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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 182 · 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 fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  2. 2.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 80° (c) 155° (d) 100°
  3. 3.What is the midpoint of the line joining (2, 10) and (6, 0)? (a) (5, 4) (b) (2, 5) (c) (4, 5) (d) (8, 10)
  4. 4.What is the 16th term of the AP 13, 20, 27, 34, …? (a) 112 (b) 105 (c) 125 (d) 118
  5. 5.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 81 (b) 18 (c) 72 (d) 36
  6. 6.What is the median of 19, 15, 32, 9, 33, 16 and 28? (a) 28 (b) 16 (c) 19 (d) 9
  7. 7.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 12 (c) 70 (d) 35
  8. 8.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 64 (c) 112 (d) 15
  9. 9.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 280 (b) 161 (c) 38 (d) 140
  10. 10.A bag has 11 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 6 (c) 2 (d) 12
  11. 11.What is the 10th term of the AP 10, 12, 14, 16, …? (a) 30 (b) 28 (c) 18 (d) 20
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 130° (b) 260° (c) 50° (d) 80°
  13. 13.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 124 (c) 114 (d) 132
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  15. 15.What is the median of 38, 7, 40, 15, 20, 36 and 39? (a) 15 (b) 38 (c) 20 (d) 36
  16. 16.What is the mode of 5, 3, 6, 6, 3, 6 and 19? (a) 3 (b) 19 (c) 6 (d) 5
  17. 17.What is the sum of the roots of x² − 12x + 27 = 0? (a) 11 (b) 27 (c) 12 (d) 13
  18. 18.In a class of 29 children, 23 like tea, 13 like coffee and 8 like both. How many like neither? (a) 8 (b) 2 (c) 9 (d) 1
  19. 19.What is the median of 27, 7, 11, 23 and 36? (a) 23 (b) 11 (c) 27 (d) 24
  20. 20.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  21. 21.In a class of 39 children, 16 like cricket, 18 like football and 8 like neither. How many like both? (a) 3 (b) 31 (c) 8 (d) 4
  22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
  23. 23.What is the sum of all the whole numbers from 1 to 69? (a) 2346 (b) 2415 (c) 4830 (d) 2416
  24. 24.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 2 (d) 4
  25. 25.What is the midpoint of the line joining (1, 6) and (13, 0)? (a) (7, 3) (b) (14, 6) (c) (6, 3) (d) (3, 7)
  26. 26.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 28 (c) 21 (d) 42
  27. 27.What is the distance between the points (8, 0) and (16, 15)? (a) 23 (b) 289 (c) 17 (d) 18
  28. 28.How many factors does 56 have? (a) 8 (b) 7 (c) 9 (d) 6
  29. 29.Two angles of a triangle are 45° and 60°. What is the third angle? (a) 120° (b) 135° (c) 105° (d) 75°
  30. 30.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 42 (d) 45
  31. 31.What is the missing term in the AP 13, 17, 21, ?, 29? (a) 25 (b) 29 (c) 26 (d) 24
  32. 32.How many prime numbers are there between 60 and 90? (a) 8 (b) 6 (c) 7 (d) 9
  33. 33.How many factors does 64 have? (a) 8 (b) 6 (c) 7 (d) 5
  34. 34.What is the mode of 15, 15, 14, 13, 14, 8 and 15? (a) 13 (b) 14 (c) 8 (d) 15
  35. 35.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 160° (d) 80°
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 18 (b) 7 (c) 17 (d) 19
  37. 37.What is the mode of 3, 1, 10, 10, 10, 20 and 3? (a) 20 (b) 1 (c) 10 (d) 3
  38. 38.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
  39. 39.Two angles of a triangle are 75° and 55°. What is the third angle? (a) 130° (b) 50° (c) 105° (d) 125°
  40. 40.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 18 (d) 81

Answer key

  1. 1/2
  2. 100°
  3. (4, 5)
  4. 118
  5. 72
  6. 19
  7. 35
  8. 56
  9. 140
  10. 12
  11. 28
  12. 130°
  13. 123
  14. 20
  15. 36
  16. 6
  17. 12
  18. 1
  19. 23
  20. 91
  21. 3
  22. 88 cm
  23. 2415
  24. 3
  25. (7, 3)
  26. 21
  27. 17
  28. 8
  29. 75°
  30. 42
  31. 25
  32. 7
  33. 7
  34. 15
  35. 80°
  36. 18
  37. 10
  38. 8 and 9
  39. 50°
  40. 36

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