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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 616 · 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 two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  2. 2.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 440 cm (d) 220 cm
  3. 3.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 8 (d) 24
  4. 4.What is the distance between the points (9, 0) and (15, 8)? (a) 11 (b) 14 (c) 100 (d) 10
  5. 5.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x + 3)(x + 9) (c) (x − 3)(x − 9) (d) (x + 1)(x + 11)
  6. 6.What is the median of 4, 31, 12, 14 and 29? (a) 12 (b) 14 (c) 29 (d) 18
  7. 7.In how many different ways can the letters of the word MANGO be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  8. 8.In a class of 36 children, 8 like cricket, 22 like football and 3 like both. How many like at least one of the two? (a) 27 (b) 36 (c) 24 (d) 30
  9. 9.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 132 (c) 24 (d) 66
  10. 10.A cuboid is 7 cm long, 6 cm wide and 10 cm high. What is its volume? (a) 420 cu cm (b) 344 cu cm (c) 42 cu cm (d) 23 cu cm
  11. 11.In a class of 24 children, 13 like mangoes, 12 like bananas and 8 like both. How many like neither? (a) 6 (b) 15 (c) 8 (d) 7
  12. 12.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 41 (b) 34 (c) 35 (d) 33
  13. 13.What is the 21st term of the AP 5, 14, 23, 32, …? (a) 194 (b) 189 (c) 180 (d) 185
  14. 14.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 12 (c) 25 (d) 13
  15. 15.What is the missing term in the AP 4, ?, 14, 19, 24? (a) 8 (b) 9 (c) 10 (d) 14
  16. 16.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 384 sq cm (d) 256 sq cm
  17. 17.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 11 (c) 35 (d) 30
  18. 18.What is the mode of 20, 16, 20, 2, 16, 20 and 8? (a) 8 (b) 16 (c) 20 (d) 2
  19. 19.What is the distance between the points (9, 2) and (21, 11)? (a) 15 (b) 16 (c) 225 (d) 21
  20. 20.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 12 (c) 24 (d) 16
  21. 21.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 55° (d) 46°
  22. 22.What is the 11th term of the AP 7, 15, 23, 31, …? (a) 87 (b) 80 (c) 95 (d) 88
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
  24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 132 (d) 144
  25. 25.What is the distance between the points (5, 0) and (17, 16)? (a) 20 (b) 28 (c) 21 (d) 400
  26. 26.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 16 (c) 18 (d) 72
  27. 27.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) 48 (b) 37 (c) 49 (d) 36
  28. 28.The mean of 9 numbers is 29. When the number 19 is added to them, what is the new mean? (a) 28 (b) 29 (c) 24 (d) 27
  29. 29.How many factors does 90 have? (a) 13 (b) 10 (c) 11 (d) 12
  30. 30.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
  31. 31.Which term of the AP 6, 8, 10, 12, … is 80? (a) 40th (b) 39th (c) 38th (d) 37th
  32. 32.What is the median of 9, 1, 10, 11 and 29? (a) 9 (b) 11 (c) 10 (d) 12
  33. 33.Two angles of a triangle are 55° and 95°. What is the exterior angle at the third corner? (a) 150° (b) 125° (c) 30° (d) 85°
  34. 34.A bag has 3 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 4 (c) 2 (d) 5
  35. 35.What is the midpoint of the line joining (9, 10) and (13, 14)? (a) (22, 24) (b) (2, 2) (c) (11, 12) (d) (12, 11)
  36. 36.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 60° (c) 70° (d) 120°
  37. 37.What is the mean of 14, 20, 4, 11, 19 and 4? (a) 12 (b) 13 (c) 11 (d) 14
  38. 38.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 20 (c) 8 (d) 15
  39. 39.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 82 (c) 74 (d) 73
  40. 40.A bag has 3 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 4 (c) 2 (d) 7

Answer key

  1. 6
  2. 220 cm
  3. 24
  4. 10
  5. (x + 3)(x + 9)
  6. 14
  7. 120
  8. 27
  9. 66
  10. 420 cu cm
  11. 7
  12. 34
  13. 185
  14. 13
  15. 9
  16. 384 sq cm
  17. 30
  18. 20
  19. 15
  20. 24
  21. 45°
  22. 87
  23. 17
  24. 66
  25. 20
  26. 17
  27. 37
  28. 28
  29. 12
  30. 4 times
  31. 38th
  32. 10
  33. 150°
  34. 5
  35. (11, 12)
  36. 60°
  37. 12
  38. 15
  39. 73
  40. 5

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