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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 263 · 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.A bag has 7 green balls and 10 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) 2 (c) 8 (d) 17
  2. 2.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
  3. 3.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 6 (d) 18
  4. 4.A bag has 5 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 8 (c) 6 (d) 7
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/18 (c) 1/11 (d) 1/36
  6. 6.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 504 (b) 32 (c) 264 (d) 252
  7. 7.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100
  8. 8.What is the mean of 5, 11, 5 and 11? (a) 10 (b) 9 (c) 7 (d) 8
  9. 9.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  10. 10.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7 (c) 2 × 3² × 7² (d) 2³ × 3² × 7
  11. 11.The mean of 5 numbers is 26. When the number 32 is added to them, what is the new mean? (a) 28 (b) 27 (c) 26 (d) 29
  12. 12.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 125° (b) 135° (c) 55° (d) 100°
  13. 13.A bag has 4 green balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 5 (b) 11 (c) 6 (d) 2
  14. 14.In a class of 43 children, 19 like tea, 28 like coffee and 9 like both. How many like at least one of the two? (a) 47 (b) 29 (c) 43 (d) 38
  15. 15.A cuboid is 3 cm long, 2 cm wide and 3 cm high. What is its total surface area? (a) 18 sq cm (b) 42 sq cm (c) 84 sq cm (d) 21 sq cm
  16. 16.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 6 (d) 8
  17. 17.What is the mode of 13, 13, 13, 15, 17, 10 and 15? (a) 17 (b) 10 (c) 15 (d) 13
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 12 (c) 14 (d) 3
  19. 19.What is the median of 6, 22, 23, 34, 38, 39 and 15? (a) 22 (b) 23 (c) 34 (d) 24
  20. 20.In a class of 28 children, 10 like dance, 13 like music and 8 like neither. How many like both? (a) 8 (b) 20 (c) 4 (d) 3
  21. 21.In a class of 28 children, 17 like maths, 19 like science and 9 like both. How many like neither? (a) 1 (b) 9 (c) 2 (d) 10
  22. 22.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) 13 (b) 25 (c) 24 (d) 12
  23. 23.A bag has 6 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 7 (b) 16 (c) 2 (d) 8
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 7 (c) 16 (d) 17
  25. 25.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
  26. 26.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 57 (c) 171 (d) 60
  27. 27.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 46° (c) 45° (d) 90°
  28. 28.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 264 (b) 27 (c) 132 (d) 144
  29. 29.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  30. 30.A bag has 7 yellow, 7 blue and 4 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 7/9 (c) 2/7 (d) 2/9
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 76° (c) 105° (d) 75°
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
  33. 33.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 273 (c) 254 (d) 264
  34. 34.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 21 (c) 42 (d) 24
  35. 35.What is the distance between the points (3, 13) and (11, 7)? (a) 100 (b) 10 (c) 11 (d) 14
  36. 36.What is the mean of 18, 12, 6, 4 and 15? (a) 10 (b) 12 (c) 13 (d) 11
  37. 37.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 200° (d) 20°
  38. 38.What is the median of 16, 28, 12, 29 and 37? (a) 12 (b) 29 (c) 28 (d) 16
  39. 39.What is the mean of 11, 20, 18, 15 and 16? (a) 16 (b) 20 (c) 15 (d) 17
  40. 40.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 5 (c) 7 (d) 6

Answer key

  1. 11
  2. 5
  3. 18
  4. 7
  5. 1/36
  6. 252
  7. 45
  8. 8
  9. 24
  10. 2 × 3² × 7
  11. 27
  12. 55°
  13. 6
  14. 38
  15. 42 sq cm
  16. 6
  17. 13
  18. 13
  19. 23
  20. 3
  21. 1
  22. 13
  23. 8
  24. 17
  25. 64 cu cm
  26. 57
  27. 45°
  28. 132
  29. 1/2
  30. 2/9
  31. 75°
  32. 5
  33. 273
  34. 21
  35. 10
  36. 11
  37. 20°
  38. 28
  39. 16
  40. 5

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