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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 848 · 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 bag has 7 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 8 (c) 2 (d) 9
  2. 2.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2 × 3 × 7³ (c) 2⁴ × 3 × 7 (d) 2² × 3 × 7
  3. 3.How many factors does 65 have? (a) 3 (b) 5 (c) 4 (d) 2
  4. 4.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 45 (c) 36 (d) 46
  5. 5.Two angles of a triangle are 40° and 125°. What is the third angle? (a) 55° (b) 165° (c) 15° (d) 140°
  6. 6.What is the mean of 8, 3, 12 and 9? (a) 9 (b) 10 (c) 8 (d) 7
  7. 7.Two angles of a triangle are 35° and 75°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 105° (d) 145°
  8. 8.What is the sum of the first 10 terms of the AP 7, 11, 15, …? (a) 500 (b) 250 (c) 43 (d) 270
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
  10. 10.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
  11. 11.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 543 (c) 552 (d) 440
  12. 12.The mean of 8 numbers is 40. When the number 31 is added to them, what is the new mean? (a) 38 (b) 41 (c) 39 (d) 40
  13. 13.In a class of 46 children, 21 like cricket, 29 like football and 7 like neither. How many like both? (a) 4 (b) 7 (c) 11 (d) 39
  14. 14.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/4 (d) 1/3
  15. 15.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 6 times (c) 4 times (d) 2 times
  16. 16.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
  17. 17.In which quadrant does the point (−3, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the mode of 15, 20, 8, 8, 13, 15 and 15? (a) 13 (b) 20 (c) 8 (d) 15
  19. 19.How many factors does 39 have? (a) 4 (b) 3 (c) 5 (d) 2
  20. 20.A bag has 12 black balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 2 (c) 18 (d) 13
  21. 21.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 59 (d) 50
  22. 22.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 145° (d) 85°
  23. 23.In a class of 41 children, 27 like cricket, 20 like football and 11 like both. How many like neither? (a) 11 (b) 6 (c) 16 (d) 5
  24. 24.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5 × 7 (d) 5³ × 7
  25. 25.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 6 (c) 3 (d) 9
  26. 26.Which term of the AP 19, 28, 37, 46, … is 145? (a) 16th (b) 17th (c) 14th (d) 15th
  27. 27.What is the median of 2, 12, 35, 10 and 1? (a) 2 (b) 12 (c) 35 (d) 10
  28. 28.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 90 (d) 100
  29. 29.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 36 (c) 81 (d) 45
  30. 30.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 7/8 (c) 1/8 (d) 1/4
  31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  32. 32.In a class of 28 children, 16 like tea, 14 like coffee and 11 like both. How many like neither? (a) 10 (b) 11 (c) 9 (d) 20
  33. 33.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 820 (c) 1722 (d) 862
  34. 34.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  35. 35.A bag has 6 black balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 2 (c) 10 (d) 7
  36. 36.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 10° (c) 100° (d) 50°
  37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
  39. 39.In a class of 26 children, 14 like tea, 16 like coffee and 5 like neither. How many like both? (a) 5 (b) 4 (c) 9 (d) 21
  40. 40.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 130° (c) 10° (d) 170°

Answer key

  1. 9
  2. 2³ × 3 × 7
  3. 4
  4. 45
  5. 15°
  6. 8
  7. 110°
  8. 250
  9. 5
  10. 64 cu cm
  11. 552
  12. 39
  13. 11
  14. 2/3
  15. 8 times
  16. 72
  17. Second quadrant
  18. 15
  19. 4
  20. 14
  21. 59
  22. 85°
  23. 5
  24. 5 × 7
  25. 6
  26. 15th
  27. 10
  28. 90
  29. 36
  30. 1/8
  31. 1/2
  32. 9
  33. 861
  34. 3 × 5 × 7
  35. 8
  36. 50°
  37. 220 cm
  38. 85°
  39. 9
  40. 10°

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