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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 815 · 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.What is the median of 24, 2, 16, 32 and 11? (a) 24 (b) 11 (c) 16 (d) 17
  2. 2.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 17 (c) 72 (d) 18
  3. 3.In a class of 42 children, 26 like cricket, 20 like football and 7 like both. How many like neither? (a) 4 (b) 10 (c) 3 (d) 7
  4. 4.The mean of 5 numbers is 31. When the number 49 is added to them, what is the new mean? (a) 31 (b) 40 (c) 35 (d) 34
  5. 5.How many prime numbers are there between 80 and 110? (a) 6 (b) 7 (c) 8 (d) 9
  6. 6.A bag has 5 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 2 (c) 6 (d) 7
  7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
  8. 8.What is the mean of 7, 15, 12 and 6? (a) 8 (b) 10 (c) 11 (d) 9
  9. 9.In a class of 33 children, 17 like maths, 17 like science and 3 like both. How many like only maths? (a) 16 (b) 14 (c) 17 (d) 3
  10. 10.What is the missing term in the AP 8, 11, 14, ?, 20? (a) 17 (b) 20 (c) 16 (d) 18
  11. 11.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
  12. 12.What is the mode of 17, 17, 15, 15, 10, 5 and 17? (a) 17 (b) 5 (c) 15 (d) 10
  13. 13.What is the missing term in the AP 9, 11, ?, 15, 17? (a) 12 (b) 14 (c) 13 (d) 15
  14. 14.In a class of 36 children, 14 like tea, 21 like coffee and 2 like both. How many like neither? (a) 2 (b) 5 (c) 1 (d) 3
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/6 (c) 6/11 (d) 1/11
  16. 16.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
  17. 17.A bag has 3 green balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 4 (c) 2 (d) 10
  18. 18.What is the 18th term of the AP 16, 25, 34, 43, …? (a) 169 (b) 162 (c) 153 (d) 178
  19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
  20. 20.In a class of 43 children, 24 like tea, 28 like coffee and 12 like both. How many like neither? (a) 4 (b) 3 (c) 15 (d) 12
  21. 21.A cuboid is 7 cm long, 6 cm wide and 2 cm high. What is its total surface area? (a) 68 sq cm (b) 272 sq cm (c) 136 sq cm (d) 84 sq cm
  22. 22.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
  23. 23.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
  24. 24.What is the midpoint of the line joining (6, 11) and (18, 5)? (a) (12, 8) (b) (6, 3) (c) (24, 16) (d) (8, 12)
  25. 25.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) 8 (c) 15 (d) 14
  26. 26.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 5 (b) 12 (c) 6 (d) 9
  27. 27.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 144 (d) 66
  28. 28.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 13 (d) 42
  29. 29.In a class of 20 children, 13 like mangoes, 8 like bananas and 2 like both. How many like only mangoes? (a) 11 (b) 13 (c) 12 (d) 6
  30. 30.What is the sum of the first 7 terms of the AP 2, 3, 4, …? (a) 35 (b) 70 (c) 36 (d) 8
  31. 31.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 28 (c) 21 (d) 42
  32. 32.In a class of 29 children, 24 like cricket, 9 like football and 6 like both. How many like neither? (a) 8 (b) 2 (c) 3 (d) 6
  33. 33.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
  34. 34.A drawer has lots of blue, green and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 6 (c) 2 (d) 4
  35. 35.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  36. 36.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
  37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 5/6 (d) 1/4
  38. 38.How many factors does 83 have? (a) 3 (b) 1 (c) 2 (d) 4
  39. 39.What is the 12th term of the AP 7, 12, 17, 22, …? (a) 62 (b) 55 (c) 60 (d) 67
  40. 40.What is the 15th term of the AP 17, 19, 21, 23, …? (a) 47 (b) 28 (c) 45 (d) 30

Answer key

  1. 16
  2. 17
  3. 3
  4. 34
  5. 7
  6. 7
  7. 1/12
  8. 10
  9. 14
  10. 17
  11. 1/2
  12. 17
  13. 13
  14. 3
  15. 1/6
  16. 15
  17. 10
  18. 169
  19. 5/36
  20. 3
  21. 136 sq cm
  22. 88 cm
  23. 85°
  24. (12, 8)
  25. 8
  26. 6
  27. 132
  28. 39
  29. 11
  30. 35
  31. 21
  32. 2
  33. 1/3
  34. 4
  35. First quadrant
  36. 2/3
  37. 2/3
  38. 2
  39. 62
  40. 45

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