Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 286 · 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 bag has 4 green, 4 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 2/3 (c) 1/12 (d) 3/4
2. 2.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 676 (b) 1156 (c) 916 (d) 1166
3. 3.A bag has 8 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 12 (b) 9 (c) 10 (d) 2
4. 4.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 5)(x + 6) (c) (x + 1)(x + 30) (d) (x + 1)(x + 10)
5. 5.A bag has 6 green, 7 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 4/17 (c) 13/17 (d) 4/13
6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 36 (c) 81 (d) 18
7. 7.A drawer has lots of black, white, blue 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) 4 (b) 2 (c) 5 (d) 8
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 64 times (c) 8 times (d) 4 times
9. 9.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 80 (c) 40 (d) 13
10. 10.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 7 (c) 21 (d) 63
11. 11.What is the mode of 6, 4, 6, 6, 8, 8 and 20? (a) 4 (b) 6 (c) 20 (d) 8
12. 12.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 50 (d) 49
13. 13.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2 × 5 × 7²
14. 14.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 25 (d) 10
15. 15.What is the distance between the points (0, 21) and (16, 9)? (a) 21 (b) 400 (c) 20 (d) 28
16. 16.Two angles of a triangle are 25° and 55°. What is the exterior angle at the third corner? (a) 155° (b) 100° (c) 125° (d) 80°
17. 17.In a class of 29 children, 14 like cricket, 16 like football and 6 like neither. How many like both? (a) 1 (b) 6 (c) 7 (d) 23
18. 18.What is the 23rd term of the AP 20, 24, 28, 32, …? (a) 88 (b) 92 (c) 108 (d) 112
19. 19.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 6 (d) 4
20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 4 (b) 8 (c) 7 (d) 5
21. 21.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 270 (b) 250 (c) 43 (d) 500
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 1/11 (d) 6/11
23. 23.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) 29 (c) 22 (d) 28
24. 24.What is the 37th term of the AP 12, 15, 18, 21, …? (a) 108 (b) 111 (c) 120 (d) 123
25. 25.A bag has 6 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 7 (c) 2 (d) 13
26. 26.A drawer has lots of red, yellow, blue, black 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) 5 (b) 6 (c) 10 (d) 2
27. 27.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 30° (d) 120°
28. 28.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 5 (d) 3
29. 29.A bag has 10 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 14 (d) 5
30. 30.In a class of 51 children, 30 like mangoes, 28 like bananas and 10 like both. How many like at least one of the two? (a) 51 (b) 38 (c) 58 (d) 48
31. 31.In a class of 50 children, 27 like maths, 24 like science and 9 like both. How many like only maths? (a) 15 (b) 27 (c) 26 (d) 18
32. 32.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2³ × 3
33. 33.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 64 (c) 56 (d) 16
34. 34.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/5 (c) 5/6 (d) 1/6
35. 35.How many factors does 63 have? (a) 7 (b) 4 (c) 5 (d) 6
36. 36.What is the median of 33, 4, 34, 16, 24, 14 and 40? (a) 16 (b) 24 (c) 33 (d) 25
37. 37.What is the median of 18, 32, 25, 1 and 3? (a) 3 (b) 18 (c) 19 (d) 25
38. 38.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 18 (c) 162 (d) 54
39. 39.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
40. 40.What is the distance between the points (9, 8) and (17, 23)? (a) 18 (b) 17 (c) 23 (d) 289

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