Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 922 · 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 9 terms of the AP 8, 11, 14, …? (a) 183 (b) 32 (c) 180 (d) 360
2. 2.What is the distance between the points (8, 26) and (15, 2)? (a) 625 (b) 31 (c) 25 (d) 26
3. 3.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
4. 4.In a class of 28 children, 15 like maths, 13 like science and 3 like neither. How many like both? (a) 2 (b) 25 (c) 4 (d) 3
5. 5.What is the mode of 1, 5, 20, 20, 1, 14 and 20? (a) 20 (b) 1 (c) 14 (d) 5
6. 6.8 T-shirts and 6 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) 48 (d) 96
7. 7.A bag has 2 green, 5 white and 7 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 13/14 (b) 6/7 (c) 1/7 (d) 1/3
8. 8.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 260° (d) 130°
9. 9.A bag has 7 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 12 (c) 8 (d) 2
10. 10.How many factors does 54 have? (a) 6 (b) 9 (c) 7 (d) 8
11. 11.A drawer has lots of red 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) 3 (b) 5 (c) 2 (d) 4
12. 12.Which is the correct factorisation of x² + 9x + 18? (a) (x + 1)(x + 8) (b) (x + 3)(x + 6) (c) (x + 1)(x + 18) (d) (x − 3)(x − 6)
13. 13.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
14. 14.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
15. 15.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 7225 (b) 5635 (c) 6375 (d) 5625
16. 16.A bag has 10 blue 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) 19 (b) 11 (c) 2 (d) 10
17. 17.In a class of 30 children, 9 like maths, 15 like science and 4 like both. How many like neither? (a) 14 (b) 6 (c) 10 (d) 4
18. 18.The mean of 5 numbers is 36. When the number 18 is added to them, what is the new mean? (a) 34 (b) 27 (c) 33 (d) 36
19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
20. 20.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
21. 21.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
22. 22.How many prime numbers are there between 90 and 120? (a) 5 (b) 6 (c) 8 (d) 7
23. 23.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 17 (d) 2
24. 24.What is the 19th term of the AP 2, 8, 14, 20, …? (a) 116 (b) 108 (c) 110 (d) 114
25. 25.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 110 (d) 92
26. 26.In a class of 38 children, 12 like tea, 20 like coffee and 8 like neither. How many like both? (a) 8 (b) 2 (c) 3 (d) 30
27. 27.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
28. 28.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 33 cu cm (d) 1331 cu cm
29. 29.In a class of 31 children, 18 like cricket, 19 like football and 11 like both. How many like at least one of the two? (a) 31 (b) 37 (c) 15 (d) 26
30. 30.How many prime numbers are there between 60 and 70? (a) 4 (b) 2 (c) 3 (d) 1
31. 31.What is the distance between the points (7, 24) and (15, 9)? (a) 17 (b) 289 (c) 18 (d) 23
32. 32.Two angles of a triangle are 45° and 45°. What is the third angle? (a) 90° (b) 91° (c) 135° (d) 270°
33. 33.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
34. 34.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 36 (c) 33 (d) 99
35. 35.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 25° (d) 130°
36. 36.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
37. 37.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 50° (c) 130° (d) 85°
38. 38.A bag has 2 blue, 5 yellow and 4 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 2/11 (b) 9/11 (c) 1/3 (d) 2/9
39. 39.In a class of 24 children, 6 like maths, 19 like science and 2 like both. How many like neither? (a) 1 (b) 3 (c) 0 (d) 2
40. 40.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7

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