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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 34 · 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.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
  2. 2.A bag has 8 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 2 (c) 10 (d) 19
  3. 3.What is the sum of the first 9 terms of the AP 5, 6, 7, …? (a) 13 (b) 162 (c) 81 (d) 82
  4. 4.What is the smallest prime factor of 187? (a) 17 (b) 2 (c) 1 (d) 11
  5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  6. 6.In a class of 23 children, 17 like dance, 11 like music and 7 like both. How many like neither? (a) 3 (b) 7 (c) 2 (d) 9
  7. 7.In a class of 27 children, 10 like maths, 15 like science and 5 like both. How many like at least one of the two? (a) 25 (b) 27 (c) 20 (d) 15
  8. 8.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
  9. 9.What is the distance between the points (0, 15) and (12, 6)? (a) 16 (b) 225 (c) 15 (d) 21
  10. 10.The mean of 3 numbers is 20. When the number 32 is added to them, what is the new mean? (a) 23 (b) 26 (c) 20 (d) 24
  11. 11.How many factors does 74 have? (a) 2 (b) 3 (c) 5 (d) 4
  12. 12.What is the mode of 14, 7, 14, 18, 14, 7 and 19? (a) 7 (b) 18 (c) 19 (d) 14
  13. 13.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 20 (d) 45
  14. 14.Two angles of a triangle are 60° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 120° (c) 110° (d) 70°
  15. 15.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
  16. 16.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) 8 (c) 7 (d) 14
  17. 17.The mean of 8 numbers is 28. When the number 1 is added to them, what is the new mean? (a) 26 (b) 28 (c) 25 (d) 24
  18. 18.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 25 (c) 10 (d) 11
  19. 19.What is the sum of the roots of x² − 5x + 6 = 0? (a) 5 (b) 4 (c) 7 (d) 6
  20. 20.What is the missing term in the AP 13, 19, 25, ?, 37? (a) 31 (b) 37 (c) 32 (d) 30
  21. 21.What is the distance between the points (3, 6) and (6, 2)? (a) 7 (b) 5 (c) 6 (d) 25
  22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
  23. 23.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 333 (c) 343 (d) 342
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 7/36 (c) 1/6 (d) 1/11
  25. 25.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 42 (b) 49 (c) 14 (d) 21
  26. 26.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45
  27. 27.What is the mean of 8, 19, 4, 18 and 11? (a) 12 (b) 15 (c) 13 (d) 10
  28. 28.What is the sum of the first 12 terms of the AP 6, 10, 14, …? (a) 672 (b) 336 (c) 50 (d) 360
  29. 29.What is the mode of 10, 2, 16, 2, 2, 16 and 1? (a) 16 (b) 1 (c) 2 (d) 10
  30. 30.What is the mode of 14, 6, 20, 14, 6, 6 and 10? (a) 10 (b) 14 (c) 20 (d) 6
  31. 31.There are 8 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 13 (b) 80 (c) 48 (d) 40
  32. 32.A bag has 4 red balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 5 (c) 6 (d) 12
  33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
  34. 34.A bag has 9 black balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 10 (c) 13 (d) 2
  35. 35.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x + 1)(x + 11) (c) (x − 3)(x − 9) (d) (x + 3)(x + 9)
  36. 36.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 1/4 (d) 2/3
  37. 37.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  38. 38.A bag has 6 red, 4 yellow and 9 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 9/19 (b) 1/3 (c) 10/19 (d) 11/19
  39. 39.How many factors does 32 have? (a) 6 (b) 4 (c) 5 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6

Answer key

  1. 3/8
  2. 10
  3. 81
  4. 11
  5. 6
  6. 2
  7. 20
  8. 9 times
  9. 15
  10. 23
  11. 4
  12. 14
  13. 90
  14. 110°
  15. (x + 8)(x + 9)
  16. 8
  17. 25
  18. 10
  19. 5
  20. 31
  21. 5
  22. 1/36
  23. 342
  24. 1/6
  25. 21
  26. 45
  27. 12
  28. 336
  29. 2
  30. 6
  31. 40
  32. 6
  33. 88 cm
  34. 13
  35. (x + 3)(x + 9)
  36. 2/3
  37. 2³ × 5 × 7
  38. 10/19
  39. 6
  40. 5

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