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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 443 · 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.A bag has 7 black balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 4 (c) 2 (d) 10
  2. 2.What is the mode of 16, 2, 20, 11, 16, 11 and 11? (a) 11 (b) 2 (c) 20 (d) 16
  3. 3.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 16 (b) 56 (c) 28 (d) 64
  4. 4.What is the 33rd term of the AP 1, 4, 7, 10, …? (a) 100 (b) 96 (c) 99 (d) 97
  5. 5.Two angles of a triangle are 20° and 75°. What is the third angle? (a) 95° (b) 160° (c) 105° (d) 85°
  6. 6.If a + b = 21 and ab = 108, what is a² + b²? (a) 657 (b) 225 (c) 333 (d) 441
  7. 7.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 15) (c) (x + 7)(x + 9) (d) (x + 1)(x + 63)
  8. 8.A bag has 3 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 2 (c) 4 (d) 6
  9. 9.A cuboid is 8 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 123 sq cm (b) 246 sq cm (c) 216 sq cm (d) 492 sq cm
  10. 10.In a class of 28 children, 19 like dance, 15 like music and 9 like both. How many like only dance? (a) 19 (b) 6 (c) 13 (d) 10
  11. 11.If a + b = 11 and ab = 30, what is (a − b)²? (a) 91 (b) 121 (c) 1 (d) 61
  12. 12.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
  13. 13.What is the smallest prime factor of 247? (a) 19 (b) 1 (c) 13 (d) 2
  14. 14.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
  15. 15.A bag has 6 blue, 5 green and 4 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/3 (b) 2/5 (c) 3/5 (d) 1/3
  16. 16.In a class of 39 children, 23 like maths, 19 like science and 11 like both. How many like neither? (a) 8 (b) 9 (c) 11 (d) 19
  17. 17.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) 22 (b) 21 (c) 14 (d) 15
  18. 18.In a class of 34 children, 27 like cricket, 14 like football and 8 like both. How many like neither? (a) 9 (b) 8 (c) 1 (d) 2
  19. 19.A bag has 8 red balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 9 (c) 11 (d) 2
  20. 20.What is the mode of 1, 1, 7, 17, 6, 6 and 6? (a) 7 (b) 1 (c) 6 (d) 17
  21. 21.In a class of 35 children, 23 like cricket, 22 like football and 12 like both. How many like only cricket? (a) 13 (b) 11 (c) 10 (d) 23
  22. 22.What is the mode of 12, 1, 8, 1, 8, 7 and 1? (a) 12 (b) 7 (c) 1 (d) 8
  23. 23.What is the mode of 6, 15, 15, 8, 13, 8 and 8? (a) 6 (b) 13 (c) 15 (d) 8
  24. 24.8 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) 24 (b) 16 (c) 10 (d) 32
  25. 25.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 1 (d) 3
  26. 26.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
  27. 27.A bag has 10 blue balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 2 (c) 15 (d) 11
  28. 28.What is the distance between the points (0, 9) and (8, 24)? (a) 23 (b) 18 (c) 17 (d) 289
  29. 29.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  30. 30.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9226 (b) 10816 (c) 9216 (d) 9984
  31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 100 (d) 45
  32. 32.What is the median of 14, 25, 8, 1, 9, 27 and 2? (a) 1 (b) 14 (c) 8 (d) 9
  33. 33.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
  34. 34.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 1 (d) 3
  35. 35.What is the distance between the points (6, 13) and (15, 1)? (a) 21 (b) 225 (c) 15 (d) 16
  36. 36.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) 25 (b) 37 (c) 36 (d) 24
  37. 37.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 1 (d) 2
  38. 38.How many factors does 105 have? (a) 9 (b) 6 (c) 7 (d) 8
  39. 39.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 9025 (b) 11035 (c) 11025 (d) 10025
  40. 40.What is the sum of the first 9 terms of the AP 4, 7, 10, …? (a) 147 (b) 144 (c) 28 (d) 288

Answer key

  1. 8
  2. 11
  3. 56
  4. 97
  5. 85°
  6. 225
  7. (x + 7)(x + 9)
  8. 5
  9. 246 sq cm
  10. 10
  11. 1
  12. 1/4
  13. 13
  14. 10
  15. 3/5
  16. 8
  17. 15
  18. 1
  19. 11
  20. 6
  21. 11
  22. 1
  23. 8
  24. 16
  25. 3
  26. 7/8
  27. 12
  28. 17
  29. 7
  30. 9216
  31. 45
  32. 9
  33. (x + 8)(x + 9)
  34. 11
  35. 15
  36. 25
  37. 3
  38. 8
  39. 11025
  40. 144

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