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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 917 · 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. 1.8 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 96 (b) 56 (c) 48 (d) 14
  2. 2.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 5 (d) 6
  3. 3.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 115° (d) 50°
  4. 4.What is the distance between the points (0, 31) and (7, 7)? (a) 625 (b) 26 (c) 31 (d) 25
  5. 5.Two angles of a triangle are 75° and 65°. What is the third angle? (a) 115° (b) 40° (c) 105° (d) 140°
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/12 (c) 1/9 (d) 3/11
  7. 7.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  8. 8.A bag has 12 yellow balls and 11 green 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) 12 (c) 13 (d) 23
  9. 9.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) 15 (b) 8 (c) 7 (d) 14
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  11. 11.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x − 6)(x − 8) (c) (x + 6)(x + 8) (d) (x + 1)(x + 13)
  12. 12.What is the smallest prime factor of 49? (a) 2 (b) 1 (c) 3 (d) 7
  13. 13.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 5 (d) 4
  14. 14.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 300° (d) 120°
  15. 15.What is the mean of 4, 14, 5 and 21? (a) 10 (b) 11 (c) 13 (d) 12
  16. 16.The mean of 9 numbers is 36. When the number 66 is added to them, what is the new mean? (a) 51 (b) 39 (c) 40 (d) 36
  17. 17.In a class of 27 children, 9 like dance, 19 like music and 4 like both. How many like neither? (a) 4 (b) 2 (c) 3 (d) 7
  18. 18.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 13 (b) 21 (c) 15 (d) 14
  19. 19.In a class of 49 children, 31 like dance, 29 like music and 12 like both. How many like at least one of the two? (a) 49 (b) 48 (c) 36 (d) 60
  20. 20.What is the 14th term of the AP 3, 8, 13, 18, …? (a) 65 (b) 73 (c) 68 (d) 70
  21. 21.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 20 (d) 100
  22. 22.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
  23. 23.In a class of 40 children, 20 like cricket, 19 like football and 8 like both. How many like only cricket? (a) 20 (b) 11 (c) 21 (d) 12
  24. 24.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 100 (c) 20 (d) 90
  25. 25.In a class of 20 children, 15 like maths, 15 like science and 11 like both. How many like only maths? (a) 4 (b) 11 (c) 15 (d) 5
  26. 26.What is the distance between the points (5, 31) and (12, 7)? (a) 26 (b) 25 (c) 31 (d) 625
  27. 27.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
  28. 28.What is the midpoint of the line joining (3, 17) and (5, 9)? (a) (4, 13) (b) (8, 26) (c) (13, 4) (d) (1, 4)
  29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
  30. 30.A bag has 7 blue balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 11 (c) 2 (d) 8
  31. 31.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 9 (d) 19
  33. 33.What is the median of 39, 13, 40, 32 and 23? (a) 23 (b) 40 (c) 39 (d) 32
  34. 34.What is the median of 8, 18, 24, 6 and 14? (a) 18 (b) 14 (c) 8 (d) 24
  35. 35.What is the 14th term of the AP 14, 16, 18, 20, …? (a) 26 (b) 42 (c) 40 (d) 28
  36. 36.In a class of 47 children, 19 like cricket, 23 like football and 3 like both. How many like at least one of the two? (a) 39 (b) 47 (c) 42 (d) 36
  37. 37.What is the mean of 6, 16, 14, 10, 3 and 5? (a) 8 (b) 10 (c) 11 (d) 9
  38. 38.In a class of 27 children, 11 like dance, 13 like music and 5 like both. How many like neither? (a) 5 (b) 3 (c) 8 (d) 13
  39. 39.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 32 (b) 504 (c) 264 (d) 252
  40. 40.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm

Answer key

  1. 48
  2. 5
  3. 50°
  4. 25
  5. 40°
  6. 1/12
  7. Fourth quadrant
  8. 13
  9. 8
  10. 17
  11. (x + 6)(x + 8)
  12. 7
  13. 4
  14. 120°
  15. 11
  16. 39
  17. 3
  18. 14
  19. 48
  20. 68
  21. 90
  22. 3/4
  23. 12
  24. 45
  25. 4
  26. 25
  27. 70°
  28. (4, 13)
  29. 1/18
  30. 8
  31. 66
  32. 19
  33. 32
  34. 14
  35. 40
  36. 39
  37. 9
  38. 8
  39. 252
  40. 132 cm

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