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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 721 · 40 questions
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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. 1.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  2. 2.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 468 (b) 50 (c) 234 (d) 261
  3. 3.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 400 cu cm (c) 30 cu cm (d) 600 cu cm
  4. 4.Which term of the AP 1, 3, 5, 7, … is 29? (a) 17th (b) 15th (c) 16th (d) 14th
  5. 5.What is the midpoint of the line joining (10, 1) and (20, 9)? (a) (5, 4) (b) (30, 10) (c) (15, 5) (d) (5, 15)
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/18 (c) 1/12 (d) 1/11
  7. 7.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 75° (d) 255°
  8. 8.A bag has 11 blue balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 16 (c) 2 (d) 12
  9. 9.What is the missing term in the AP 20, 23, ?, 29, 32? (a) 25 (b) 29 (c) 26 (d) 27
  10. 10.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) 22 (c) 21 (d) 14
  11. 11.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 12 (d) 13
  12. 12.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 110° (b) 145° (c) 105° (d) 70°
  13. 13.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 49 (c) 42 (d) 13
  14. 14.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
  15. 15.A bag has 8 blue 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
  16. 16.A drawer has lots of green, red, white, blue 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) 6 (b) 10 (c) 5 (d) 2
  17. 17.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 105 (c) 210 (d) 120
  18. 18.What is the median of 28, 11, 26, 22 and 20? (a) 20 (b) 23 (c) 26 (d) 22
  19. 19.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
  20. 20.The mean of 5 numbers is 30. When the number 42 is added to them, what is the new mean? (a) 30 (b) 32 (c) 33 (d) 36
  21. 21.What is the median of 1, 12, 18, 19, 40, 25 and 2? (a) 18 (b) 19 (c) 17 (d) 12
  22. 22.A cube has edges of 3 cm. What is its volume? (a) 36 cu cm (b) 27 cu cm (c) 54 cu cm (d) 9 cu cm
  23. 23.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  24. 24.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 200 (b) 112 (c) 23 (d) 100
  25. 25.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 17 (c) 90 (d) 45
  26. 26.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 45° (d) 100°
  27. 27.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 55° (b) 70° (c) 110° (d) 20°
  28. 28.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/8 (d) 3/5
  29. 29.In a class of 32 children, 16 like cricket, 16 like football and 4 like both. How many like neither? (a) 0 (b) 8 (c) 4 (d) 5
  30. 30.What is the midpoint of the line joining (5, 14) and (15, 10)? (a) (5, 2) (b) (10, 12) (c) (12, 10) (d) (20, 24)
  31. 31.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 16 (b) 10 (c) 11 (d) 12
  32. 32.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°
  33. 33.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 135° (b) 45° (c) 100° (d) 125°
  34. 34.Which is the correct factorisation of x² + 10x + 21? (a) (x + 1)(x + 9) (b) (x + 3)(x + 7) (c) (x − 3)(x − 7) (d) (x + 1)(x + 21)
  35. 35.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 20 (d) 45
  36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
  37. 37.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
  38. 38.Two angles of a triangle are 65° and 105°. What is the third angle? (a) 170° (b) 75° (c) 115° (d) 10°
  39. 39.A bag has 6 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 5 (c) 2 (d) 7
  40. 40.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) 7 (c) 14 (d) 8

Answer key

  1. 66
  2. 234
  3. 1000 cu cm
  4. 15th
  5. (15, 5)
  6. 1/36
  7. 75°
  8. 13
  9. 26
  10. 15
  11. 13
  12. 70°
  13. 42
  14. 11
  15. 10
  16. 6
  17. 105
  18. 22
  19. 4
  20. 32
  21. 18
  22. 27 cu cm
  23. 6
  24. 100
  25. 81
  26. 135°
  27. 55°
  28. 3/8
  29. 4
  30. (10, 12)
  31. 11
  32. 50°
  33. 45°
  34. (x + 3)(x + 7)
  35. 45
  36. 17
  37. 579
  38. 10°
  39. 7
  40. 8

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