Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 357 · 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.There are 4 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 11 (c) 28 (d) 56
2. 2.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
3. 3.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 48 (d) 24
4. 4.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
5. 5.The mean of 6 numbers is 25. When the number 18 is added to them, what is the new mean? (a) 26 (b) 23 (c) 24 (d) 25
6. 6.In a class of 35 children, 23 like tea, 12 like coffee and 6 like both. How many like neither? (a) 7 (b) 12 (c) 0 (d) 6
7. 7.A bag has 3 green balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 2 (c) 5 (d) 4
8. 8.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 225° (b) 135° (c) 46° (d) 45°
9. 9.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
10. 10.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 80° (b) 100° (c) 81° (d) 260°
11. 11.In a class of 31 children, 16 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two? (a) 30 (b) 12 (c) 21 (d) 31
12. 12.What is the mode of 17, 1, 5, 10, 10, 10 and 17? (a) 10 (b) 5 (c) 17 (d) 1
13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 12 (b) 5 (c) 11 (d) 13
14. 14.If a + b = 19 and ab = 90, what is (a − b)²? (a) 361 (b) 181 (c) 1 (d) 271
15. 15.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 40° (b) 30° (c) 60° (d) 120°
16. 16.How many factors does 66 have? (a) 7 (b) 6 (c) 9 (d) 8
17. 17.8 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) 40 (b) 12 (c) 64 (d) 32
18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 78 (d) 66
19. 19.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 14 (c) 28 (d) 9
20. 20.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 130° (b) 70° (c) 110° (d) 160°
21. 21.A bag has 9 red, 9 green and 3 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/6 (b) 1/7 (c) 1/3 (d) 6/7
22. 22.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 2 (d) 31
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 month? (a) 12 (b) 24 (c) 25 (d) 13
24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
25. 25.A drawer has lots of green, white, red, yellow 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) 6 (c) 5 (d) 10
26. 26.What is the median of 20, 3, 10, 16 and 12? (a) 12 (b) 10 (c) 13 (d) 16
27. 27.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 48 (c) 80 (d) 40
28. 28.How many factors does 28 have? (a) 6 (b) 5 (c) 7 (d) 4
29. 29.What is the smallest prime factor of 57? (a) 19 (b) 3 (c) 2 (d) 1
30. 30.Two angles of a triangle are 65° and 50°. What is the third angle? (a) 130° (b) 115° (c) 245° (d) 65°
31. 31.The mean of 3 numbers is 30. When the number 46 is added to them, what is the new mean? (a) 34 (b) 30 (c) 35 (d) 38
32. 32.What is the midpoint of the line joining (2, 8) and (8, 6)? (a) (3, 1) (b) (5, 7) (c) (7, 5) (d) (10, 14)
33. 33.What is the midpoint of the line joining (1, 4) and (3, 6)? (a) (1, 1) (b) (2, 5) (c) (5, 2) (d) (4, 10)
34. 34.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
35. 35.A bag has 8 blue, 9 white and 3 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/5 (b) 3/5 (c) 1/3 (d) 13/20
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 88 cm (d) 154 cm
37. 37.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 50° (c) 130° (d) 125°
38. 38.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
39. 39.A bag has 6 green 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) 15 (b) 10 (c) 2 (d) 7
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/11 (c) 1/6 (d) 7/36

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