Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 338 · 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 sum of the first 8 terms of the AP 4, 10, 16, …? (a) 46 (b) 400 (c) 200 (d) 224
2. 2.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 40° (d) 100°
3. 3.A drawer has lots of white, green, yellow, black 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) 5 (b) 6 (c) 10 (d) 2
4. 4.A cuboid is 7 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 122 cu cm (b) 28 cu cm (c) 14 cu cm (d) 84 cu cm
5. 5.What are the roots of x² − 11x + 24 = 0? (a) 3 and 8 (b) 2 and 12 (c) 1 and 24 (d) 1 and 10
6. 6.What is the mode of 2, 3, 2, 3, 18, 20 and 3? (a) 2 (b) 20 (c) 3 (d) 18
7. 7.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
8. 8.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 16) (c) (x + 1)(x + 72) (d) (x − 8)(x − 9)
9. 9.In a class of 31 children, 17 like dance, 16 like music and 3 like both. How many like at least one of the two? (a) 31 (b) 30 (c) 27 (d) 33
10. 10.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
12. 12.A bag has 7 white, 5 red and 6 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 5/18 (c) 13/18 (d) 7/9
13. 13.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
14. 14.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 75° (d) 30°
15. 15.A bag has 5 blue balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 12 (c) 6 (d) 7
16. 16.What is the sum of all the whole numbers from 1 to 36? (a) 630 (b) 1332 (c) 648 (d) 666
17. 17.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 120° (d) 30°
18. 18.A bag has 7 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 8 (c) 19 (d) 2
19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
20. 20.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 115° (d) 66°
21. 21.What is the 26th term of the AP 19, 27, 35, 43, …? (a) 219 (b) 208 (c) 227 (d) 200
22. 22.What is the smallest prime factor of 55? (a) 5 (b) 11 (c) 1 (d) 2
23. 23.A drawer has lots of black, green, blue 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) 4 (b) 5 (c) 2 (d) 8
24. 24.How many factors does 64 have? (a) 6 (b) 7 (c) 8 (d) 5
25. 25.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 80° (c) 100° (d) 280°
26. 26.What is the smallest prime factor of 49? (a) 7 (b) 3 (c) 1 (d) 2
27. 27.What is the mode of 3, 6, 3, 2, 2, 8 and 2? (a) 8 (b) 2 (c) 3 (d) 6
28. 28.How many factors does 27 have? (a) 4 (b) 5 (c) 2 (d) 3
29. 29.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 25 (c) 10 (d) 21
30. 30.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 15 (d) 45
31. 31.A bag has 4 red balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 9 (c) 6 (d) 2
32. 32.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 67 (b) 11 (c) 132 (d) 66
33. 33.What is the 11th term of the AP 1, 8, 15, 22, …? (a) 78 (b) 77 (c) 70 (d) 71
34. 34.What is the smallest prime factor of 217? (a) 7 (b) 31 (c) 2 (d) 1
35. 35.The mean of 7 numbers is 18. When the number 42 is added to them, what is the new mean? (a) 21 (b) 30 (c) 18 (d) 22
36. 36.How many factors does 32 have? (a) 4 (b) 7 (c) 6 (d) 5
37. 37.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 25 (d) 20
38. 38.Which is the correct factorisation of x² + 10x + 24? (a) (x − 4)(x − 6) (b) (x + 1)(x + 9) (c) (x + 4)(x + 6) (d) (x + 1)(x + 24)
39. 39.A drawer has lots of yellow, red, white, 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) 6 (b) 5 (c) 2 (d) 10
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm

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