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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 532 · 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 team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 36 (d) 81
  2. 2.If a + b = 16 and ab = 60, what is (a − b)²? (a) 136 (b) 256 (c) 4 (d) 16
  3. 3.Two angles of a triangle are 30° and 80°. What is the third angle? (a) 70° (b) 150° (c) 110° (d) 100°
  4. 4.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 17 (c) 15 (d) 16
  5. 5.What is the 11th term of the AP 4, 10, 16, 22, …? (a) 70 (b) 66 (c) 60 (d) 64
  6. 6.What is the 12th term of the AP 13, 17, 21, 25, …? (a) 61 (b) 44 (c) 57 (d) 48
  7. 7.What is the 23rd term of the AP 2, 7, 12, 17, …? (a) 117 (b) 115 (c) 112 (d) 110
  8. 8.A bag has 7 blue balls and 3 red 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) 10 (c) 4 (d) 8
  9. 9.What is the sum of the first 6 terms of the AP 7, 12, 17, …? (a) 132 (b) 234 (c) 117 (d) 32
  10. 10.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
  11. 11.What is the product of the roots of x² − 10x + 16 = 0? (a) 10 (b) 17 (c) 16 (d) 15
  12. 12.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 121 (c) 55 (d) 66
  13. 13.Which term of the AP 3, 6, 9, 12, … is 72? (a) 23rd (b) 25th (c) 24th (d) 26th
  14. 14.What is the 33rd term of the AP 10, 15, 20, 25, …? (a) 170 (b) 160 (c) 165 (d) 175
  15. 15.A bag has 9 white, 4 red and 8 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 13/21 (b) 3/7 (c) 4/7 (d) 1/3
  16. 16.A cube has edges of 2 cm. What is its volume? (a) 6 cu cm (b) 16 cu cm (c) 24 cu cm (d) 8 cu cm
  17. 17.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 155° (b) 130° (c) 105° (d) 75°
  18. 18.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) 7 (b) 14 (c) 15 (d) 8
  19. 19.What is the midpoint of the line joining (0, 14) and (4, 6)? (a) (2, 4) (b) (10, 2) (c) (4, 20) (d) (2, 10)
  20. 20.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  22. 22.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 110° (b) 135° (c) 115° (d) 70°
  23. 23.Which term of the AP 2, 9, 16, 23, … is 121? (a) 18th (b) 17th (c) 19th (d) 20th
  24. 24.A bag has 10 yellow balls and 9 green 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) 10 (c) 19 (d) 11
  25. 25.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 2/3 (d) 5/6
  26. 26.What is the sum of all the whole numbers from 1 to 54? (a) 1431 (b) 1458 (c) 1485 (d) 2970
  27. 27.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 16 (d) 28
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 17 (d) 7
  29. 29.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
  30. 30.What is the missing term in the AP 5, 14, 23, ?, 41? (a) 33 (b) 41 (c) 31 (d) 32
  31. 31.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 66 (c) 132 (d) 78
  32. 32.What is the mean of 3, 16, 10, 12, 6 and 13? (a) 11 (b) 12 (c) 10 (d) 9
  33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  34. 34.Two angles of a triangle are 75° and 20°. What is the third angle? (a) 105° (b) 160° (c) 95° (d) 85°
  35. 35.A drawer has lots of green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 3 (c) 5 (d) 4
  36. 36.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 3035 (b) 2525 (c) 3025 (d) 2025
  37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 120° (c) 70° (d) 60°
  38. 38.What is the median of 4, 20, 33, 19, 11, 23 and 14? (a) 20 (b) 19 (c) 14 (d) 18
  39. 39.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 160° (d) 115°
  40. 40.How many factors does 36 have? (a) 8 (b) 7 (c) 9 (d) 10

Answer key

  1. 36
  2. 16
  3. 70°
  4. 16
  5. 64
  6. 57
  7. 112
  8. 8
  9. 117
  10. 169
  11. 16
  12. 55
  13. 24th
  14. 170
  15. 4/7
  16. 8 cu cm
  17. 75°
  18. 8
  19. (2, 10)
  20. (x + 7)(x + 8)
  21. 5
  22. 70°
  23. 18th
  24. 11
  25. 2/3
  26. 1485
  27. 56
  28. 18
  29. 10
  30. 32
  31. 66
  32. 10
  33. 10
  34. 85°
  35. 3
  36. 3025
  37. 60°
  38. 19
  39. 85°
  40. 9

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