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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 440 · 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.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  2. 2.What is the mean of 12, 17, 4, 19 and 23? (a) 15 (b) 16 (c) 17 (d) 14
  3. 3.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 120° (c) 70° (d) 110°
  4. 4.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 7 (d) 5
  5. 5.What is the sum of the first 6 terms of the AP 3, 7, 11, …? (a) 90 (b) 23 (c) 156 (d) 78
  6. 6.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 8 (c) 18 (d) 30
  7. 7.In a class of 15 children, 11 like maths, 7 like science and 4 like both. How many like neither? (a) 4 (b) 5 (c) 1 (d) 2
  8. 8.What is the mean of 20, 19, 11 and 18? (a) 18 (b) 19 (c) 17 (d) 16
  9. 9.What is the distance between the points (0, 3) and (12, 8)? (a) 13 (b) 169 (c) 14 (d) 17
  10. 10.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 115° (c) 65° (d) 155°
  11. 11.In a class of 30 children, 10 like dance, 24 like music and 7 like both. How many like at least one of the two? (a) 27 (b) 20 (c) 34 (d) 30
  12. 12.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 20 (c) 45 (d) 100
  13. 13.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
  14. 14.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
  15. 15.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 501 (c) 406 (d) 502
  16. 16.How many factors does 114 have? (a) 9 (b) 8 (c) 6 (d) 7
  17. 17.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 100° (c) 40° (d) 80°
  18. 18.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 90 (b) 45 (c) 55 (d) 17
  19. 19.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) 132 (d) 66
  20. 20.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 110° (d) 145°
  21. 21.The mean of 9 numbers is 16. When the number 6 is added to them, what is the new mean? (a) 11 (b) 14 (c) 16 (d) 15
  22. 22.What is the median of 8, 12, 13, 21, 29, 5 and 26? (a) 21 (b) 12 (c) 13 (d) 14
  23. 23.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 2 and 36 (c) 1 and 72 (d) 1 and 16
  24. 24.What is the 19th term of the AP 7, 14, 21, 28, …? (a) 140 (b) 126 (c) 133 (d) 134
  25. 25.In a class of 46 children, 25 like maths, 18 like science and 7 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 17
  26. 26.What is the distance between the points (4, 9) and (7, 13)? (a) 25 (b) 5 (c) 6 (d) 7
  27. 27.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 40° (c) 50° (d) 130°
  28. 28.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) 13 (b) 25 (c) 24 (d) 12
  29. 29.In a class of 33 children, 16 like cricket, 15 like football and 4 like both. How many like at least one of the two? (a) 23 (b) 31 (c) 33 (d) 27
  30. 30.A bag has 3 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 4 (d) 8
  31. 31.A drawer has lots of blue, red, yellow, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
  32. 32.What is the product of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 31 (d) 29
  33. 33.Two angles of a triangle are 35° and 20°. What is the exterior angle at the third corner? (a) 125° (b) 145° (c) 160° (d) 55°
  34. 34.If a + b = 13 and ab = 36, what is a² + b²? (a) 97 (b) 133 (c) 169 (d) 241
  35. 35.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 32 (c) 24 (d) 10
  36. 36.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 125° (b) 95° (c) 85° (d) 150°
  37. 37.What is the sum of the first 12 terms of the AP 1, 6, 11, …? (a) 372 (b) 342 (c) 56 (d) 684
  38. 38.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 130° (d) 50°
  39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  40. 40.Two angles of a triangle are 45° and 35°. What is the third angle? (a) 145° (b) 100° (c) 80° (d) 135°

Answer key

  1. 10
  2. 15
  3. 70°
  4. 6
  5. 78
  6. 15
  7. 1
  8. 17
  9. 13
  10. 115°
  11. 27
  12. 45
  13. 4 times
  14. 7/8
  15. 501
  16. 8
  17. 40°
  18. 45
  19. 132
  20. 110°
  21. 15
  22. 13
  23. 8 and 9
  24. 133
  25. 10
  26. 5
  27. 80°
  28. 13
  29. 27
  30. 6
  31. 6
  32. 30
  33. 55°
  34. 97
  35. 16
  36. 95°
  37. 342
  38. 130°
  39. 17
  40. 100°

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