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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 271 · 40 questions
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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 drawer has lots of white, red, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 8 (c) 5 (d) 2
  2. 2.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
  3. 3.Two angles of a triangle are 45° and 75°. What is the third angle? (a) 105° (b) 120° (c) 135° (d) 60°
  4. 4.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
  5. 5.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 135° (c) 45° (d) 90°
  6. 6.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
  7. 7.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 4 (c) 16 (d) 324
  8. 8.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 45 (d) 100
  9. 9.What is the distance between the points (5, 12) and (20, 4)? (a) 23 (b) 17 (c) 289 (d) 18
  10. 10.What is the 13th term of the AP 14, 18, 22, 26, …? (a) 62 (b) 52 (c) 66 (d) 48
  11. 11.A bag has 5 white balls and 3 red 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) 8 (c) 4 (d) 6
  12. 12.What is the product of the roots of x² − 12x + 35 = 0? (a) 12 (b) 34 (c) 35 (d) 36
  13. 13.The mean of 9 numbers is 39. When the number 69 is added to them, what is the new mean? (a) 39 (b) 42 (c) 43 (d) 54
  14. 14.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7
  15. 15.What is the sum of the first 5 terms of the AP 3, 6, 9, …? (a) 45 (b) 15 (c) 90 (d) 48
  16. 16.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 42 (c) 28 (d) 21
  17. 17.What is the mean of 2, 14, 3 and 17? (a) 9 (b) 12 (c) 8 (d) 10
  18. 18.The mean of 5 numbers is 19. When the number 37 is added to them, what is the new mean? (a) 23 (b) 19 (c) 22 (d) 28
  19. 19.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 125 sq cm (c) 100 sq cm (d) 150 sq cm
  20. 20.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 25 (c) 12 (d) 13
  22. 22.A bag has 10 green balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 12 (c) 2 (d) 21
  23. 23.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 8 times (c) 64 times (d) 16 times
  24. 24.A drawer has lots of red, black, yellow, green and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 6 (d) 5
  25. 25.What is the distance between the points (8, 13) and (14, 5)? (a) 100 (b) 11 (c) 10 (d) 14
  26. 26.What is the mean of 11, 11, 16, 7 and 5? (a) 11 (b) 9 (c) 12 (d) 10
  27. 27.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 100° (b) 130° (c) 80° (d) 150°
  28. 28.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 6 (d) 3
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  30. 30.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6724 (b) 6094 (c) 6396 (d) 6084
  31. 31.What is the prime factorisation of 12? (a) 2 × 3² (b) 2 × 3 (c) 2³ × 3 (d) 2² × 3
  32. 32.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
  33. 33.What is the mean of 13, 15, 9 and 19? (a) 15 (b) 13 (c) 14 (d) 16
  34. 34.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/4 (b) 2/3 (c) 1/3 (d) 5/6
  35. 35.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) 21 (b) 15 (c) 22 (d) 14
  36. 36.A bag has 12 green balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 13 (c) 20 (d) 2
  37. 37.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
  38. 38.In a class of 24 children, 16 like mangoes, 16 like bananas and 9 like both. How many like at least one of the two? (a) 23 (b) 32 (c) 24 (d) 14
  39. 39.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 42 (c) 12 (d) 36
  40. 40.If a + b = 17 and ab = 66, what is a² + b²? (a) 157 (b) 289 (c) 223 (d) 421

Answer key

  1. 5
  2. 27 times
  3. 60°
  4. 6
  5. 45°
  6. 64 times
  7. 16
  8. 45
  9. 17
  10. 62
  11. 6
  12. 35
  13. 42
  14. 2² × 3² × 7
  15. 45
  16. 21
  17. 9
  18. 22
  19. 150 sq cm
  20. Third quadrant
  21. 13
  22. 12
  23. 16 times
  24. 6
  25. 10
  26. 10
  27. 100°
  28. 4
  29. 19
  30. 6084
  31. 2² × 3
  32. 5
  33. 14
  34. 2/3
  35. 15
  36. 14
  37. 1/2
  38. 23
  39. 36
  40. 157

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