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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 866 · 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.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 115° (b) 70° (c) 110° (d) 135°
  2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  3. 3.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 2 times (d) 5 times
  4. 4.What is the distance between the points (1, 19) and (9, 4)? (a) 18 (b) 289 (c) 17 (d) 23
  5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 130° (c) 25° (d) 155°
  6. 6.What is the distance between the points (1, 6) and (25, 13)? (a) 26 (b) 25 (c) 625 (d) 31
  7. 7.How many prime numbers are there between 70 and 100? (a) 6 (b) 5 (c) 7 (d) 8
  8. 8.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 60° (b) 35° (c) 145° (d) 155°
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  10. 10.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 23 (b) 25 (c) 24 (d) 31
  11. 11.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 20 (d) 10
  12. 12.In a class of 34 children, 19 like dance, 14 like music and 9 like both. How many like at least one of the two? (a) 33 (b) 34 (c) 24 (d) 15
  13. 13.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 145° (d) 120°
  14. 14.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
  15. 15.A drawer has lots of blue, red, white, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 6 (d) 10
  16. 16.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  18. 18.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 258 (c) 244 (d) 259
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 18 (d) 16
  21. 21.How many factors does 50 have? (a) 4 (b) 5 (c) 6 (d) 7
  22. 22.What is the distance between the points (4, 11) and (12, 5)? (a) 10 (b) 11 (c) 14 (d) 100
  23. 23.What is the 16th term of the AP 11, 13, 15, 17, …? (a) 32 (b) 30 (c) 43 (d) 41
  24. 24.What is the mean of 10, 2, 19 and 9? (a) 9 (b) 10 (c) 8 (d) 11
  25. 25.In a class of 42 children, 27 like maths, 20 like science and 11 like both. How many like neither? (a) 11 (b) 7 (c) 6 (d) 17
  26. 26.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 66 (c) 144 (d) 24
  27. 27.A drawer has lots of blue, red, white, 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) 5 (c) 10 (d) 6
  28. 28.What is the distance between the points (1, 7) and (10, 19)? (a) 225 (b) 21 (c) 15 (d) 16
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 16 (b) 17 (c) 15 (d) 5
  30. 30.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 50° (c) 10° (d) 100°
  31. 31.What is the sum of all the whole numbers from 1 to 74? (a) 2775 (b) 2701 (c) 2738 (d) 5550
  32. 32.A drawer has lots of blue, red, white and green 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) 5 (d) 8
  33. 33.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 120° (b) 61° (c) 60° (d) 240°
  34. 34.A cuboid is 6 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 144 sq cm (b) 72 sq cm (c) 36 sq cm (d) 73 sq cm
  35. 35.What is the distance between the points (6, 6) and (30, 13)? (a) 625 (b) 26 (c) 25 (d) 31
  36. 36.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 21 (d) 22
  37. 37.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  38. 38.A bag has 6 yellow, 6 green and 4 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/8 (b) 3/8 (c) 11/16 (d) 1/3
  39. 39.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 224 (c) 229 (d) 219
  40. 40.What is the missing term in the AP 7, ?, 13, 16, 19? (a) 10 (b) 11 (c) 9 (d) 13

Answer key

  1. 70°
  2. 3
  3. 4 times
  4. 17
  5. 130°
  6. 25
  7. 6
  8. 35°
  9. 10
  10. 24
  11. 20
  12. 24
  13. 60°
  14. 125 cu cm
  15. 6
  16. 1/2
  17. 17
  18. 258
  19. 1/9
  20. 17
  21. 6
  22. 10
  23. 41
  24. 10
  25. 6
  26. 66
  27. 6
  28. 15
  29. 16
  30. 50°
  31. 2775
  32. 5
  33. 60°
  34. 72 sq cm
  35. 25
  36. 22
  37. 27
  38. 5/8
  39. 228
  40. 10

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