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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 418 · 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.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 150° (d) 110°
  2. 2.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 21 (c) 10 (d) 20
  3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 65° (c) 25° (d) 115°
  4. 4.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  5. 5.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
  6. 6.How many factors does 94 have? (a) 2 (b) 3 (c) 4 (d) 5
  7. 7.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 7 (d) 3
  8. 8.What is the median of 38, 7, 23, 34 and 33? (a) 34 (b) 33 (c) 27 (d) 23
  9. 9.A bag has 10 white balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 16 (d) 11
  10. 10.How many factors does 70 have? (a) 6 (b) 8 (c) 7 (d) 9
  11. 11.A cube has edges of 10 cm. What is its total surface area? (a) 100 sq cm (b) 600 sq cm (c) 400 sq cm (d) 1000 sq cm
  12. 12.How many factors does 46 have? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 1 (d) 2
  14. 14.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 15 (d) 21
  15. 15.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2² × 3
  16. 16.What is the sum of all the whole numbers from 1 to 49? (a) 1176 (b) 2450 (c) 1225 (d) 1226
  17. 17.What is the mean of 6, 3, 3 and 12? (a) 6 (b) 5 (c) 8 (d) 7
  18. 18.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) 15 (c) 8 (d) 14
  19. 19.What is the distance between the points (8, 9) and (20, 25)? (a) 400 (b) 21 (c) 20 (d) 28
  20. 20.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 48 (c) 36 (d) 37
  21. 21.The mean of 8 numbers is 14. When the number 23 is added to them, what is the new mean? (a) 16 (b) 17 (c) 15 (d) 14
  22. 22.What is the 38th term of the AP 6, 12, 18, 24, …? (a) 228 (b) 229 (c) 222 (d) 234
  23. 23.The mean of 3 numbers is 17. When the number 5 is added to them, what is the new mean? (a) 17 (b) 14 (c) 15 (d) 11
  24. 24.The mean of 9 numbers is 40. When the number 80 is added to them, what is the new mean? (a) 60 (b) 44 (c) 40 (d) 45
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 18 (d) 8
  26. 26.A bag has 9 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 10 (c) 18 (d) 11
  27. 27.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 196 (c) 105 (d) 182
  28. 28.A bag has 3 white, 4 red and 6 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 6/13 (c) 6/7 (d) 7/13
  29. 29.A cuboid is 6 cm long, 2 cm wide and 10 cm high. What is its total surface area? (a) 184 sq cm (b) 120 sq cm (c) 92 sq cm (d) 368 sq cm
  30. 30.What is the 12th term of the AP 6, 12, 18, 24, …? (a) 73 (b) 66 (c) 72 (d) 78
  31. 31.There are 8 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) 10 (b) 24 (c) 32 (d) 16
  32. 32.What is the mode of 19, 1, 4, 4, 19, 18 and 4? (a) 18 (b) 4 (c) 19 (d) 1
  33. 33.What is the mode of 6, 15, 6, 15, 2, 6 and 11? (a) 6 (b) 11 (c) 2 (d) 15
  34. 34.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 120° (b) 80° (c) 140° (d) 100°
  35. 35.What is the sum of the first 9 terms of the AP 6, 7, 8, …? (a) 14 (b) 180 (c) 91 (d) 90
  36. 36.What is the mean of 18, 17, 14, 16, 3 and 10? (a) 12 (b) 14 (c) 15 (d) 13
  37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  39. 39.The mean of 3 numbers is 17. When the number 1 is added to them, what is the new mean? (a) 9 (b) 13 (c) 17 (d) 14
  40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm

Answer key

  1. 150°
  2. 20
  3. 50°
  4. 21
  5. 3/4
  6. 4
  7. 3
  8. 33
  9. 11
  10. 8
  11. 600 sq cm
  12. 4
  13. 3
  14. 15
  15. 2³ × 3
  16. 1225
  17. 6
  18. 8
  19. 20
  20. 37
  21. 15
  22. 228
  23. 14
  24. 44
  25. 19
  26. 11
  27. 91
  28. 6/13
  29. 184 sq cm
  30. 72
  31. 16
  32. 4
  33. 6
  34. 80°
  35. 90
  36. 13
  37. 6
  38. 5
  39. 13
  40. 88 cm

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