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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 774 · 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 times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 1 (c) 3 (d) 2
  2. 2.How many factors does 30 have? (a) 6 (b) 9 (c) 7 (d) 8
  3. 3.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 22 (d) 198
  4. 4.A drawer has lots of red, blue, black, white and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 5 (d) 10
  5. 5.A drawer has lots of yellow, green, red, black and white 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) 10 (c) 2 (d) 5
  6. 6.A bag has 5 white balls and 11 blue 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) 16 (c) 6 (d) 12
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  8. 8.How many factors does 89 have? (a) 2 (b) 4 (c) 3 (d) 1
  9. 9.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 6 (d) 7
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  12. 12.Two straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 60° (b) 30° (c) 150° (d) 31°
  13. 13.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 160 cu cm (b) 17 cu cm (c) 100 cu cm (d) 10 cu cm
  14. 14.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  15. 15.What is the distance between the points (4, 10) and (12, 4)? (a) 100 (b) 11 (c) 10 (d) 14
  16. 16.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 94 cu cm (b) 60 cu cm (c) 12 cu cm (d) 61 cu cm
  17. 17.In a class of 30 children, 9 like tea, 17 like coffee and 6 like both. How many like only tea? (a) 9 (b) 13 (c) 11 (d) 3
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 3 (b) 4 (c) 5 (d) 6
  19. 19.What is the median of 21, 10, 2, 19 and 12? (a) 19 (b) 12 (c) 10 (d) 2
  20. 20.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 18 (b) 12 (c) 24 (d) 8
  21. 21.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
  22. 22.In a class of 25 children, 12 like maths, 19 like science and 9 like both. How many like neither? (a) 12 (b) 3 (c) 4 (d) 9
  23. 23.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
  24. 24.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 135° (b) 80° (c) 35° (d) 145°
  25. 25.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6404 (b) 6724 (c) 6084 (d) 6734
  26. 26.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) 25 (b) 12 (c) 13 (d) 24
  27. 27.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
  28. 28.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 8 (c) 16 (d) 20
  29. 29.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 8 (b) 18 (c) 12 (d) 24
  30. 30.In a class of 41 children, 22 like cricket, 27 like football and 11 like both. How many like only cricket? (a) 22 (b) 14 (c) 11 (d) 16
  31. 31.What is the distance between the points (0, 8) and (6, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  33. 33.Two angles of a triangle are 70° and 70°. What is the third angle? (a) 40° (b) 140° (c) 220° (d) 110°
  34. 34.A drawer has lots of black, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 3 (d) 4
  35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  36. 36.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 225 (b) 36 (c) 240 (d) 450
  37. 37.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 120° (b) 150° (c) 30° (d) 60°
  38. 38.What is the distance between the points (2, 4) and (6, 1)? (a) 7 (b) 5 (c) 6 (d) 25
  39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
  40. 40.What is the distance between the points (1, 10) and (5, 7)? (a) 7 (b) 5 (c) 6 (d) 25

Answer key

  1. 3
  2. 8
  3. 66
  4. 6
  5. 6
  6. 12
  7. 6
  8. 2
  9. First quadrant
  10. 7
  11. 120
  12. 30°
  13. 100 cu cm
  14. 7
  15. 10
  16. 60 cu cm
  17. 3
  18. 5
  19. 12
  20. 12
  21. 40°
  22. 3
  23. 90
  24. 35°
  25. 6724
  26. 13
  27. 44 cm
  28. 16
  29. 12
  30. 11
  31. 10
  32. 15
  33. 40°
  34. 4
  35. 13
  36. 225
  37. 120°
  38. 5
  39. (x + 8)(x + 9)
  40. 5

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