Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 146 · 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.What is the sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 1081 (d) 2162
2. 2.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
3. 3.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 17 (d) 19
5. 5.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/8 (d) 3/5
6. 6.A bag has 5 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 7 (c) 6 (d) 2
7. 7.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 100 (b) 55 (c) 90 (d) 45
8. 8.What is the mode of 14, 14, 7, 17, 6, 7 and 14? (a) 7 (b) 14 (c) 17 (d) 6
9. 9.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 36 (d) 45
10. 10.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
11. 11.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
12. 12.A drawer has lots of white 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) 5 (b) 3 (c) 4 (d) 2
13. 13.What is the sum of all the whole numbers from 1 to 86? (a) 3655 (b) 7482 (c) 3698 (d) 3741
14. 14.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) 2 (b) 4 (c) 3 (d) 5
15. 15.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 15 (c) 30 (d) 36
16. 16.What is the median of 18, 5, 14, 20 and 9? (a) 15 (b) 18 (c) 14 (d) 9
17. 17.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 8 times (c) 2 times (d) 6 times
18. 18.In a class of 33 children, 14 like mangoes, 26 like bananas and 8 like both. How many like at least one of the two? (a) 24 (b) 40 (c) 32 (d) 33
19. 19.What is the mean of 3, 3, 10, 20 and 14? (a) 10 (b) 11 (c) 12 (d) 9
20. 20.If a + b = 14 and ab = 45, what is (a − b)²? (a) 4 (b) 196 (c) 16 (d) 106
21. 21.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
22. 22.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
23. 23.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 4096 (b) 3136 (c) 3616 (d) 4106
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/12 (c) 1/36 (d) 1/18
25. 25.What is the 40th term of the AP 5, 13, 21, 29, …? (a) 317 (b) 312 (c) 320 (d) 325
26. 26.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) 14 (c) 8 (d) 7
27. 27.What is the mean of 2, 5, 3, 16 and 14? (a) 7 (b) 9 (c) 8 (d) 10
28. 28.A bag has 11 blue balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 15 (b) 2 (c) 12 (d) 13
29. 29.Two angles of a triangle are 75° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 105° (c) 145° (d) 35°
30. 30.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 3/8 (d) 1/4
31. 31.There are 6 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 42 (c) 72 (d) 12
32. 32.Which term of the AP 1, 9, 17, 25, … is 241? (a) 33rd (b) 31st (c) 32nd (d) 30th
33. 33.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 15 (c) 110 (d) 220
34. 34.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 25° (c) 15° (d) 150°
35. 35.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
36. 36.In a class of 51 children, 23 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 51 (b) 44 (c) 38 (d) 41
37. 37.A bag has 4 green balls and 5 black 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) 9 (c) 6 (d) 5
38. 38.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
39. 39.How many factors does 88 have? (a) 8 (b) 6 (c) 7 (d) 9
40. 40.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 140° (c) 40° (d) 280°

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