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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 156 · 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 factors does 91 have? (a) 5 (b) 3 (c) 4 (d) 2
  2. 2.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 7 (b) 12 (c) 16 (d) 24
  3. 3.What is the midpoint of the line joining (6, 1) and (16, 3)? (a) (22, 4) (b) (11, 2) (c) (2, 11) (d) (5, 1)
  4. 4.What is the distance between the points (8, 6) and (16, 12)? (a) 10 (b) 100 (c) 14 (d) 11
  5. 5.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 56 (b) 28 (c) 11 (d) 35
  6. 6.The numbers 9 to 17 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) 13 (c) 39 (d) 117
  7. 7.In a class of 61 children, 31 like cricket, 31 like football and 10 like neither. How many like both? (a) 11 (b) 51 (c) 1 (d) 10
  8. 8.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 3 (d) 0
  9. 9.A bag has 11 green balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 2 (c) 14 (d) 12
  10. 10.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  11. 11.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 18 cu cm (b) 146 cu cm (c) 16 cu cm (d) 90 cu cm
  12. 12.In a class of 43 children, 20 like dance, 17 like music and 4 like both. How many like neither? (a) 6 (b) 14 (c) 4 (d) 10
  13. 13.A cuboid is 4 cm long, 3 cm wide and 4 cm high. What is its volume? (a) 11 cu cm (b) 80 cu cm (c) 12 cu cm (d) 48 cu cm
  14. 14.A bag has 9 red balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 15 (d) 7
  15. 15.What is the distance between the points (8, 17) and (20, 1)? (a) 21 (b) 28 (c) 400 (d) 20
  16. 16.In a class of 41 children, 27 like mangoes, 22 like bananas and 10 like both. How many like only mangoes? (a) 19 (b) 12 (c) 17 (d) 27
  17. 17.A bag has 6 green balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 6 (d) 11
  18. 18.There are 8 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) 56 (b) 112 (c) 15 (d) 64
  19. 19.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 11° (b) 160° (c) 20° (d) 10°
  20. 20.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 176 sq cm
  21. 21.What is the mean of 8, 13, 8 and 7? (a) 12 (b) 9 (c) 10 (d) 8
  22. 22.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 53 (b) 729 (c) 378 (d) 756
  23. 23.If a + b = 16 and ab = 63, what is (a − b)²? (a) 130 (b) 2 (c) 256 (d) 4
  24. 24.Which term of the AP 3, 8, 13, 18, … is 113? (a) 24th (b) 25th (c) 22nd (d) 23rd
  25. 25.What is the midpoint of the line joining (1, 10) and (5, 6)? (a) (2, 2) (b) (8, 3) (c) (3, 8) (d) (6, 16)
  26. 26.If a + b = 10 and ab = 16, what is a² + b²? (a) 100 (b) 68 (c) 132 (d) 84
  27. 27.What is the 37th term of the AP 3, 9, 15, 21, …? (a) 222 (b) 225 (c) 219 (d) 216
  28. 28.In a class of 36 children, 16 like mangoes, 16 like bananas and 3 like both. How many like at least one of the two? (a) 36 (b) 32 (c) 29 (d) 26
  29. 29.What is the smallest prime factor of 51? (a) 3 (b) 1 (c) 2 (d) 17
  30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/36 (c) 1/11 (d) 5/11
  31. 31.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 280° (b) 10° (c) 100° (d) 80°
  32. 32.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 56 (d) 28
  33. 33.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  34. 34.What is the sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 15 (c) 16 (d) 17
  35. 35.What is the median of 11, 5, 7, 21, 37, 40 and 36? (a) 36 (b) 21 (c) 22 (d) 11
  36. 36.What is the smallest prime factor of 95? (a) 1 (b) 19 (c) 5 (d) 2
  37. 37.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 95° (b) 105° (c) 20° (d) 160°
  38. 38.In a class of 42 children, 19 like tea, 20 like coffee and 6 like both. How many like only tea? (a) 19 (b) 22 (c) 14 (d) 13
  39. 39.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
  40. 40.What is the sum of the first 10 terms of the AP 6, 8, 10, …? (a) 24 (b) 150 (c) 300 (d) 160

Answer key

  1. 4
  2. 12
  3. (11, 2)
  4. 10
  5. 28
  6. 39
  7. 11
  8. 1
  9. 12
  10. 7
  11. 90 cu cm
  12. 10
  13. 48 cu cm
  14. 10
  15. 20
  16. 17
  17. 7
  18. 56
  19. 10°
  20. 2464 sq cm
  21. 9
  22. 729
  23. 4
  24. 23rd
  25. (3, 8)
  26. 68
  27. 219
  28. 29
  29. 3
  30. 5/36
  31. 100°
  32. 49
  33. 2² × 3² × 5
  34. 16
  35. 21
  36. 5
  37. 20°
  38. 13
  39. 10
  40. 150

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