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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 464 · 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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
  2. 2.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
  3. 3.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2 × 7³ (c) 2⁴ × 7 (d) 2² × 7
  4. 4.In a class of 35 children, 13 like dance, 18 like music and 6 like both. How many like neither? (a) 10 (b) 16 (c) 6 (d) 4
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  6. 6.What is the mode of 3, 2, 5, 3, 3, 1 and 2? (a) 1 (b) 5 (c) 3 (d) 2
  7. 7.What is the smallest prime factor of 85? (a) 5 (b) 1 (c) 17 (d) 2
  8. 8.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 125° (b) 55° (c) 150° (d) 155°
  9. 9.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 36 (d) 72
  10. 10.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 20 (b) 11 (c) 10 (d) 25
  11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 22 cm (d) 154 cm
  12. 12.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 48 (c) 32 (d) 24
  13. 13.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 108 (b) 24 (c) 210 (d) 105
  14. 14.What is the 11th term of the AP 17, 22, 27, 32, …? (a) 50 (b) 72 (c) 67 (d) 55
  15. 15.A drawer has lots of red, blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 3 (c) 4 (d) 2
  16. 16.Using (a + b)² = a² + 2ab + b², what is 42²? (a) 1604 (b) 1764 (c) 1444 (d) 1774
  17. 17.A bag has 6 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 7 (c) 2 (d) 12
  18. 18.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 25 (c) 24 (d) 36
  19. 19.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/8 (d) 1/4
  20. 20.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x − 7)(x − 8) (c) (x + 1)(x + 56) (d) (x + 7)(x + 8)
  21. 21.In a class of 48 children, 31 like mangoes, 26 like bananas and 2 like neither. How many like both? (a) 9 (b) 11 (c) 46 (d) 2
  22. 22.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 145° (b) 125° (c) 90° (d) 270°
  23. 23.How many factors does 39 have? (a) 5 (b) 3 (c) 2 (d) 4
  24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
  25. 25.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 160° (c) 155° (d) 135°
  26. 26.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
  27. 27.What is the mode of 11, 19, 18, 9, 9, 18 and 9? (a) 11 (b) 18 (c) 19 (d) 9
  28. 28.In a class of 49 children, 28 like cricket, 23 like football and 8 like both. How many like at least one of the two? (a) 35 (b) 43 (c) 51 (d) 49
  29. 29.What is the midpoint of the line joining (2, 6) and (4, 8)? (a) (6, 14) (b) (1, 1) (c) (3, 7) (d) (7, 3)
  30. 30.What is the smallest prime factor of 119? (a) 2 (b) 1 (c) 7 (d) 17
  31. 31.The mean of 8 numbers is 40. When the number 49 is added to them, what is the new mean? (a) 42 (b) 40 (c) 43 (d) 41
  32. 32.In a class of 33 children, 20 like cricket, 17 like football and 11 like both. How many like at least one of the two? (a) 33 (b) 15 (c) 26 (d) 37
  33. 33.What is the mean of 10, 9, 5, 15, 5 and 10? (a) 8 (b) 11 (c) 10 (d) 9
  34. 34.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
  35. 35.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2601 (b) 2401 (c) 2611 (d) 2501
  36. 36.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 66 (c) 110 (d) 55
  37. 37.In a class of 40 children, 14 like dance, 27 like music and 8 like neither. How many like both? (a) 32 (b) 8 (c) 1 (d) 9
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  39. 39.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 20 (c) 90 (d) 45
  40. 40.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

Answer key

  1. 44 cm
  2. 154 sq cm
  3. 2³ × 7
  4. 10
  5. 10
  6. 3
  7. 5
  8. 125°
  9. 72
  10. 10
  11. 44 cm
  12. 24
  13. 105
  14. 67
  15. 4
  16. 1764
  17. 12
  18. 25
  19. 7/8
  20. (x + 7)(x + 8)
  21. 11
  22. 90°
  23. 4
  24. 5/6
  25. 135°
  26. 132 cm
  27. 9
  28. 43
  29. (3, 7)
  30. 7
  31. 41
  32. 26
  33. 9
  34. 40°
  35. 2601
  36. 55
  37. 9
  38. 6
  39. 90
  40. 16 times

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