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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 881 · 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.What are the roots of x² − 13x + 36 = 0? (a) 4 and 9 (b) 1 and 12 (c) 1 and 36 (d) 2 and 18
  2. 2.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 726 cu cm (c) 484 cu cm (d) 33 cu cm
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  4. 4.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) 2 (b) 7 (c) 8 (d) 6
  5. 5.If a + b = 18 and ab = 80, what is a² + b²? (a) 484 (b) 244 (c) 324 (d) 164
  6. 6.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 121 (d) 110
  7. 7.In which quadrant does the point (−9, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  9. 9.What are the roots of x² − 15x + 54 = 0? (a) 6 and 9 (b) 2 and 27 (c) 1 and 14 (d) 1 and 54
  10. 10.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
  11. 11.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 91 (c) 78 (d) 169
  12. 12.In which quadrant does the point (3, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.A drawer has lots of red, yellow, blue, 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) 2 (b) 5 (c) 6 (d) 10
  14. 14.What is the 32nd term of the AP 1, 7, 13, 19, …? (a) 186 (b) 193 (c) 192 (d) 187
  15. 15.A drawer has lots of green, black and red 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
  16. 16.What is the mode of 4, 12, 5, 5, 10, 4 and 4? (a) 4 (b) 5 (c) 12 (d) 10
  17. 17.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) 14 (b) 7 (c) 15 (d) 8
  18. 18.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 16 (d) 28
  19. 19.What is the mode of 19, 7, 19, 19, 15, 7 and 14? (a) 15 (b) 19 (c) 14 (d) 7
  20. 20.How many factors does 28 have? (a) 5 (b) 7 (c) 4 (d) 6
  21. 21.In a class of 38 children, 30 like dance, 18 like music and 12 like both. How many like only dance? (a) 20 (b) 18 (c) 30 (d) 6
  22. 22.What is the distance between the points (6, 8) and (12, 16)? (a) 100 (b) 10 (c) 11 (d) 14
  23. 23.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°
  24. 24.What is the mean of 10, 14, 6 and 14? (a) 13 (b) 11 (c) 12 (d) 10
  25. 25.What is the sum of the roots of x² − 11x + 24 = 0? (a) 11 (b) 10 (c) 24 (d) 12
  26. 26.In a class of 27 children, 19 like cricket, 14 like football and 9 like both. How many like only cricket? (a) 5 (b) 19 (c) 10 (d) 13
  27. 27.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
  28. 28.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
  29. 29.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/8 (c) 3/8 (d) 1/4
  30. 30.A drawer has lots of blue and red 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) 3 (c) 2 (d) 4
  31. 31.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 55 (c) 66 (d) 67
  32. 32.The mean of 8 numbers is 27. When the number 63 is added to them, what is the new mean? (a) 31 (b) 32 (c) 45 (d) 27
  33. 33.How many factors does 83 have? (a) 4 (b) 3 (c) 1 (d) 2
  34. 34.A bag has 8 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 14 (c) 10 (d) 2
  35. 35.In a class of 40 children, 23 like dance, 14 like music and 10 like neither. How many like both? (a) 7 (b) 8 (c) 10 (d) 30
  36. 36.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 438 (c) 370 (d) 447
  37. 37.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
  38. 38.What is the product of the roots of x² − 12x + 32 = 0? (a) 31 (b) 12 (c) 32 (d) 33
  39. 39.In a class of 34 children, 20 like mangoes, 15 like bananas and 5 like both. How many like at least one of the two? (a) 35 (b) 30 (c) 34 (d) 25
  40. 40.What are the roots of x² − 10x + 24 = 0? (a) 1 and 9 (b) 2 and 12 (c) 1 and 24 (d) 4 and 6

Answer key

  1. 4 and 9
  2. 1331 cu cm
  3. 6
  4. 7
  5. 164
  6. 55
  7. Second quadrant
  8. 17
  9. 6 and 9
  10. 4
  11. 78
  12. Fourth quadrant
  13. 6
  14. 187
  15. 4
  16. 4
  17. 8
  18. 28
  19. 19
  20. 6
  21. 18
  22. 10
  23. 125°
  24. 11
  25. 11
  26. 10
  27. 1/2
  28. 3/4
  29. 7/8
  30. 3
  31. 66
  32. 31
  33. 2
  34. 10
  35. 7
  36. 447
  37. 1/2
  38. 32
  39. 30
  40. 4 and 6

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