Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 757 · 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 cube has edges of 6 cm. What is its total surface area? (a) 216 sq cm (b) 144 sq cm (c) 217 sq cm (d) 36 sq cm
2. 2.In a class of 24 children, 13 like mangoes, 12 like bananas and 2 like both. How many like only mangoes? (a) 12 (b) 13 (c) 11 (d) 10
3. 3.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 7406 (b) 8084 (c) 7396 (d) 8836
4. 4.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
5. 5.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
6. 6.A bag has 5 green, 8 yellow and 8 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 8/13 (c) 8/21 (d) 13/21
7. 7.What is the distance between the points (0, 8) and (3, 12)? (a) 7 (b) 6 (c) 25 (d) 5
8. 8.How many factors does 43 have? (a) 4 (b) 3 (c) 1 (d) 2
9. 9.There are 8 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) 64 (b) 40 (c) 32 (d) 12
10. 10.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 2/3 (d) 5/6
11. 11.The mean of 5 numbers is 22. When the number 40 is added to them, what is the new mean? (a) 22 (b) 26 (c) 31 (d) 25
12. 12.A bag has 4 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 7 (d) 4
13. 13.A bag has 6 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 7 (c) 18 (d) 8
14. 14.The mean of 9 numbers is 10. When the number 40 is added to them, what is the new mean? (a) 10 (b) 13 (c) 25 (d) 14
15. 15.Using (a − b)² = a² − 2ab + b², what is 28²? (a) 794 (b) 784 (c) 896 (d) 1024
16. 16.What is the mean of 6, 14, 7, 3, 11 and 19? (a) 11 (b) 9 (c) 12 (d) 10
17. 17.7 T-shirts and 3 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) 21 (c) 10 (d) 42
18. 18.If a + b = 5 and ab = 6, what is a² + b²? (a) 13 (b) 37 (c) 25 (d) 19
19. 19.What is the midpoint of the line joining (4, 3) and (6, 13)? (a) (10, 16) (b) (5, 8) (c) (1, 5) (d) (8, 5)
20. 20.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
21. 21.What is the median of 18, 16, 3, 22, 7, 38 and 11? (a) 18 (b) 22 (c) 11 (d) 16
22. 22.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 50° (b) 125° (c) 130° (d) 105°
23. 23.A bag has 3 yellow, 7 white and 7 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/14 (b) 1/3 (c) 14/17 (d) 3/17
24. 24.A bag has 3 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 4 (c) 5 (d) 8
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
26. 26.A bag has 11 white balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 23 (b) 13 (c) 2 (d) 12
27. 27.What is the mean of 19, 8, 4, 19 and 15? (a) 14 (b) 13 (c) 12 (d) 15
28. 28.What is the mode of 5, 12, 12, 3, 12, 15 and 15? (a) 5 (b) 3 (c) 12 (d) 15
29. 29.In a class of 50 children, 32 like cricket, 23 like football and 7 like neither. How many like both? (a) 5 (b) 12 (c) 7 (d) 43
30. 30.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 105 (c) 196 (d) 91
31. 31.How many factors does 24 have? (a) 6 (b) 9 (c) 7 (d) 8
32. 32.What is the distance between the points (1, 31) and (8, 7)? (a) 625 (b) 26 (c) 31 (d) 25
33. 33.The mean of 6 numbers is 35. When the number 14 is added to them, what is the new mean? (a) 31 (b) 33 (c) 35 (d) 32
34. 34.What is the mode of 19, 2, 12, 12, 2, 14 and 2? (a) 12 (b) 2 (c) 14 (d) 19
35. 35.What is the midpoint of the line joining (3, 5) and (9, 7)? (a) (6, 6) (b) (12, 12) (c) (7, 6) (d) (3, 1)
36. 36.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 160 (c) 142 (d) 152
37. 37.What is the mode of 2, 2, 13, 15, 13, 13 and 8? (a) 13 (b) 15 (c) 8 (d) 2
38. 38.A drawer has lots of white, green, blue and black 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) 8
39. 39.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 635 (c) 625 (d) 225
40. 40.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3

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