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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 550 · 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 sum of the roots of x² − 16x + 63 = 0? (a) 63 (b) 17 (c) 15 (d) 16
  2. 2.If the radius of a circle 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
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 150° (b) 105° (c) 76° (d) 75°
  4. 4.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 75° (b) 145° (c) 110° (d) 105°
  5. 5.What is the mode of 7, 14, 6, 14, 14, 5 and 6? (a) 6 (b) 14 (c) 5 (d) 7
  6. 6.A cuboid is 12 cm long, 3 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 36 cu cm (c) 72 cu cm (d) 132 cu cm
  7. 7.If a + b = 4 and ab = 3, what is a² + b²? (a) 16 (b) 22 (c) 10 (d) 13
  8. 8.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 5 (d) 6
  9. 9.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 3 times (d) 9 times
  10. 10.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x − 6)(x − 7) (c) (x + 6)(x + 7) (d) (x + 1)(x + 12)
  11. 11.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 1386 cm (d) 264 cm
  12. 12.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
  13. 13.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 30 (c) 35 (d) 11
  14. 14.What is the median of 1, 33, 22, 9 and 38? (a) 9 (b) 23 (c) 22 (d) 33
  15. 15.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 36 (d) 15
  16. 16.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 370 (b) 200 (c) 185 (d) 32
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 100° (c) 80° (d) 20°
  18. 18.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 494 (c) 624 (d) 634
  19. 19.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 398 (c) 490 (d) 489
  20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  21. 21.Two angles of a triangle are 80° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 140° (c) 60° (d) 100°
  22. 22.What is the product of the roots of x² − 14x + 45 = 0? (a) 44 (b) 14 (c) 46 (d) 45
  23. 23.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 70 (c) 35 (d) 12
  24. 24.What is the mode of 18, 13, 13, 5, 6, 6 and 13? (a) 5 (b) 6 (c) 18 (d) 13
  25. 25.What is the smallest prime factor of 299? (a) 2 (b) 13 (c) 1 (d) 23
  26. 26.The mean of 5 numbers is 18. When the number 30 is added to them, what is the new mean? (a) 24 (b) 20 (c) 18 (d) 21
  27. 27.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
  28. 28.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 81° (b) 260° (c) 100° (d) 80°
  29. 29.What is the mean of 2, 2, 2, 6 and 3? (a) 2 (b) 5 (c) 4 (d) 3
  30. 30.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 6 (b) 9 (c) 5 (d) 12
  31. 31.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 24 sq cm (d) 4 sq cm
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
  33. 33.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.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) 36 (b) 24 (c) 37 (d) 25
  35. 35.A bag has 6 yellow, 5 white and 7 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 13/18 (c) 1/18 (d) 2/3
  36. 36.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 140° (d) 135°
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
  38. 38.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) 8 (b) 15 (c) 7 (d) 14
  39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
  40. 40.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 290° (d) 20°

Answer key

  1. 16
  2. 4 times
  3. 75°
  4. 75°
  5. 14
  6. 72 cu cm
  7. 10
  8. 4
  9. 9 times
  10. (x + 6)(x + 7)
  11. 132 cm
  12. 10
  13. 30
  14. 22
  15. 15
  16. 185
  17. 100°
  18. 633
  19. 489
  20. 17
  21. 120°
  22. 45
  23. 35
  24. 13
  25. 13
  26. 20
  27. 5
  28. 80°
  29. 3
  30. 6
  31. 24 sq cm
  32. 1/36
  33. First quadrant
  34. 25
  35. 2/3
  36. 85°
  37. 1/12
  38. 8
  39. 70°
  40. 110°

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