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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 471 · 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.What is the mode of 12, 13, 11, 11, 3, 11 and 13? (a) 11 (b) 12 (c) 13 (d) 3
  2. 2.In a class of 37 children, 23 like tea, 15 like coffee and 11 like both. How many like only tea? (a) 4 (b) 22 (c) 23 (d) 12
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  4. 4.What is the 17th term of the AP 8, 12, 16, 20, …? (a) 72 (b) 68 (c) 64 (d) 76
  5. 5.How many factors does 91 have? (a) 3 (b) 2 (c) 4 (d) 5
  6. 6.What is the distance between the points (3, 0) and (10, 24)? (a) 26 (b) 31 (c) 25 (d) 625
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  8. 8.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2509 (b) 2209 (c) 2819 (d) 2809
  9. 9.In a class of 36 children, 22 like cricket, 8 like football and 4 like both. How many like neither? (a) 4 (b) 10 (c) 6 (d) 14
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  11. 11.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 25 times (c) 10 times (d) 5 times
  12. 12.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
  13. 13.What is the mean of 14, 16, 2, 17, 13 and 10? (a) 13 (b) 11 (c) 14 (d) 12
  14. 14.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 135° (b) 315° (c) 136° (d) 45°
  15. 15.Which term of the AP 19, 28, 37, 46, … is 154? (a) 16th (b) 15th (c) 17th (d) 18th
  16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
  17. 17.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 42 (d) 14
  18. 18.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  20. 20.In a class of 46 children, 27 like tea, 17 like coffee and 7 like both. How many like only tea? (a) 29 (b) 20 (c) 10 (d) 27
  21. 21.A bag has 5 yellow, 2 white and 5 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/12 (b) 1/3 (c) 5/7 (d) 5/12
  22. 22.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1099 (b) 729 (c) 909 (d) 1089
  23. 23.In a class of 37 children, 26 like tea, 14 like coffee and 6 like both. How many like at least one of the two? (a) 37 (b) 40 (c) 34 (d) 28
  24. 24.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 25 (c) 20 (d) 10
  25. 25.In a class of 40 children, 19 like mangoes, 29 like bananas and 12 like both. How many like at least one of the two? (a) 48 (b) 24 (c) 40 (d) 36
  26. 26.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 115° (d) 110°
  27. 27.What is the product of the roots of x² − 15x + 56 = 0? (a) 55 (b) 56 (c) 15 (d) 57
  28. 28.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 105° (c) 145° (d) 75°
  29. 29.Two angles of a triangle are 65° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 90° (c) 115° (d) 270°
  30. 30.In a class of 47 children, 29 like tea, 19 like coffee and 10 like neither. How many like both? (a) 10 (b) 1 (c) 37 (d) 11
  31. 31.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  32. 32.A bag has 12 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 15 (c) 2 (d) 4
  33. 33.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
  34. 34.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
  36. 36.What are the roots of x² − 12x + 27 = 0? (a) 1 and 27 (b) 3 and 9 (c) 1 and 11 (d) 2 and 10
  37. 37.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 210 (d) 225
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 8 (d) 7
  39. 39.If a + b = 14 and ab = 33, what is (a − b)²? (a) 8 (b) 196 (c) 64 (d) 130
  40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26

Answer key

  1. 11
  2. 12
  3. 9
  4. 72
  5. 4
  6. 25
  7. 8
  8. 2809
  9. 10
  10. 6
  11. 25 times
  12. 1/2
  13. 12
  14. 135°
  15. 16th
  16. 44 cm
  17. 21
  18. 15
  19. 5
  20. 20
  21. 5/12
  22. 1089
  23. 34
  24. 10
  25. 36
  26. 135°
  27. 56
  28. 105°
  29. 90°
  30. 11
  31. Third quadrant
  32. 13
  33. 78
  34. 6
  35. 1/18
  36. 3 and 9
  37. 105
  38. 8
  39. 64
  40. 25

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