Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 955 · 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 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) 22 (b) 21 (c) 28 (d) 29
2. 2.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 78 (d) 132
3. 3.A drawer has lots of white, 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) 3 (b) 4 (c) 2 (d) 6
4. 4.A bag has 8 yellow, 5 red and 5 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 13/18 (c) 5/18 (d) 7/9
5. 5.A drawer has lots of green, blue, 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) 8 (b) 2 (c) 4 (d) 5
6. 6.In a class of 36 children, 22 like cricket, 13 like football and 4 like both. How many like only cricket? (a) 9 (b) 23 (c) 22 (d) 18
7. 7.How many factors does 19 have? (a) 3 (b) 4 (c) 2 (d) 1
8. 8.A drawer has lots of black, white 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) 3 (b) 4 (c) 2 (d) 6
9. 9.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 5486 (b) 5476 (c) 4356 (d) 4916
10. 10.What is the median of 32, 16, 11, 24, 7, 30 and 12? (a) 24 (b) 12 (c) 17 (d) 16
11. 11.What is the mean of 3, 6, 18 and 9? (a) 10 (b) 9 (c) 12 (d) 8
12. 12.In a class of 43 children, 19 like dance, 19 like music and 3 like both. How many like at least one of the two? (a) 43 (b) 32 (c) 38 (d) 35
13. 13.What is the distance between the points (5, 10) and (11, 2)? (a) 10 (b) 100 (c) 11 (d) 14
14. 14.In a class of 25 children, 12 like cricket, 14 like football and 7 like both. How many like neither? (a) 7 (b) 5 (c) 13 (d) 6
15. 15.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
17. 17.What is the sum of the roots of x² − 12x + 32 = 0? (a) 11 (b) 32 (c) 12 (d) 13
18. 18.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 7 (d) 6
19. 19.In a class of 37 children, 15 like mangoes, 23 like bananas and 3 like both. How many like at least one of the two? (a) 32 (b) 35 (c) 38 (d) 37
20. 20.What is the mode of 4, 7, 4, 5, 7, 7 and 3? (a) 4 (b) 3 (c) 7 (d) 5
21. 21.A bag has 10 green balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 12 (c) 21 (d) 2
22. 22.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 18 (c) 16 (d) 17
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
24. 24.What is the product of the roots of x² − 11x + 28 = 0? (a) 27 (b) 11 (c) 29 (d) 28
25. 25.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 86° (d) 95°
26. 26.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 35° (c) 60° (d) 145°
27. 27.A bag has 7 black balls and 8 red 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) 15 (c) 9 (d) 8
28. 28.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
29. 29.What is the mean of 20, 8, 5, 17 and 5? (a) 13 (b) 11 (c) 12 (d) 10
30. 30.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 150° (c) 75° (d) 105°
31. 31.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 2 (d) 7
32. 32.A bag has 9 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 17 (d) 11
33. 33.A bag has 7 green, 3 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/6 (b) 1/3 (c) 5/6 (d) 11/12
34. 34.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 10201 (b) 9999 (c) 9811 (d) 9801
35. 35.A cube has edges of 2 cm. What is its total surface area? (a) 4 sq cm (b) 24 sq cm (c) 8 sq cm (d) 16 sq cm
36. 36.What is the distance between the points (3, 6) and (11, 0)? (a) 11 (b) 10 (c) 100 (d) 14
37. 37.Two angles of a triangle are 65° and 30°. What is the exterior angle at the third corner? (a) 95° (b) 150° (c) 85° (d) 115°
38. 38.Which is the correct factorisation of x² + 10x + 16? (a) (x − 2)(x − 8) (b) (x + 2)(x + 8) (c) (x + 1)(x + 16) (d) (x + 1)(x + 9)
39. 39.What is the mean of 7, 7, 13, 20, 7 and 24? (a) 15 (b) 14 (c) 12 (d) 13
40. 40.What is the distance between the points (5, 9) and (13, 3)? (a) 100 (b) 11 (c) 14 (d) 10

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