Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 846 · 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, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 91 (d) 169
2. 2.A bag has 12 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 21 (c) 13 (d) 14
3. 3.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
4. 4.The mean of 9 numbers is 21. When the number 11 is added to them, what is the new mean? (a) 19 (b) 20 (c) 16 (d) 21
5. 5.A bag has 6 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 7 (c) 2 (d) 9
6. 6.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 66 (d) 144
7. 7.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
8. 8.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 35 (c) 56 (d) 11
9. 9.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 99 (d) 36
10. 10.If a + b = 14 and ab = 40, what is (a − b)²? (a) 6 (b) 36 (c) 196 (d) 116
11. 11.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 105° (b) 20° (c) 95° (d) 160°
12. 12.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 35° (b) 36° (c) 215° (d) 145°
13. 13.What is the mode of 5, 7, 1, 4, 5, 7 and 7? (a) 5 (b) 7 (c) 4 (d) 1
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 3 (c) 12 (d) 13
15. 15.What is the missing term in the AP 1, 5, 9, ?, 17? (a) 13 (b) 17 (c) 12 (d) 14
16. 16.What is the sum of the first 11 terms of the AP 8, 11, 14, …? (a) 256 (b) 38 (c) 506 (d) 253
17. 17.A drawer has lots of red, 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) 2 (b) 10 (c) 5 (d) 6
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
19. 19.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
20. 20.How many factors does 22 have? (a) 2 (b) 3 (c) 4 (d) 5
21. 21.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
22. 22.What is the mode of 14, 18, 8, 12, 14, 14 and 8? (a) 12 (b) 18 (c) 14 (d) 8
23. 23.What is the mode of 5, 7, 5, 11, 3, 7 and 5? (a) 5 (b) 11 (c) 3 (d) 7
24. 24.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 5 (d) 2
25. 25.The mean of 5 numbers is 20. When the number 44 is added to them, what is the new mean? (a) 24 (b) 20 (c) 32 (d) 25
26. 26.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 90 (d) 100
27. 27.In a class of 25 children, 6 like mangoes, 20 like bananas and 1 like neither. How many like both? (a) 2 (b) 1 (c) 3 (d) 24
28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 9 (b) 6 (c) 10 (d) 7
29. 29.In a class of 38 children, 30 like cricket, 18 like football and 12 like both. How many like at least one of the two? (a) 24 (b) 36 (c) 38 (d) 48
30. 30.What is the distance between the points (8, 3) and (32, 10)? (a) 625 (b) 25 (c) 31 (d) 26
31. 31.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) 14 (b) 8 (c) 7 (d) 15
32. 32.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 99 (b) 90 (c) 108 (d) 100
33. 33.What is the sum of the first 6 terms of the AP 1, 3, 5, …? (a) 11 (b) 36 (c) 42 (d) 72
34. 34.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 43 (b) 506 (c) 484 (d) 253
35. 35.A drawer has lots of green, 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) 5 (c) 8 (d) 4
36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 14 (d) 16
37. 37.The mean of 8 numbers is 35. When the number 17 is added to them, what is the new mean? (a) 26 (b) 35 (c) 33 (d) 34
38. 38.What is the midpoint of the line joining (5, 3) and (11, 11)? (a) (16, 14) (b) (3, 4) (c) (7, 8) (d) (8, 7)
39. 39.What is the mean of 2, 15, 9 and 10? (a) 12 (b) 10 (c) 8 (d) 9
40. 40.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 45° (b) 130° (c) 95° (d) 135°

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