Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 997 · 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 league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 120 (d) 105
2. 2.In a class of 50 children, 26 like dance, 28 like music and 10 like both. How many like neither? (a) 7 (b) 6 (c) 10 (d) 16
3. 3.What are the roots of x² − 11x + 24 = 0? (a) 1 and 24 (b) 3 and 8 (c) 2 and 12 (d) 1 and 10
4. 4.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 30 (c) 15 (d) 20
5. 5.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 0 (d) 3
6. 6.A bag has 9 white, 6 blue and 5 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 3/4 (b) 1/3 (c) 3/10 (d) 1/4
7. 7.In a class of 26 children, 21 like maths, 10 like science and 6 like both. How many like only maths? (a) 16 (b) 21 (c) 4 (d) 15
8. 8.What is the 33rd term of the AP 15, 24, 33, 42, …? (a) 303 (b) 288 (c) 312 (d) 297
9. 9.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°
10. 10.What is the mean of 6, 14, 11, 8, 2 and 13? (a) 8 (b) 10 (c) 11 (d) 9
11. 11.In a class of 36 children, 20 like tea, 20 like coffee and 8 like both. How many like neither? (a) 12 (b) 8 (c) 4 (d) 5
12. 12.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 150° (c) 60° (d) 120°
13. 13.What is the missing term in the AP 14, 22, ?, 38, 46? (a) 30 (b) 29 (c) 31 (d) 38
14. 14.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 11 (c) 35 (d) 28
15. 15.A bag has 8 blue, 8 yellow and 2 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 4/9 (b) 11/18 (c) 5/9 (d) 1/3
16. 16.In a class of 33 children, 21 like cricket, 15 like football and 7 like both. How many like at least one of the two? (a) 33 (b) 36 (c) 22 (d) 29
17. 17.What is the mean of 16, 17, 2 and 13? (a) 11 (b) 16 (c) 12 (d) 13
18. 18.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 39 (d) 13
19. 19.What is the sum of the first 8 terms of the AP 1, 2, 3, …? (a) 72 (b) 8 (c) 40 (d) 36
20. 20.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 126 (c) 14 (d) 42
21. 21.In a class of 27 children, 13 like cricket, 18 like football and 2 like neither. How many like both? (a) 4 (b) 25 (c) 6 (d) 2
22. 22.A drawer has lots of green 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) 3 (b) 4 (c) 2 (d) 5
23. 23.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) 8 (c) 14 (d) 7
24. 24.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 8 times (c) 6 times (d) 4 times
25. 25.What is the midpoint of the line joining (1, 9) and (7, 3)? (a) (3, 3) (b) (4, 6) (c) (8, 12) (d) (6, 4)
26. 26.Two angles of a triangle are 70° and 75°. What is the third angle? (a) 145° (b) 35° (c) 105° (d) 110°
27. 27.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
28. 28.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 11 (d) 10
29. 29.A bag has 6 blue, 8 red and 9 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 14/23 (c) 15/23 (d) 9/23
30. 30.What is the sum of the roots of x² − 8x + 15 = 0? (a) 9 (b) 8 (c) 7 (d) 15
31. 31.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 57 (d) 66
32. 32.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 334 (c) 384 (d) 393
33. 33.In a class of 40 children, 29 like dance, 20 like music and 12 like both. How many like only dance? (a) 17 (b) 20 (c) 8 (d) 29
34. 34.5 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 25 (c) 40 (d) 20
35. 35.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
36. 36.In a class of 35 children, 25 like cricket, 14 like football and 6 like neither. How many like both? (a) 6 (b) 29 (c) 10 (d) 4
37. 37.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4761 (b) 4771 (c) 4899 (d) 5041
38. 38.A drawer has lots of red and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 3 (d) 5
39. 39.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 3/8 (d) 1/8
40. 40.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2

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