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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 106 · 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.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  2. 2.What is the mean of 14, 13, 10 and 7? (a) 12 (b) 13 (c) 10 (d) 11
  3. 3.In which quadrant does the point (−6, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.What is the median of 35, 9, 34, 11 and 4? (a) 34 (b) 9 (c) 11 (d) 12
  5. 5.In a class of 47 children, 20 like tea, 25 like coffee and 10 like neither. How many like both? (a) 37 (b) 9 (c) 10 (d) 8
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  7. 7.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  8. 8.In a class of 35 children, 26 like cricket, 14 like football and 8 like both. How many like only cricket? (a) 18 (b) 26 (c) 21 (d) 6
  9. 9.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 66 (c) 55 (d) 110
  10. 10.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 160° (c) 11° (d) 10°
  11. 11.A bag has 4 yellow, 7 red and 5 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/16 (b) 3/4 (c) 1/4 (d) 1/3
  12. 12.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 36 (c) 72 (d) 81
  13. 13.A cuboid is 3 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 6 cu cm (b) 15 cu cm (c) 112 cu cm (d) 60 cu cm
  14. 14.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
  15. 15.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
  16. 16.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  17. 17.What is the smallest prime factor of 35? (a) 7 (b) 5 (c) 1 (d) 2
  18. 18.What is the distance between the points (3, 1) and (19, 13)? (a) 400 (b) 20 (c) 28 (d) 21
  19. 19.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
  20. 20.What is the median of 5, 31, 19, 27, 38, 40 and 9? (a) 19 (b) 28 (c) 31 (d) 27
  21. 21.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 1/12 (c) 1/11 (d) 2/11
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 3 (b) 6 (c) 5 (d) 4
  23. 23.A bag has 8 blue balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 10 (c) 2 (d) 19
  24. 24.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 9 (c) 6 (d) 12
  25. 25.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 10° (d) 95°
  26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
  27. 27.What is the mean of 7, 11, 5, 2 and 15? (a) 9 (b) 7 (c) 10 (d) 8
  28. 28.How many factors does 108 have? (a) 13 (b) 12 (c) 11 (d) 10
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 14 (c) 4 (d) 12
  30. 30.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  31. 31.A cube has edges of 3 cm. What is its total surface area? (a) 9 sq cm (b) 54 sq cm (c) 36 sq cm (d) 27 sq cm
  32. 32.In a class of 45 children, 26 like tea, 27 like coffee and 12 like both. How many like only tea? (a) 15 (b) 14 (c) 18 (d) 26
  33. 33.The mean of 5 numbers is 35. When the number 29 is added to them, what is the new mean? (a) 33 (b) 32 (c) 34 (d) 35
  34. 34.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  35. 35.In a class of 35 children, 13 like tea, 17 like coffee and 3 like both. How many like at least one of the two? (a) 30 (b) 24 (c) 27 (d) 35
  36. 36.A drawer has lots of yellow 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) 5 (b) 3 (c) 4 (d) 2
  37. 37.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
  38. 38.What is the mode of 10, 13, 13, 7, 10, 19 and 10? (a) 7 (b) 13 (c) 19 (d) 10
  39. 39.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 3 (d) 2
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17

Answer key

  1. 3
  2. 11
  3. Third quadrant
  4. 11
  5. 8
  6. 10
  7. Third quadrant
  8. 18
  9. 55
  10. 10°
  11. 1/4
  12. 36
  13. 60 cu cm
  14. 3/4
  15. 157
  16. 6
  17. 5
  18. 20
  19. 44 cm
  20. 27
  21. 1/18
  22. 5
  23. 10
  24. 9
  25. 10°
  26. 1386 sq cm
  27. 8
  28. 12
  29. 13
  30. 10
  31. 54 sq cm
  32. 14
  33. 34
  34. 2⁴ × 3
  35. 27
  36. 3
  37. 16 times
  38. 10
  39. 2
  40. 13

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