Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 342 · 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 captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
2. 2.What is the smallest prime factor of 33? (a) 11 (b) 3 (c) 1 (d) 2
3. 3.How many prime numbers are there between 70 and 80? (a) 4 (b) 3 (c) 2 (d) 5
4. 4.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
5. 5.A bag has 10 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 4 (c) 11 (d) 2
6. 6.In a class of 31 children, 11 like mangoes, 16 like bananas and 4 like both. How many like at least one of the two? (a) 31 (b) 23 (c) 27 (d) 19
7. 7.In a league, 9 teams each play every other team once. How many matches are played? (a) 36 (b) 45 (c) 81 (d) 72
8. 8.In a class of 32 children, 18 like mangoes, 22 like bananas and 11 like both. How many like neither? (a) 14 (b) 11 (c) 3 (d) 4
9. 9.The mean of 5 numbers is 10. When the number 16 is added to them, what is the new mean? (a) 12 (b) 11 (c) 10 (d) 13
10. 10.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 20 (d) 10
11. 11.Which is the correct factorisation of x² + 15x + 54? (a) (x + 1)(x + 14) (b) (x + 6)(x + 9) (c) (x + 1)(x + 54) (d) (x − 6)(x − 9)
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
15. 15.What is the median of 38, 27, 9, 4 and 24? (a) 27 (b) 24 (c) 25 (d) 9
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
17. 17.In a class of 21 children, 16 like tea, 10 like coffee and 2 like neither. How many like both? (a) 5 (b) 7 (c) 19 (d) 2
18. 18.What is the median of 4, 29, 28, 3, 30, 10 and 38? (a) 3 (b) 29 (c) 28 (d) 10
19. 19.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 6 (c) 9 (d) 12
20. 20.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 48 (d) 16
21. 21.A bag has 8 green, 8 white and 5 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 16/21 (b) 5/21 (c) 1/3 (d) 5/16
22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
23. 23.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 414 (b) 43 (c) 212 (d) 207
24. 24.A drawer has lots of black, 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) 2 (b) 6 (c) 3 (d) 4
25. 25.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 168 (d) 186
26. 26.In a class of 37 children, 23 like cricket, 12 like football and 6 like neither. How many like both? (a) 6 (b) 5 (c) 31 (d) 4
27. 27.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 135° (b) 155° (c) 160° (d) 45°
28. 28.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 401 (b) 441 (c) 451 (d) 361
29. 29.What is the sum of all the whole numbers from 1 to 70? (a) 2485 (b) 2450 (c) 4970 (d) 2415
30. 30.A drawer has lots of yellow, green, red, black 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) 5 (b) 6 (c) 2 (d) 10
31. 31.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
32. 32.What is the median of 36, 5, 20, 39, 2, 13 and 25? (a) 39 (b) 13 (c) 25 (d) 20
33. 33.A bag has 9 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 12 (c) 2 (d) 11
34. 34.A cuboid is 6 cm long, 5 cm wide and 6 cm high. What is its volume? (a) 192 cu cm (b) 180 cu cm (c) 30 cu cm (d) 17 cu cm
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 4/11 (c) 1/11 (d) 5/36
36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
37. 37.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 110° (c) 45° (d) 70°
38. 38.What is the median of 9, 35, 10, 38, 30, 32 and 13? (a) 13 (b) 32 (c) 38 (d) 30
39. 39.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 40° (c) 140° (d) 100°
40. 40.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2

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