Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 294 · 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 fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
3. 3.A drawer has lots of green, red, 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) 2 (b) 4 (c) 5 (d) 8
4. 4.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 60° (d) 150°
5. 5.What is the median of 17, 5, 36, 33 and 20? (a) 36 (b) 20 (c) 17 (d) 33
6. 6.A bag has 5 red balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 9 (d) 6
7. 7.A bag has 8 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 17 (d) 10
8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
9. 9.In a class of 26 children, 13 like maths, 10 like science and 6 like both. How many like at least one of the two? (a) 26 (b) 11 (c) 17 (d) 23
10. 10.If a + b = 14 and ab = 48, what is (a − b)²? (a) 100 (b) 4 (c) 2 (d) 196
11. 11.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 160° (b) 105° (c) 125° (d) 75°
12. 12.What are the roots of x² − 16x + 63 = 0? (a) 7 and 9 (b) 1 and 63 (c) 1 and 15 (d) 3 and 21
13. 13.In a class of 22 children, 13 like dance, 13 like music and 7 like both. How many like at least one of the two? (a) 22 (b) 19 (c) 12 (d) 26
14. 14.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 15 (d) 12
15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 25° (d) 50°
16. 16.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 7 (d) 8
17. 17.In which quadrant does the point (−3, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
18. 18.What is the 24th term of the AP 2, 4, 6, 8, …? (a) 46 (b) 50 (c) 48 (d) 49
19. 19.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 14 (c) 22 (d) 21
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
21. 21.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
23. 23.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 169 (c) 91 (d) 156
24. 24.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
25. 25.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 12 (c) 9 (d) 6
26. 26.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
27. 27.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)
28. 28.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
29. 29.What is the mean of 15, 9, 19, 16, 6 and 7? (a) 14 (b) 12 (c) 13 (d) 11
30. 30.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 160°
31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
32. 32.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 3/4
33. 33.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 125° (b) 140° (c) 55° (d) 95°
34. 34.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 8 (d) 5
35. 35.What is the 12th term of the AP 16, 21, 26, 31, …? (a) 55 (b) 60 (c) 76 (d) 71
36. 36.In a class of 39 children, 13 like tea, 21 like coffee and 3 like both. How many like neither? (a) 8 (b) 5 (c) 11 (d) 3
37. 37.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 40 (c) 31 (d) 32
38. 38.In a class of 20 children, 10 like tea, 8 like coffee and 4 like both. How many like neither? (a) 2 (b) 10 (c) 6 (d) 4
39. 39.What is the median of 15, 21, 32, 30, 12, 34 and 5? (a) 22 (b) 15 (c) 21 (d) 30
40. 40.How many prime numbers are there between 40 and 70? (a) 7 (b) 8 (c) 6 (d) 9

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