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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 378 · 40 questions
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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.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
  2. 2.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
  3. 3.Which term of the AP 12, 15, 18, 21, … is 117? (a) 35th (b) 39th (c) 37th (d) 36th
  4. 4.A bag has 5 green, 7 red and 8 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/10 (b) 13/20 (c) 7/20 (d) 1/3
  5. 5.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 20 (d) 40
  6. 6.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 676 (d) 702
  7. 7.If a + b = 6 and ab = 5, what is a² + b²? (a) 26 (b) 31 (c) 36 (d) 46
  8. 8.A bag has 9 blue balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 10 (c) 2 (d) 21
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 7 (b) 5 (c) 8 (d) 6
  10. 10.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 256 sq cm (c) 512 sq cm (d) 384 sq cm
  11. 11.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 50° (d) 130°
  12. 12.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
  13. 13.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 5° (d) 275°
  14. 14.What is the sum of the roots of x² − 13x + 40 = 0? (a) 14 (b) 13 (c) 12 (d) 40
  15. 15.Two angles of a triangle are 75° and 20°. What is the exterior angle at the third corner? (a) 105° (b) 85° (c) 95° (d) 160°
  16. 16.If a + b = 7 and ab = 10, what is (a − b)²? (a) 49 (b) 9 (c) 29 (d) 3
  17. 17.What is the distance between the points (5, 8) and (13, 23)? (a) 289 (b) 17 (c) 23 (d) 18
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 6 (b) 7 (c) 4 (d) 5
  19. 19.How many factors does 100 have? (a) 10 (b) 8 (c) 7 (d) 9
  20. 20.What is the distance between the points (3, 12) and (8, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  21. 21.What is the distance between the points (7, 13) and (19, 8)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.What is the smallest prime factor of 253? (a) 1 (b) 23 (c) 2 (d) 11
  23. 23.Two angles of a triangle are 30° and 100°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 80° (d) 150°
  24. 24.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 265° (c) 95° (d) 86°
  25. 25.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
  27. 27.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1225 (b) 1575 (c) 1235 (d) 2025
  28. 28.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 1 (d) 7
  29. 29.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 135° (c) 136° (d) 45°
  30. 30.What is the distance between the points (8, 4) and (14, 12)? (a) 14 (b) 11 (c) 100 (d) 10
  31. 31.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7056 (b) 7066 (c) 6416 (d) 5776
  32. 32.What is the sum of the first 10 terms of the AP 6, 10, 14, …? (a) 42 (b) 480 (c) 260 (d) 240
  33. 33.How many factors does 120 have? (a) 16 (b) 15 (c) 17 (d) 14
  34. 34.What is the mean of 18, 2, 14 and 14? (a) 16 (b) 11 (c) 12 (d) 13
  35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
  36. 36.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  37. 37.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 144 (c) 132 (d) 24
  38. 38.What is the mean of 18, 7, 13, 8 and 9? (a) 10 (b) 11 (c) 13 (d) 12
  39. 39.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 96 (c) 48 (d) 56
  40. 40.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 200° (d) 20°

Answer key

  1. 120°
  2. 1386 sq cm
  3. 36th
  4. 13/20
  5. 20
  6. 676
  7. 26
  8. 13
  9. 7
  10. 384 sq cm
  11. 130°
  12. 60°
  13. 95°
  14. 13
  15. 95°
  16. 9
  17. 17
  18. 6
  19. 9
  20. 13
  21. 13
  22. 11
  23. 130°
  24. 85°
  25. 1/3
  26. 154 sq cm
  27. 1225
  28. 7
  29. 135°
  30. 10
  31. 7056
  32. 240
  33. 16
  34. 12
  35. 4 times
  36. 45
  37. 66
  38. 11
  39. 48
  40. 20°

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