Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 530 · 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 drawer has lots of black, red, green 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) 4 (b) 8 (c) 5 (d) 2
2. 2.A bag has 10 green balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 19 (b) 2 (c) 11 (d) 12
3. 3.In a class of 40 children, 19 like cricket, 26 like football and 9 like both. How many like neither? (a) 5 (b) 13 (c) 9 (d) 4
4. 4.If a + b = 14 and ab = 45, what is a² + b²? (a) 286 (b) 106 (c) 151 (d) 196
5. 5.What is the distance between the points (6, 3) and (18, 19)? (a) 20 (b) 21 (c) 400 (d) 28
6. 6.What is the mode of 11, 14, 18, 14, 1, 18 and 18? (a) 11 (b) 18 (c) 1 (d) 14
7. 7.What is the mode of 20, 6, 20, 15, 6, 8 and 6? (a) 15 (b) 20 (c) 6 (d) 8
8. 8.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6724 (b) 6094 (c) 6396 (d) 6084
9. 9.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 16 (c) 7 (d) 12
10. 10.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) 5 (b) 3 (c) 4 (d) 2
11. 11.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 10 (d) 5
12. 12.A bag has 9 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 16 (c) 2 (d) 10
13. 13.A bag has 8 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 9 (c) 10 (d) 2
14. 14.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 28 (c) 10 (d) 21
15. 15.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x + 1)(x + 14)
16. 16.What is the sum of the roots of x² − 12x + 32 = 0? (a) 13 (b) 11 (c) 12 (d) 32
17. 17.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
18. 18.What is the missing term in the AP 3, ?, 9, 12, 15? (a) 6 (b) 9 (c) 5 (d) 7
19. 19.What is the distance between the points (2, 12) and (18, 0)? (a) 28 (b) 400 (c) 20 (d) 21
20. 20.What is the mean of 10, 7, 18 and 13? (a) 16 (b) 12 (c) 11 (d) 13
21. 21.In a class of 36 children, 15 like dance, 19 like music and 6 like neither. How many like both? (a) 6 (b) 4 (c) 5 (d) 30
22. 22.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 105° (b) 60° (c) 135° (d) 120°
23. 23.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1681 (b) 1691 (c) 1521 (d) 1601
24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
25. 25.What is the distance between the points (9, 25) and (16, 1)? (a) 31 (b) 26 (c) 625 (d) 25
26. 26.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 36 (c) 49 (d) 37
27. 27.What is the mode of 5, 4, 2, 19, 4, 4 and 19? (a) 2 (b) 4 (c) 19 (d) 5
28. 28.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 145° (b) 120° (c) 95° (d) 85°
29. 29.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 7921 (b) 8099 (c) 8281 (d) 7931
30. 30.What is the median of 37, 22, 11, 12, 25, 13 and 8? (a) 14 (b) 12 (c) 22 (d) 13
31. 31.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 60 (c) 19 (d) 57
32. 32.What is the sum of the roots of x² − 15x + 56 = 0? (a) 15 (b) 16 (c) 56 (d) 14
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 2 (d) 4
34. 34.What is the median of 9, 12, 20, 30 and 7? (a) 9 (b) 12 (c) 13 (d) 20
35. 35.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
36. 36.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 95° (d) 120°
37. 37.How many factors does 31 have? (a) 1 (b) 2 (c) 4 (d) 3
38. 38.A bag has 5 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 7 (c) 2 (d) 11
39. 39.What is the missing term in the AP 7, 9, ?, 13, 15? (a) 13 (b) 12 (c) 10 (d) 11
40. 40.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°

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