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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 813 · 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.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
  2. 2.What is the mode of 2, 9, 9, 9, 5, 1 and 5? (a) 5 (b) 1 (c) 9 (d) 2
  3. 3.A bag has 9 red balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 15 (b) 10 (c) 2 (d) 11
  4. 4.How many factors does 96 have? (a) 12 (b) 11 (c) 13 (d) 10
  5. 5.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 207 (d) 198
  6. 6.What is the product of the roots of x² − 8x + 15 = 0? (a) 15 (b) 8 (c) 14 (d) 16
  7. 7.If a + b = 11 and ab = 30, what is a² + b²? (a) 181 (b) 121 (c) 61 (d) 91
  8. 8.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 78 (c) 132 (d) 66
  9. 9.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) 21 (c) 22 (d) 14
  10. 10.What is the distance between the points (2, 1) and (7, 13)? (a) 13 (b) 14 (c) 169 (d) 17
  11. 11.In a class of 32 children, 16 like maths, 17 like science and 11 like both. How many like only maths? (a) 6 (b) 15 (c) 16 (d) 5
  12. 12.A bag has 9 red, 9 white and 2 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 9/10 (b) 1/9 (c) 1/3 (d) 1/10
  13. 13.What is the 20th term of the AP 14, 17, 20, 23, …? (a) 74 (b) 57 (c) 60 (d) 71
  14. 14.In a class of 37 children, 18 like cricket, 16 like football and 5 like both. How many like neither? (a) 8 (b) 13 (c) 3 (d) 5
  15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 18 (c) 16 (d) 7
  16. 16.What is the mode of 4, 4, 11, 5, 4, 16 and 11? (a) 5 (b) 11 (c) 16 (d) 4
  17. 17.What is the 19th term of the AP 13, 20, 27, 34, …? (a) 139 (b) 126 (c) 146 (d) 133
  18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
  19. 19.A bag has 7 yellow, 6 white and 8 red balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/5 (b) 2/7 (c) 5/7 (d) 1/3
  20. 20.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 141 (b) 142 (c) 132 (d) 150
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  22. 22.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 66 cm (d) 264 cm
  23. 23.What is the mode of 19, 19, 19, 3, 3, 14 and 13? (a) 14 (b) 19 (c) 3 (d) 13
  24. 24.What are the roots of x² − 12x + 35 = 0? (a) 1 and 11 (b) 2 and 10 (c) 1 and 35 (d) 5 and 7
  25. 25.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 126 (c) 135 (d) 144
  26. 26.What is the median of 39, 1, 16, 29 and 34? (a) 16 (b) 29 (c) 30 (d) 34
  27. 27.The mean of 9 numbers is 24. When the number 64 is added to them, what is the new mean? (a) 29 (b) 44 (c) 24 (d) 28
  28. 28.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 165° (b) 50° (c) 15° (d) 145°
  29. 29.What is the mean of 15, 18, 10, 7 and 20? (a) 15 (b) 16 (c) 14 (d) 13
  30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 16 (c) 64 (d) 56
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 19 (d) 8
  32. 32.If a + b = 10 and ab = 24, what is a² + b²? (a) 76 (b) 100 (c) 148 (d) 52
  33. 33.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 260° (b) 50° (c) 130° (d) 80°
  34. 34.Two angles of a triangle are 30° and 35°. What is the exterior angle at the third corner? (a) 150° (b) 65° (c) 145° (d) 115°
  35. 35.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 20 (d) 90
  36. 36.What is the median of 31, 40, 16, 32 and 12? (a) 30 (b) 31 (c) 32 (d) 16
  37. 37.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
  38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
  39. 39.What is the 20th term of the AP 17, 23, 29, 35, …? (a) 114 (b) 120 (c) 137 (d) 131
  40. 40.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 132 sq cm

Answer key

  1. 1/2
  2. 9
  3. 11
  4. 12
  5. 207
  6. 15
  7. 61
  8. 66
  9. 15
  10. 13
  11. 5
  12. 1/10
  13. 71
  14. 8
  15. 17
  16. 4
  17. 139
  18. 40°
  19. 2/7
  20. 141
  21. 2
  22. 132 cm
  23. 19
  24. 5 and 7
  25. 135
  26. 29
  27. 28
  28. 15°
  29. 14
  30. 28
  31. 19
  32. 52
  33. 130°
  34. 65°
  35. 90
  36. 31
  37. 1/2
  38. 1/2
  39. 131
  40. 1386 sq cm

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