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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 70 · 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 missing term in the AP 3, 10, 17, ?, 31? (a) 24 (b) 25 (c) 23 (d) 31
  2. 2.What is the median of 8, 23, 29, 13 and 16? (a) 13 (b) 16 (c) 29 (d) 23
  3. 3.In a class of 21 children, 17 like dance, 15 like music and 1 like neither. How many like both? (a) 1 (b) 20 (c) 12 (d) 11
  4. 4.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 156 (d) 78
  5. 5.A bag has 3 green balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 10 (c) 2 (d) 8
  6. 6.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x + 6)(x + 8) (c) (x − 6)(x − 8) (d) (x + 1)(x + 13)
  7. 7.A bag has 6 red, 5 yellow and 3 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 6/7 (b) 3/14 (c) 1/3 (d) 11/14
  8. 8.Which term of the AP 6, 12, 18, 24, … is 222? (a) 39th (b) 37th (c) 38th (d) 36th
  9. 9.In which quadrant does the point (−4, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the sum of all the whole numbers from 1 to 100? (a) 4950 (b) 10100 (c) 5000 (d) 5050
  11. 11.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 9) (b) (x + 1)(x + 16) (c) (x + 2)(x + 8) (d) (x − 2)(x − 8)
  12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  13. 13.What is the sum of the roots of x² − 9x + 20 = 0? (a) 10 (b) 8 (c) 20 (d) 9
  14. 14.What is the mean of 13, 2, 5, 5 and 20? (a) 8 (b) 11 (c) 10 (d) 9
  15. 15.A bag has 4 blue, 6 green and 2 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/3 (b) 3/4 (c) 1/3 (d) 1/12
  16. 16.A bag has 10 white balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 17 (d) 8
  17. 17.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
  18. 18.What is the sum of the first 7 terms of the AP 8, 11, 14, …? (a) 238 (b) 26 (c) 122 (d) 119
  19. 19.What is the sum of all the whole numbers from 1 to 58? (a) 1653 (b) 1711 (c) 3422 (d) 1682
  20. 20.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 17 (c) 15 (d) 16
  21. 21.In a class of 40 children, 24 like cricket, 17 like football and 9 like both. How many like at least one of the two? (a) 40 (b) 41 (c) 32 (d) 23
  22. 22.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) 12 (c) 24 (d) 13
  23. 23.What is the median of 11, 23, 22, 1 and 35? (a) 11 (b) 23 (c) 21 (d) 22
  24. 24.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 30 (d) 12
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  26. 26.Which is the correct factorisation of x² + 10x + 21? (a) (x − 3)(x − 7) (b) (x + 1)(x + 9) (c) (x + 1)(x + 21) (d) (x + 3)(x + 7)
  27. 27.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 290° (b) 145° (c) 70° (d) 110°
  28. 28.Two angles of a triangle are 40° and 115°. What is the third angle? (a) 25° (b) 140° (c) 155° (d) 65°
  29. 29.The mean of 6 numbers is 20. When the number 27 is added to them, what is the new mean? (a) 22 (b) 20 (c) 21 (d) 23
  30. 30.In a class of 24 children, 15 like dance, 12 like music and 4 like both. How many like neither? (a) 2 (b) 1 (c) 5 (d) 4
  31. 31.What are the roots of x² − 15x + 56 = 0? (a) 2 and 28 (b) 1 and 14 (c) 7 and 8 (d) 1 and 56
  32. 32.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/7 (c) 1/8 (d) 7/8
  33. 33.A drawer has lots of white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 3 (d) 5
  34. 34.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 80 (d) 70
  35. 35.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 57 (c) 171 (d) 19
  36. 36.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
  37. 37.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 45 (b) 552 (c) 276 (d) 300
  38. 38.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 66 (d) 132
  39. 39.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2⁴ × 3² (c) 2² × 3² (d) 2³ × 3²
  40. 40.What is the mode of 6, 4, 10, 20, 20, 4 and 4? (a) 20 (b) 6 (c) 10 (d) 4

Answer key

  1. 24
  2. 16
  3. 12
  4. 78
  5. 8
  6. (x + 6)(x + 8)
  7. 11/14
  8. 37th
  9. Third quadrant
  10. 5050
  11. (x + 2)(x + 8)
  12. 20
  13. 9
  14. 9
  15. 2/3
  16. 11
  17. 85°
  18. 119
  19. 1711
  20. 16
  21. 32
  22. 13
  23. 22
  24. 30
  25. 10
  26. (x + 3)(x + 7)
  27. 70°
  28. 25°
  29. 21
  30. 1
  31. 7 and 8
  32. 1/8
  33. 3
  34. 79
  35. 57
  36. 1/2
  37. 276
  38. 132
  39. 2³ × 3²
  40. 4

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