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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 649 · 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.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 27 times (d) 6 times
  2. 2.In a class of 30 children, 13 like maths, 10 like science and 3 like both. How many like neither? (a) 10 (b) 13 (c) 7 (d) 3
  3. 3.What is the mode of 14, 20, 19, 20, 7, 20 and 14? (a) 20 (b) 7 (c) 14 (d) 19
  4. 4.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 86 (c) 94 (d) 76
  5. 5.How many factors does 88 have? (a) 6 (b) 7 (c) 9 (d) 8
  6. 6.In a class of 32 children, 9 like maths, 24 like science and 5 like both. How many like at least one of the two? (a) 28 (b) 23 (c) 32 (d) 33
  7. 7.A cuboid is 7 cm long, 6 cm wide and 4 cm high. What is its volume? (a) 188 cu cm (b) 42 cu cm (c) 17 cu cm (d) 168 cu cm
  8. 8.What is the median of 27, 14, 26, 21, 24, 9 and 37? (a) 21 (b) 24 (c) 26 (d) 25
  9. 9.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
  10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/36 (c) 1/11 (d) 1/18
  11. 11.In a class of 29 children, 22 like mangoes, 18 like bananas and 1 like neither. How many like both? (a) 1 (b) 11 (c) 12 (d) 28
  12. 12.A cube has edges of 12 cm. What is its volume? (a) 864 cu cm (b) 1728 cu cm (c) 576 cu cm (d) 36 cu cm
  13. 13.A cuboid is 7 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 21 cu cm (b) 336 cu cm (c) 292 cu cm (d) 42 cu cm
  14. 14.What is the 35th term of the AP 16, 22, 28, 34, …? (a) 204 (b) 210 (c) 220 (d) 226
  15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  17. 17.How many factors does 61 have? (a) 1 (b) 4 (c) 2 (d) 3
  18. 18.A bag has 5 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 6 (c) 2 (d) 5
  19. 19.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7²
  20. 20.What is the mode of 11, 5, 5, 11, 17, 11 and 13? (a) 5 (b) 11 (c) 17 (d) 13
  21. 21.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 25 (c) 10 (d) 15
  22. 22.In a class of 35 children, 24 like maths, 19 like science and 3 like neither. How many like both? (a) 8 (b) 11 (c) 32 (d) 3
  23. 23.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
  24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 9856 sq cm
  25. 25.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 61° (b) 120° (c) 60° (d) 30°
  26. 26.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 21 (c) 10 (d) 24
  27. 27.What is the product of the roots of x² − 12x + 32 = 0? (a) 31 (b) 12 (c) 33 (d) 32
  28. 28.What is the median of 19, 6, 11, 8, 14, 23 and 9? (a) 14 (b) 9 (c) 11 (d) 8
  29. 29.What are the roots of x² − 9x + 20 = 0? (a) 4 and 5 (b) 1 and 20 (c) 2 and 10 (d) 1 and 8
  30. 30.What is the product of the roots of x² − 14x + 45 = 0? (a) 44 (b) 46 (c) 45 (d) 14
  31. 31.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 45 (c) 14 (d) 126
  32. 32.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 1 (d) 2
  33. 33.If a + b = 6 and ab = 5, what is a² + b²? (a) 36 (b) 31 (c) 26 (d) 46
  34. 34.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 20° (b) 70° (c) 40° (d) 110°
  35. 35.What is the mean of 19, 8, 12, 2, 5 and 14? (a) 9 (b) 12 (c) 10 (d) 11
  36. 36.A bag has 7 blue, 5 white and 8 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/5 (b) 1/3 (c) 2/3 (d) 2/5
  37. 37.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 125 times (b) 10 times (c) 25 times (d) 5 times
  38. 38.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 235° (b) 125° (c) 56° (d) 55°
  39. 39.What is the mode of 6, 8, 8, 19, 5, 8 and 5? (a) 5 (b) 19 (c) 8 (d) 6
  40. 40.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2

Answer key

  1. 9 times
  2. 10
  3. 20
  4. 85
  5. 8
  6. 28
  7. 168 cu cm
  8. 24
  9. 70°
  10. 1/36
  11. 12
  12. 1728 cu cm
  13. 336 cu cm
  14. 220
  15. 1/2
  16. 2
  17. 2
  18. 6
  19. 2² × 7
  20. 11
  21. 10
  22. 11
  23. 616 sq cm
  24. 2464 sq cm
  25. 60°
  26. 21
  27. 32
  28. 11
  29. 4 and 5
  30. 45
  31. 42
  32. 2
  33. 26
  34. 40°
  35. 10
  36. 2/5
  37. 25 times
  38. 55°
  39. 8
  40. 1/2

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