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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 585 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/11 (c) 1/12 (d) 2/11
  2. 2.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 2 (d) 7
  3. 3.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  4. 4.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the distance between the points (7, 6) and (15, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  6. 6.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
  7. 7.There are 3 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 8 (c) 30 (d) 18
  8. 8.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 16 (c) 51 (d) 144
  9. 9.What is the midpoint of the line joining (2, 6) and (6, 16)? (a) (4, 11) (b) (2, 5) (c) (11, 4) (d) (8, 22)
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  11. 11.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
  12. 12.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 25 (d) 20
  13. 13.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
  14. 14.What is the distance between the points (0, 9) and (5, 21)? (a) 17 (b) 13 (c) 169 (d) 14
  15. 15.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 1 (d) 7
  16. 16.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
  17. 17.How many factors does 111 have? (a) 5 (b) 2 (c) 3 (d) 4
  18. 18.What is the mode of 11, 11, 1, 4, 4, 11 and 10? (a) 10 (b) 4 (c) 11 (d) 1
  19. 19.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 135° (c) 45° (d) 150°
  20. 20.In a class of 32 children, 12 like maths, 27 like science and 8 like both. How many like at least one of the two? (a) 32 (b) 39 (c) 31 (d) 23
  21. 21.What is the distance between the points (2, 8) and (14, 13)? (a) 17 (b) 13 (c) 14 (d) 169
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  23. 23.What is the distance between the points (0, 9) and (7, 33)? (a) 625 (b) 26 (c) 25 (d) 31
  24. 24.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 25° (c) 50° (d) 65°
  25. 25.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 100° (b) 140° (c) 40° (d) 120°
  26. 26.What is the 25th term of the AP 16, 21, 26, 31, …? (a) 141 (b) 120 (c) 136 (d) 125
  27. 27.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 9 (d) 7
  28. 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 8 (c) 15 (d) 14
  29. 29.Two angles of a triangle are 80° and 70°. What is the third angle? (a) 30° (b) 110° (c) 100° (d) 150°
  30. 30.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
  31. 31.Two angles of a triangle are 70° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 110° (c) 270° (d) 90°
  32. 32.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 24 (d) 144
  33. 33.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
  34. 34.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 42 (b) 21 (c) 36 (d) 11
  35. 35.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  36. 36.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) 36 (b) 37 (c) 49 (d) 48
  37. 37.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 20° (b) 10° (c) 80° (d) 100°
  38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  39. 39.What is the sum of all the whole numbers from 1 to 97? (a) 4656 (b) 9506 (c) 4753 (d) 4754
  40. 40.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 125° (b) 35° (c) 70° (d) 55°

Answer key

  1. 1/18
  2. 7
  3. 7
  4. First quadrant
  5. 10
  6. 4 times
  7. 15
  8. 48
  9. (4, 11)
  10. 20
  11. 15
  12. 10
  13. 25 times
  14. 13
  15. 7
  16. 36
  17. 4
  18. 11
  19. 45°
  20. 31
  21. 13
  22. 19
  23. 25
  24. 50°
  25. 40°
  26. 136
  27. 7
  28. 8
  29. 30°
  30. 1000 cu cm
  31. 90°
  32. 132
  33. 60 cu cm
  34. 36
  35. 1/2
  36. 37
  37. 20°
  38. 10
  39. 4753
  40. 70°

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