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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 726 · 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 many factors does 48 have? (a) 9 (b) 11 (c) 8 (d) 10
  2. 2.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 100 (d) 45
  3. 3.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 5 (d) 9
  4. 4.In a class of 42 children, 23 like maths, 20 like science and 4 like both. How many like neither? (a) 7 (b) 3 (c) 2 (d) 4
  5. 5.Which term of the AP 18, 20, 22, 24, … is 52? (a) 17th (b) 19th (c) 26th (d) 18th
  6. 6.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
  7. 7.What is the distance between the points (9, 7) and (13, 10)? (a) 25 (b) 5 (c) 7 (d) 6
  8. 8.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 19 (d) 8
  10. 10.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 36 (c) 37 (d) 24
  11. 11.What is the 17th term of the AP 11, 14, 17, 20, …? (a) 62 (b) 59 (c) 48 (d) 51
  12. 12.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 135 (b) 144 (c) 270 (d) 23
  13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 308 sq cm
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  15. 15.A bag has 9 green, 8 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 11/19 (b) 10/19 (c) 1/3 (d) 9/19
  16. 16.In a class of 40 children, 23 like tea, 27 like coffee and 12 like both. How many like only tea? (a) 23 (b) 13 (c) 15 (d) 11
  17. 17.What is the sum of the first 5 terms of the AP 10, 15, 20, …? (a) 105 (b) 30 (c) 100 (d) 200
  18. 18.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 144 (c) 132 (d) 78
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  20. 20.Which term of the AP 20, 25, 30, 35, … is 115? (a) 21st (b) 20th (c) 23rd (d) 19th
  21. 21.In which quadrant does the point (−9, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  22. 22.What is the mode of 20, 6, 20, 9, 6, 6 and 8? (a) 8 (b) 9 (c) 6 (d) 20
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 6 (d) 18
  24. 24.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  25. 25.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 15 (c) 24 (d) 7
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 18 (b) 8 (c) 20 (d) 19
  27. 27.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 29 (d) 22
  28. 28.How many factors does 98 have? (a) 7 (b) 6 (c) 4 (d) 5
  29. 29.In which quadrant does the point (4, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  30. 30.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 50° (b) 165° (c) 145° (d) 15°
  31. 31.The mean of 4 numbers is 16. When the number 31 is added to them, what is the new mean? (a) 19 (b) 18 (c) 16 (d) 20
  32. 32.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 100° (c) 230° (d) 50°
  33. 33.A cuboid is 7 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 83 sq cm (b) 166 sq cm (c) 140 sq cm (d) 332 sq cm
  34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
  35. 35.What is the median of 27, 31, 25, 21 and 5? (a) 26 (b) 25 (c) 21 (d) 27
  36. 36.Using (a + b)² = a² + 2ab + b², what is 31²? (a) 901 (b) 971 (c) 841 (d) 961
  37. 37.In which quadrant does the point (6, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  38. 38.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 290° (d) 20°
  39. 39.What is the 14th term of the AP 9, 12, 15, 18, …? (a) 48 (b) 39 (c) 42 (d) 51
  40. 40.In a class of 32 children, 19 like tea, 14 like coffee and 7 like neither. How many like both? (a) 25 (b) 7 (c) 1 (d) 8

Answer key

  1. 10
  2. 45
  3. 6
  4. 3
  5. 18th
  6. 105
  7. 5
  8. Second quadrant
  9. 19
  10. 25
  11. 59
  12. 135
  13. 616 sq cm
  14. 20
  15. 10/19
  16. 11
  17. 100
  18. 66
  19. 15
  20. 20th
  21. Third quadrant
  22. 6
  23. 17
  24. 7
  25. 12
  26. 19
  27. 22
  28. 6
  29. Fourth quadrant
  30. 15°
  31. 19
  32. 50°
  33. 166 sq cm
  34. 1/36
  35. 25
  36. 961
  37. First quadrant
  38. 110°
  39. 48
  40. 8

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