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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 900 · 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.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
  2. 2.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
  3. 3.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
  4. 4.A cube has edges of 9 cm. What is its volume? (a) 324 cu cm (b) 486 cu cm (c) 27 cu cm (d) 729 cu cm
  5. 5.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 20 (c) 25 (d) 10
  6. 6.What is the sum of the first 7 terms of the AP 8, 12, 16, …? (a) 280 (b) 140 (c) 154 (d) 32
  7. 7.In a class of 34 children, 17 like dance, 11 like music and 3 like both. How many like at least one of the two? (a) 22 (b) 25 (c) 34 (d) 28
  8. 8.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 37 (d) 48
  9. 9.What is the product of the roots of x² − 14x + 45 = 0? (a) 44 (b) 45 (c) 14 (d) 46
  10. 10.Two angles of a triangle are 35° and 30°. What is the exterior angle at the third corner? (a) 115° (b) 150° (c) 145° (d) 65°
  11. 11.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
  12. 12.A bag has 3 green, 9 yellow and 6 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 8/9 (c) 5/6 (d) 1/6
  13. 13.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
  14. 14.What is the mean of 10, 11, 12 and 15? (a) 16 (b) 12 (c) 11 (d) 13
  15. 15.If a + b = 18 and ab = 72, what is (a − b)²? (a) 180 (b) 6 (c) 324 (d) 36
  16. 16.What is the median of 2, 32, 5, 25, 4, 7 and 31? (a) 25 (b) 5 (c) 7 (d) 8
  17. 17.In a class of 23 children, 10 like cricket, 16 like football and 6 like both. How many like neither? (a) 3 (b) 4 (c) 9 (d) 6
  18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
  19. 19.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 11 (b) 24 (c) 32 (d) 48
  20. 20.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 11 (c) 60 (d) 36
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 20 (d) 19
  22. 22.What is the smallest prime factor of 65? (a) 1 (b) 5 (c) 2 (d) 13
  23. 23.In a class of 42 children, 26 like maths, 26 like science and 12 like both. How many like at least one of the two? (a) 28 (b) 52 (c) 40 (d) 42
  24. 24.What is the product of the roots of x² − 8x + 12 = 0? (a) 11 (b) 8 (c) 13 (d) 12
  25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
  26. 26.A cuboid is 8 cm long, 4 cm wide and 8 cm high. What is its total surface area? (a) 128 sq cm (b) 256 sq cm (c) 512 sq cm (d) 257 sq cm
  27. 27.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6241 (b) 6561 (c) 6571 (d) 6401
  28. 28.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 343 cu cm (d) 294 cu cm
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 3 (d) 13
  30. 30.What is the 35th term of the AP 19, 21, 23, 25, …? (a) 89 (b) 87 (c) 70 (d) 68
  31. 31.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) 15 (b) 22 (c) 21 (d) 14
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/9 (c) 1/11 (d) 3/11
  33. 33.In a class of 21 children, 13 like dance, 8 like music and 4 like both. How many like neither? (a) 0 (b) 4 (c) 5 (d) 8
  34. 34.The mean of 3 numbers is 33. When the number 21 is added to them, what is the new mean? (a) 31 (b) 27 (c) 30 (d) 33
  35. 35.Two angles of a triangle are 45° and 105°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 75° (d) 135°
  36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
  37. 37.In a class of 29 children, 17 like mangoes, 13 like bananas and 5 like neither. How many like both? (a) 5 (b) 6 (c) 24 (d) 1
  38. 38.What is the smallest prime factor of 51? (a) 17 (b) 1 (c) 3 (d) 2
  39. 39.In a class of 35 children, 10 like maths, 22 like science and 6 like both. How many like at least one of the two? (a) 20 (b) 32 (c) 26 (d) 35
  40. 40.A cube has edges of 9 cm. What is its total surface area? (a) 729 sq cm (b) 81 sq cm (c) 324 sq cm (d) 486 sq cm

Answer key

  1. 616 sq cm
  2. 72
  3. 21
  4. 729 cu cm
  5. 20
  6. 140
  7. 25
  8. 37
  9. 45
  10. 65°
  11. 1386 sq cm
  12. 5/6
  13. 7/8
  14. 12
  15. 36
  16. 7
  17. 3
  18. 30°
  19. 24
  20. 30
  21. 19
  22. 5
  23. 40
  24. 12
  25. 16 times
  26. 256 sq cm
  27. 6561
  28. 343 cu cm
  29. 14
  30. 87
  31. 15
  32. 1/12
  33. 4
  34. 30
  35. 150°
  36. 1/12
  37. 6
  38. 3
  39. 26
  40. 486 sq cm

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