Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 254 · 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 area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
2. 2.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 686 (b) 1156 (c) 884 (d) 676
3. 3.A drawer has lots of white, blue, green, 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) 2 (b) 10 (c) 5 (d) 6
4. 4.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
5. 5.What is the product of the roots of x² − 12x + 32 = 0? (a) 32 (b) 12 (c) 33 (d) 31
6. 6.What are the roots of x² − 8x + 12 = 0? (a) 3 and 4 (b) 1 and 7 (c) 2 and 6 (d) 1 and 12
7. 7.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 36 (c) 81 (d) 72
8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 17 (c) 18 (d) 6
9. 9.In a class of 29 children, 9 like cricket, 23 like football and 6 like both. How many like at least one of the two? (a) 32 (b) 26 (c) 29 (d) 20
10. 10.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
11. 11.What is the 27th term of the AP 11, 16, 21, 26, …? (a) 130 (b) 141 (c) 146 (d) 135
12. 12.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/4 (d) 3/8
13. 13.A bag has 9 green, 8 red and 6 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/23 (b) 9/14 (c) 1/3 (d) 14/23
14. 14.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 80 (c) 90 (d) 98
15. 15.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 45 (d) 20
16. 16.What is the mode of 8, 12, 8, 10, 8, 10 and 2? (a) 10 (b) 12 (c) 8 (d) 2
17. 17.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
18. 18.The mean of 5 numbers is 22. When the number 4 is added to them, what is the new mean? (a) 20 (b) 19 (c) 22 (d) 13
19. 19.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2⁴ × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
20. 20.What is the mean of 8, 9, 5 and 6? (a) 6 (b) 7 (c) 9 (d) 8
21. 21.In a class of 45 children, 25 like maths, 29 like science and 12 like both. How many like only maths? (a) 17 (b) 13 (c) 25 (d) 16
22. 22.A bag has 4 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 6 (c) 16 (d) 5
23. 23.In a class of 26 children, 13 like cricket, 11 like football and 5 like both. How many like neither? (a) 5 (b) 2 (c) 12 (d) 7
24. 24.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 30° (d) 150°
25. 25.What is the mean of 16, 14, 10 and 12? (a) 12 (b) 14 (c) 13 (d) 15
26. 26.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
27. 27.If a + b = 9 and ab = 8, what is a² + b²? (a) 65 (b) 97 (c) 81 (d) 73
28. 28.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x − 2)(x − 4) (c) (x + 1)(x + 5) (d) (x + 1)(x + 8)
29. 29.A bag has 6 blue, 4 red and 7 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 6/11 (b) 1/3 (c) 11/17 (d) 6/17
30. 30.In a class of 43 children, 30 like cricket, 15 like football and 10 like both. How many like neither? (a) 10 (b) 18 (c) 8 (d) 9
31. 31.The mean of 4 numbers is 17. When the number 7 is added to them, what is the new mean? (a) 17 (b) 15 (c) 12 (d) 16
32. 32.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/3 (c) 1/6 (d) 1/5
33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 17 (d) 15
34. 34.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
35. 35.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
36. 36.A drawer has lots of red, white 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) 6 (b) 3 (c) 2 (d) 4
37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
38. 38.A bag has 5 white balls and 6 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) 7 (c) 6 (d) 11
39. 39.A bag has 3 red balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 4 (c) 5 (d) 12
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5

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