Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 573 · 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.In a class of 39 children, 20 like cricket, 15 like football and 5 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 25 (d) 39
2. 2.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁴ × 3 × 5
3. 3.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 88 cm (d) 176 cm
4. 4.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 47 (b) 232 (c) 416 (d) 208
5. 5.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 16 (c) 24 (d) 48
6. 6.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
7. 7.A cuboid is 11 cm long, 4 cm wide and 7 cm high. What is its total surface area? (a) 596 sq cm (b) 308 sq cm (c) 298 sq cm (d) 149 sq cm
8. 8.What is the sum of the first 12 terms of the AP 6, 9, 12, …? (a) 270 (b) 288 (c) 39 (d) 540
9. 9.A bag has 6 yellow balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 7 (c) 10 (d) 8
10. 10.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 110° (d) 150°
11. 11.What is the missing term in the AP 12, ?, 28, 36, 44? (a) 28 (b) 21 (c) 20 (d) 19
12. 12.If a + b = 15 and ab = 36, what is (a − b)²? (a) 9 (b) 153 (c) 225 (d) 81
13. 13.A bag has 10 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 11 (c) 2 (d) 12
14. 14.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
15. 15.What is the distance between the points (3, 8) and (27, 15)? (a) 26 (b) 625 (c) 31 (d) 25
16. 16.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
17. 17.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) 28 (c) 22 (d) 29
18. 18.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 10° (b) 50° (c) 100° (d) 80°
19. 19.A drawer has lots of blue, black, red, green 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) 5 (b) 6 (c) 10 (d) 2
20. 20.In a class of 23 children, 10 like tea, 16 like coffee and 4 like both. How many like at least one of the two? (a) 23 (b) 26 (c) 18 (d) 22
21. 21.In a class of 22 children, 12 like cricket, 13 like football and 4 like neither. How many like both? (a) 4 (b) 3 (c) 18 (d) 7
22. 22.What is the 30th term of the AP 6, 9, 12, 15, …? (a) 87 (b) 90 (c) 96 (d) 93
23. 23.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
24. 24.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
25. 25.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 7235 (b) 7225 (c) 9025 (d) 8075
26. 26.A drawer has lots of 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) 6 (b) 2 (c) 4 (d) 3
27. 27.How many factors does 60 have? (a) 11 (b) 12 (c) 10 (d) 13
28. 28.In a class of 41 children, 17 like maths, 23 like science and 5 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 41 (d) 40
29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
30. 30.What is the 33rd term of the AP 4, 6, 8, 10, …? (a) 66 (b) 64 (c) 70 (d) 68
31. 31.Which is the correct factorisation of x² + 9x + 18? (a) (x + 1)(x + 18) (b) (x − 3)(x − 6) (c) (x + 3)(x + 6) (d) (x + 1)(x + 8)
32. 32.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 5544 sq cm
33. 33.What is the distance between the points (8, 1) and (17, 13)? (a) 225 (b) 21 (c) 15 (d) 16
34. 34.Two angles of a triangle are 75° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 135° (c) 60° (d) 105°
35. 35.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
36. 36.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 7/8 (c) 1/4 (d) 1/8
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/11 (b) 5/36 (c) 1/6 (d) 1/11
38. 38.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 8 (c) 6 (d) 12
39. 39.In a class of 32 children, 23 like maths, 14 like science and 8 like both. How many like only maths? (a) 23 (b) 15 (c) 6 (d) 18
40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100

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