. 33.How many factors does 18 have? (a) 4 (b) 6 (c) 5 (d) 7
34. 34.A bag has 6 blue balls and 7 white 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) 8 (c) 2 (d) 13
35. 35.What is the distance between the points (0, 17) and (12, 8)? (a) 21 (b) 16 (c) 15 (d) 225
36. 36.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 95° (c) 85° (d) 105°
37. 37.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7² (c) 2² × 7 (d) 2 × 7
38. 38.The mean of 4 numbers is 36. When the number 46 is added to them, what is the new mean? (a) 36 (b) 39 (c) 38 (d) 41
39. 39.What is the 11th term of the AP 16, 22, 28, 34, …? (a) 66 (b) 82 (c) 60 (d) 76
40. 40.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times

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