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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 377 · 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.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x − 4)(x − 5) (c) (x + 4)(x + 5) (d) (x + 1)(x + 8)
  2. 2.In a class of 27 children, 19 like cricket, 14 like football and 2 like neither. How many like both? (a) 8 (b) 2 (c) 6 (d) 25
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 110 (c) 66 (d) 55
  4. 4.A bag has 3 yellow, 7 red and 9 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 12/19 (c) 7/19 (d) 13/19
  5. 5.A bag has 8 blue balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 10 (c) 17 (d) 9
  6. 6.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  7. 7.What is the missing term in the AP 18, 21, ?, 27, 30? (a) 25 (b) 27 (c) 24 (d) 23
  8. 8.How many factors does 72 have? (a) 10 (b) 12 (c) 11 (d) 13
  9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 1/4 (d) 3/8
  10. 10.What is the distance between the points (9, 7) and (33, 14)? (a) 25 (b) 31 (c) 26 (d) 625
  11. 11.What is the 15th term of the AP 4, 9, 14, 19, …? (a) 79 (b) 70 (c) 75 (d) 74
  12. 12.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 18 (c) 9 (d) 36
  13. 13.Which term of the AP 19, 24, 29, 34, … is 134? (a) 25th (b) 23rd (c) 26th (d) 24th
  14. 14.What is the mode of 8, 8, 3, 17, 8, 10 and 10? (a) 10 (b) 3 (c) 17 (d) 8
  15. 15.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 3 (d) 2
  16. 16.A bag has 10 blue balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 14 (b) 11 (c) 12 (d) 2
  17. 17.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
  18. 18.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 6 (d) 4
  19. 19.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 48 (c) 11 (d) 24
  20. 20.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 30) (c) (x + 1)(x + 10) (d) (x + 5)(x + 6)
  21. 21.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 441 (d) 462
  22. 22.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x + 7)(x + 9) (c) (x − 7)(x − 9) (d) (x + 1)(x + 15)
  23. 23.In a class of 11 children, 6 like cricket, 6 like football and 2 like both. How many like at least one of the two? (a) 10 (b) 8 (c) 11 (d) 12
  24. 24.How many factors does 110 have? (a) 7 (b) 9 (c) 8 (d) 6
  25. 25.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 21 (d) 28
  26. 26.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 105 (d) 120
  27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 18 (d) 36
  28. 28.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
  29. 29.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 49 (c) 56 (d) 98
  30. 30.A drawer has lots of black, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 6 (d) 3
  31. 31.If a + b = 20 and ab = 96, what is a² + b²? (a) 208 (b) 304 (c) 400 (d) 592
  32. 32.In a class of 35 children, 19 like maths, 23 like science and 4 like neither. How many like both? (a) 11 (b) 7 (c) 4 (d) 31
  33. 33.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 24 (d) 48
  34. 34.In a class of 26 children, 13 like cricket, 17 like football and 7 like both. How many like at least one of the two? (a) 16 (b) 26 (c) 23 (d) 30
  35. 35.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 91 (d) 78
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  37. 37.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 1024 (b) 904 (c) 784 (d) 1034
  38. 38.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  40. 40.What is the distance between the points (4, 17) and (19, 9)? (a) 23 (b) 289 (c) 17 (d) 18

Answer key

  1. (x + 4)(x + 5)
  2. 8
  3. 55
  4. 12/19
  5. 10
  6. 78
  7. 24
  8. 12
  9. 3/8
  10. 25
  11. 74
  12. 18
  13. 24th
  14. 8
  15. 3
  16. 12
  17. 70°
  18. 5
  19. 24
  20. (x + 5)(x + 6)
  21. 441
  22. (x + 7)(x + 9)
  23. 10
  24. 8
  25. 22
  26. 105
  27. 36
  28. 60°
  29. 49
  30. 4
  31. 208
  32. 11
  33. 24
  34. 23
  35. 78
  36. 5
  37. 1024
  38. 132 cm
  39. 8
  40. 17

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