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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 805 · 40 questions
TalentJR

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.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  2. 2.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 9984 (b) 9226 (c) 10816 (d) 9216
  3. 3.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 110° (c) 25° (d) 95°
  4. 4.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 56 (b) 28 (c) 36 (d) 64
  5. 5.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 15 (b) 21 (c) 22 (d) 14
  6. 6.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x − 2)(x − 5) (c) (x + 2)(x + 5) (d) (x + 1)(x + 6)
  7. 7.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 42 (c) 21 (d) 14
  8. 8.What is the 22nd term of the AP 1, 3, 5, 7, …? (a) 42 (b) 44 (c) 45 (d) 43
  9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 169 (c) 91 (d) 78
  10. 10.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 95° (b) 125° (c) 140° (d) 85°
  11. 11.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
  12. 12.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 160° (b) 21° (c) 20° (d) 200°
  13. 13.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 335° (b) 25° (c) 155° (d) 65°
  14. 14.How many factors does 67 have? (a) 4 (b) 1 (c) 3 (d) 2
  15. 15.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
  16. 16.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
  17. 17.If a + b = 17 and ab = 60, what is (a − b)²? (a) 169 (b) 7 (c) 49 (d) 289
  18. 18.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 145° (c) 75° (d) 105°
  19. 19.Which is the correct factorisation of x² + 11x + 18? (a) (x + 2)(x + 9) (b) (x + 1)(x + 18) (c) (x + 1)(x + 10) (d) (x − 2)(x − 9)
  20. 20.What is the product of the roots of x² − 15x + 56 = 0? (a) 15 (b) 55 (c) 56 (d) 57
  21. 21.A drawer has lots of yellow 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) 2 (b) 4 (c) 5 (d) 3
  22. 22.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
  23. 23.What are the roots of x² − 13x + 40 = 0? (a) 1 and 12 (b) 2 and 20 (c) 1 and 40 (d) 5 and 8
  24. 24.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 110° (d) 115°
  25. 25.Using (a − b)² = a² − 2ab + b², what is 98²? (a) 9614 (b) 9996 (c) 10404 (d) 9604
  26. 26.What is the smallest prime factor of 85? (a) 17 (b) 1 (c) 2 (d) 5
  27. 27.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 145° (d) 155°
  28. 28.In a class of 37 children, 21 like tea, 18 like coffee and 3 like both. How many like only tea? (a) 18 (b) 19 (c) 15 (d) 21
  29. 29.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  30. 30.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 42 (c) 10 (d) 21
  31. 31.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 140° (c) 120° (d) 60°
  32. 32.In a class of 44 children, 30 like dance, 25 like music and 12 like both. How many like at least one of the two? (a) 44 (b) 43 (c) 55 (d) 31
  33. 33.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
  34. 34.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/8 (c) 1/7 (d) 1/4
  35. 35.There are 8 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) 48 (b) 56 (c) 96 (d) 14
  36. 36.The mean of 9 numbers is 14. When the number 34 is added to them, what is the new mean? (a) 14 (b) 16 (c) 24 (d) 17
  37. 37.What is the 31st term of the AP 6, 15, 24, 33, …? (a) 279 (b) 276 (c) 270 (d) 285
  38. 38.What is the product of the roots of x² − 14x + 45 = 0? (a) 14 (b) 46 (c) 44 (d) 45
  39. 39.What is the mean of 9, 6, 3 and 10? (a) 9 (b) 6 (c) 8 (d) 7
  40. 40.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 21 (d) 42

Answer key

  1. 1/2
  2. 9216
  3. 25°
  4. 28
  5. 15
  6. (x + 2)(x + 5)
  7. 21
  8. 43
  9. 78
  10. 85°
  11. 1/2
  12. 20°
  13. 155°
  14. 2
  15. 5
  16. 291
  17. 49
  18. 105°
  19. (x + 2)(x + 9)
  20. 56
  21. 3
  22. 9 times
  23. 5 and 8
  24. 135°
  25. 9604
  26. 5
  27. 60°
  28. 18
  29. 7
  30. 21
  31. 60°
  32. 43
  33. 4
  34. 1/8
  35. 48
  36. 16
  37. 276
  38. 45
  39. 7
  40. 21

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