Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 851 · 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 how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 20 (d) 25
2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 7 (b) 18 (c) 17 (d) 16
3. 3.A bag has 9 blue, 3 yellow and 7 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 7/19 (c) 12/19 (d) 13/19
4. 4.What is the product of the roots of x² − 15x + 56 = 0? (a) 56 (b) 55 (c) 15 (d) 57
5. 5.A bag has 12 red balls and 9 white 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) 10 (c) 13 (d) 21
6. 6.What is the distance between the points (8, 14) and (32, 7)? (a) 31 (b) 625 (c) 25 (d) 26
7. 7.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
8. 8.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
9. 9.In a class of 24 children, 10 like cricket, 13 like football and 5 like both. How many like only cricket? (a) 11 (b) 5 (c) 8 (d) 10
10. 10.A bag has 5 green, 2 red and 7 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/7 (b) 1/3 (c) 6/7 (d) 1/6
11. 11.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
12. 12.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 24 cu cm (c) 8 cu cm (d) 6 cu cm
13. 13.A bag has 5 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 16 (b) 2 (c) 7 (d) 6
14. 14.A drawer has lots of red 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) 2 (b) 3 (c) 4 (d) 5
15. 15.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 90° (b) 225° (c) 45° (d) 135°
16. 16.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 9025 (b) 8075 (c) 7235 (d) 7225
17. 17.What is the sum of the first 7 terms of the AP 8, 14, 20, …? (a) 203 (b) 182 (c) 364 (d) 44
18. 18.What is the sum of the first 5 terms of the AP 4, 10, 16, …? (a) 28 (b) 80 (c) 95 (d) 160
19. 19.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 110° (c) 145° (d) 55°
20. 20.In a league, 15 teams each play every other team once. How many matches are played? (a) 210 (b) 120 (c) 105 (d) 225
21. 21.The mean of 7 numbers is 37. When the number 13 is added to them, what is the new mean? (a) 34 (b) 25 (c) 35 (d) 37
22. 22.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 16 (c) 14 (d) 56
23. 23.A drawer has lots of white 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) 4 (b) 5 (c) 2 (d) 3
24. 24.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 5 (d) 6
25. 25.A drawer has lots of yellow, white, 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) 4 (b) 8 (c) 2 (d) 5
26. 26.A drawer has lots of black, green, white, blue 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) 5 (b) 2 (c) 10 (d) 6
27. 27.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 25 (c) 20 (d) 9
28. 28.A bag has 2 yellow, 7 white and 2 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/9 (b) 9/11 (c) 1/3 (d) 2/11
29. 29.A drawer has lots of red, 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) 3 (c) 4 (d) 6
30. 30.What is the distance between the points (7, 11) and (31, 4)? (a) 26 (b) 31 (c) 625 (d) 25
31. 31.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
32. 32.What is the mean of 7, 8, 2, 13, 9 and 9? (a) 10 (b) 8 (c) 7 (d) 9
33. 33.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 270° (b) 125° (c) 145° (d) 90°
34. 34.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
35. 35.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
36. 36.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 130° (c) 25° (d) 50°
37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
38. 38.What is the midpoint of the line joining (4, 0) and (12, 12)? (a) (8, 6) (b) (4, 6) (c) (16, 12) (d) (6, 8)
39. 39.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
40. 40.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 230° (b) 130° (c) 50° (d) 100°

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