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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 214 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 78 (c) 66 (d) 144
  2. 2.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 8 (c) 6 (d) 16
  3. 3.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 61° (d) 60°
  4. 4.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x + 1)(x + 16) (c) (x − 2)(x − 8) (d) (x + 2)(x + 8)
  5. 5.What is the mode of 3, 3, 6, 6, 10, 11 and 6? (a) 3 (b) 6 (c) 10 (d) 11
  6. 6.In a class of 39 children, 15 like mangoes, 16 like bananas and 2 like both. How many like neither? (a) 2 (b) 12 (c) 10 (d) 8
  7. 7.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 7 (d) 8
  8. 8.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
  9. 9.In a class of 28 children, 18 like dance, 9 like music and 6 like both. How many like at least one of the two? (a) 27 (b) 15 (c) 28 (d) 21
  10. 10.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 3/11 (d) 1/11
  12. 12.What is the mean of 9, 7, 11, 5, 9 and 19? (a) 12 (b) 9 (c) 10 (d) 11
  13. 13.In a class of 24 children, 12 like cricket, 10 like football and 8 like neither. How many like both? (a) 16 (b) 6 (c) 8 (d) 7
  14. 14.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 30 (d) 31
  15. 15.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 30° (d) 150°
  16. 16.What is the mode of 6, 5, 10, 16, 5, 5 and 10? (a) 10 (b) 16 (c) 5 (d) 6
  17. 17.What is the 28th term of the AP 19, 21, 23, 25, …? (a) 56 (b) 54 (c) 73 (d) 75
  18. 18.How many factors does 30 have? (a) 8 (b) 7 (c) 9 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  20. 20.Which is the correct factorisation of x² + 6x + 8? (a) (x − 2)(x − 4) (b) (x + 1)(x + 8) (c) (x + 2)(x + 4) (d) (x + 1)(x + 5)
  21. 21.What is the distance between the points (3, 13) and (15, 4)? (a) 21 (b) 225 (c) 16 (d) 15
  22. 22.A bag has 7 yellow, 7 white and 8 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 7/15 (b) 1/3 (c) 15/22 (d) 7/22
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11
  24. 24.What is the smallest prime factor of 377? (a) 29 (b) 2 (c) 1 (d) 13
  25. 25.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  27. 27.A drawer has lots of white 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) 3 (b) 5 (c) 2 (d) 4
  28. 28.What is the mode of 3, 5, 3, 4, 12, 12 and 12? (a) 12 (b) 4 (c) 3 (d) 5
  29. 29.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
  30. 30.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
  31. 31.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
  33. 33.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  34. 34.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 75° (c) 30° (d) 60°
  35. 35.A drawer has lots of black, yellow, white 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) 8 (c) 2 (d) 4
  36. 36.How many prime numbers are there between 70 and 80? (a) 3 (b) 5 (c) 2 (d) 4
  37. 37.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/8 (c) 3/4 (d) 1/4
  38. 38.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
  39. 39.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 482 (c) 615 (d) 616
  40. 40.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 36 (c) 37 (d) 25

Answer key

  1. 66
  2. 8
  3. 60°
  4. (x + 2)(x + 8)
  5. 6
  6. 10
  7. 8
  8. 28
  9. 21
  10. 1/2
  11. 1/12
  12. 10
  13. 6
  14. 30
  15. 150°
  16. 5
  17. 73
  18. 8
  19. 6
  20. (x + 2)(x + 4)
  21. 15
  22. 7/22
  23. 9
  24. 13
  25. Third quadrant
  26. 7
  27. 3
  28. 12
  29. 125 times
  30. 10°
  31. 5
  32. 1/9
  33. 49
  34. 75°
  35. 5
  36. 3
  37. 3/4
  38. 10
  39. 615
  40. 25

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