Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 886 · 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 green 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) 3 (b) 5 (c) 2 (d) 4
2. 2.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 63)
3. 3.Which term of the AP 15, 18, 21, 24, … is 45? (a) 15th (b) 10th (c) 12th (d) 11th
4. 4.A bag has 7 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 12 (b) 9 (c) 2 (d) 8
5. 5.Two angles of a triangle are 30° and 115°. What is the exterior angle at the third corner? (a) 35° (b) 145° (c) 150° (d) 65°
6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 81 (c) 36 (d) 72
7. 7.A drawer has lots of red, yellow, green, black and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 6 (d) 5
8. 8.What is the mean of 4, 7, 5 and 12? (a) 8 (b) 9 (c) 6 (d) 7
9. 9.The mean of 3 numbers is 11. When the number 15 is added to them, what is the new mean? (a) 12 (b) 13 (c) 11 (d) 14
10. 10.A cuboid is 5 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 158 cu cm (b) 16 cu cm (c) 15 cu cm (d) 120 cu cm
11. 11.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
12. 12.What is the mode of 1, 8, 6, 8, 8, 7 and 7? (a) 1 (b) 6 (c) 8 (d) 7
13. 13.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 23 (c) 78 (d) 144
14. 14.What is the sum of the first 11 terms of the AP 3, 8, 13, …? (a) 53 (b) 313 (c) 308 (d) 616
15. 15.What is the mode of 1, 4, 1, 7, 1, 13 and 13? (a) 4 (b) 7 (c) 1 (d) 13
16. 16.In a class of 31 children, 23 like dance, 14 like music and 8 like both. How many like at least one of the two? (a) 37 (b) 31 (c) 21 (d) 29
17. 17.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 72 (c) 75 (d) 24
18. 18.A bag has 4 green balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 5 (c) 6 (d) 15
19. 19.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
20. 20.A drawer has lots of red 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) 4 (b) 5 (c) 2 (d) 3
21. 21.What is the product of the roots of x² − 15x + 56 = 0? (a) 56 (b) 15 (c) 55 (d) 57
22. 22.How many prime numbers are there between 90 and 110? (a) 4 (b) 5 (c) 7 (d) 6
23. 23.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
24. 24.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 56 (c) 49 (d) 98
25. 25.A bag has 5 white balls and 9 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) 6 (c) 10 (d) 14
26. 26.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2 × 7³ (c) 2² × 7 (d) 2³ × 7
27. 27.Two angles of a triangle are 45° and 95°. What is the third angle? (a) 140° (b) 135° (c) 40° (d) 85°
28. 28.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 27 sq cm (c) 54 sq cm (d) 36 sq cm
29. 29.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 95° (c) 120° (d) 85°
30. 30.A drawer has lots of white, yellow 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) 2 (c) 6 (d) 4
31. 31.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 9 (c) 81 (d) 27
32. 32.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) 29 (b) 22 (c) 21 (d) 28
33. 33.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
35. 35.What is the sum of the roots of x² − 11x + 18 = 0? (a) 12 (b) 10 (c) 11 (d) 18
36. 36.Two angles of a triangle are 30° and 65°. What is the exterior angle at the third corner? (a) 85° (b) 115° (c) 150° (d) 95°
37. 37.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 6 (d) 4
38. 38.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 195 (c) 204 (d) 208
39. 39.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
40. 40.In a class of 26 children, 17 like dance, 15 like music and 11 like both. How many like neither? (a) 6 (b) 16 (c) 11 (d) 5

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