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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 312 · 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 two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
  2. 2.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 4 (d) 2
  3. 3.If a + b = 9 and ab = 20, what is (a − b)²? (a) 41 (b) 81 (c) 1 (d) 61
  4. 4.What is the mean of 16, 8, 5 and 3? (a) 10 (b) 7 (c) 9 (d) 8
  5. 5.What is the mode of 6, 7, 12, 3, 6, 7 and 7? (a) 12 (b) 6 (c) 3 (d) 7
  6. 6.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  7. 7.A bag has 4 yellow balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 5 (c) 2 (d) 10
  8. 8.A bag has 7 red, 6 white and 8 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 1/2 (c) 8/21 (d) 2/3
  9. 9.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 66 (d) 132
  10. 10.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 150° (b) 105° (c) 135° (d) 75°
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
  12. 12.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
  13. 13.What is the smallest prime factor of 253? (a) 23 (b) 11 (c) 1 (d) 2
  14. 14.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 169 (c) 160 (d) 178
  15. 15.What is the 26th term of the AP 2, 4, 6, 8, …? (a) 54 (b) 52 (c) 50 (d) 53
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  18. 18.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 150° (b) 145° (c) 115° (d) 65°
  19. 19.A bag has 10 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 17 (c) 12 (d) 2
  20. 20.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 71° (b) 110° (c) 70° (d) 250°
  21. 21.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 43 (c) 34 (d) 44
  22. 22.What is the distance between the points (1, 15) and (10, 3)? (a) 16 (b) 21 (c) 225 (d) 15
  23. 23.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
  24. 24.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
  27. 27.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 100 (c) 55 (d) 90
  28. 28.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 56 (c) 64 (d) 36
  29. 29.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 23 (d) 2
  30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
  31. 31.In a class of 40 children, 28 like tea, 14 like coffee and 11 like both. How many like only tea? (a) 26 (b) 3 (c) 17 (d) 28
  32. 32.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 132 (c) 122 (d) 140
  33. 33.Using (a − b)² = a² − 2ab + b², what is 38²? (a) 1596 (b) 1444 (c) 1764 (d) 1454
  34. 34.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
  35. 35.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
  36. 36.Which term of the AP 5, 9, 13, 17, … is 97? (a) 24th (b) 26th (c) 25th (d) 23rd
  37. 37.In a class of 30 children, 19 like cricket, 18 like football and 5 like neither. How many like both? (a) 7 (b) 12 (c) 5 (d) 25
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 17 (b) 16 (c) 9 (d) 14
  39. 39.In a class of 34 children, 28 like cricket, 15 like football and 11 like both. How many like at least one of the two? (a) 32 (b) 43 (c) 21 (d) 34
  40. 40.A bag has 7 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 11 (c) 8 (d) 9

Answer key

  1. 3
  2. 2
  3. 1
  4. 8
  5. 7
  6. 2⁴ × 5
  7. 7
  8. 1/3
  9. 66
  10. 105°
  11. 1/12
  12. 24
  13. 11
  14. 169
  15. 52
  16. 10
  17. 3
  18. 115°
  19. 12
  20. 70°
  21. 43
  22. 15
  23. 1/4
  24. First quadrant
  25. 7
  26. 1/3
  27. 45
  28. 28
  29. 5
  30. 1/18
  31. 17
  32. 131
  33. 1444
  34. 25 times
  35. 120°
  36. 24th
  37. 12
  38. 16
  39. 32
  40. 9

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