Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 224 · 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 bag has 3 yellow balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 2 (c) 4 (d) 5
2. 2.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 29 (c) 28 (d) 22
3. 3.A bag has 2 green, 9 red and 6 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 11/17 (b) 1/3 (c) 6/17 (d) 6/11
4. 4.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
5. 5.What is the mean of 3, 17, 18, 7, 3 and 6? (a) 11 (b) 10 (c) 8 (d) 9
6. 6.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2509 (b) 2819 (c) 2209 (d) 2809
7. 7.If a + b = 18 and ab = 72, what is (a − b)²? (a) 180 (b) 324 (c) 6 (d) 36
8. 8.What is the median of 1, 21, 22, 35 and 32? (a) 32 (b) 23 (c) 22 (d) 21
9. 9.If a + b = 14 and ab = 45, what is a² + b²? (a) 196 (b) 286 (c) 151 (d) 106
10. 10.The mean of 7 numbers is 19. When the number 51 is added to them, what is the new mean? (a) 24 (b) 19 (c) 35 (d) 23
11. 11.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
12. 12.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 155° (d) 120°
13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 1232 sq cm
14. 14.How many factors does 70 have? (a) 7 (b) 6 (c) 8 (d) 9
15. 15.A drawer has lots of red 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) 5 (c) 4 (d) 3
16. 16.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 50° (c) 40° (d) 140°
17. 17.A bag has 6 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 2 (c) 7 (d) 9
18. 18.How many factors does 25 have? (a) 1 (b) 4 (c) 3 (d) 2
19. 19.Two angles of a triangle are 70° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 35°
20. 20.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.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) 8 (b) 7 (c) 14 (d) 15
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
23. 23.What is the distance between the points (2, 26) and (9, 2)? (a) 31 (b) 25 (c) 625 (d) 26
24. 24.A bag has 11 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 4 (c) 14 (d) 2
25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
26. 26.In a class of 34 children, 12 like cricket, 23 like football and 9 like both. How many like at least one of the two? (a) 34 (b) 35 (c) 26 (d) 17
27. 27.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
28. 28.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 21 (c) 49 (d) 28
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9
30. 30.What is the median of 7, 11, 30, 28 and 38? (a) 11 (b) 28 (c) 29 (d) 30
31. 31.In a class of 31 children, 9 like mangoes, 17 like bananas and 5 like both. How many like neither? (a) 11 (b) 15 (c) 10 (d) 5
32. 32.Using (a + b)² = a² + 2ab + b², what is 91²? (a) 8291 (b) 7921 (c) 8281 (d) 8101
33. 33.The mean of 9 numbers is 26. When the number 66 is added to them, what is the new mean? (a) 26 (b) 31 (c) 46 (d) 30
34. 34.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 552 (b) 529 (c) 45 (d) 276
35. 35.In a class of 33 children, 14 like tea, 14 like coffee and 3 like both. How many like only tea? (a) 19 (b) 11 (c) 14 (d) 3
36. 36.A bag has 11 red balls and 3 yellow 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) 4 (c) 14 (d) 12
37. 37.In a class of 33 children, 17 like mangoes, 19 like bananas and 5 like both. How many like neither? (a) 7 (b) 2 (c) 3 (d) 5
38. 38.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 49 (c) 28 (d) 13
39. 39.What is the mode of 1, 1, 18, 15, 15, 16 and 15? (a) 1 (b) 15 (c) 16 (d) 18
40. 40.What is the distance between the points (8, 12) and (23, 4)? (a) 289 (b) 23 (c) 17 (d) 18

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