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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 135 · 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.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/7 (c) 7/8 (d) 1/4
  2. 2.In a class of 45 children, 24 like tea, 24 like coffee and 12 like both. How many like only tea? (a) 12 (b) 24 (c) 21 (d) 13
  3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/12 (d) 1/11
  4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/18 (b) 1/12 (c) 1/11 (d) 1/36
  5. 5.What is the missing term in the AP 3, 5, ?, 9, 11? (a) 8 (b) 6 (c) 9 (d) 7
  6. 6.A drawer has lots of green 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) 5 (b) 3 (c) 4 (d) 2
  7. 7.A bag has 11 red balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 2 (c) 23 (d) 12
  8. 8.What is the mode of 4, 5, 3, 6, 4, 4 and 5? (a) 3 (b) 4 (c) 6 (d) 5
  9. 9.A canteen sells 8 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 96 (b) 14 (c) 48 (d) 56
  10. 10.A bag has 6 red balls and 5 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) 7 (c) 6 (d) 11
  11. 11.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 28 (c) 16 (d) 64
  12. 12.What is the mean of 15, 11, 5, 2, 9 and 18? (a) 10 (b) 9 (c) 12 (d) 11
  13. 13.In a class of 38 children, 25 like cricket, 20 like football and 9 like both. How many like at least one of the two? (a) 36 (b) 45 (c) 38 (d) 27
  14. 14.What is the mode of 10, 1, 15, 5, 5, 10 and 10? (a) 1 (b) 15 (c) 5 (d) 10
  15. 15.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  16. 16.What is the distance between the points (8, 16) and (24, 4)? (a) 20 (b) 400 (c) 21 (d) 28
  17. 17.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 2)(x + 3) (c) (x + 1)(x + 6) (d) (x + 1)(x + 4)
  18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 6/11 (c) 1/11 (d) 7/36
  19. 19.A drawer has lots of green, white 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) 3 (b) 4 (c) 2 (d) 6
  20. 20.In a class of 32 children, 21 like maths, 7 like science and 4 like both. How many like at least one of the two? (a) 28 (b) 24 (c) 20 (d) 32
  21. 21.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 88 sq cm (d) 308 sq cm
  22. 22.Which term of the AP 2, 7, 12, 17, … is 192? (a) 41st (b) 39th (c) 40th (d) 38th
  23. 23.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 120°
  24. 24.What is the sum of all the whole numbers from 1 to 81? (a) 3321 (b) 3240 (c) 3322 (d) 6642
  25. 25.How many prime numbers are there between 30 and 40? (a) 1 (b) 2 (c) 4 (d) 3
  26. 26.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 110° (c) 70° (d) 145°
  27. 27.Two angles of a triangle are 30° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 140° (d) 70°
  28. 28.What is the distance between the points (9, 0) and (21, 5)? (a) 17 (b) 13 (c) 169 (d) 14
  29. 29.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  30. 30.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
  31. 31.What is the mean of 6, 4, 6, 20, 3 and 15? (a) 8 (b) 11 (c) 9 (d) 10
  32. 32.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
  33. 33.How many factors does 60 have? (a) 13 (b) 12 (c) 11 (d) 10
  34. 34.What is the distance between the points (4, 4) and (16, 9)? (a) 169 (b) 14 (c) 17 (d) 13
  35. 35.In a league, 11 teams each play every other team once. How many matches are played? (a) 66 (b) 121 (c) 110 (d) 55
  36. 36.What is the missing term in the AP 18, ?, 32, 39, 46? (a) 26 (b) 24 (c) 25 (d) 32
  37. 37.What is the 15th term of the AP 2, 6, 10, 14, …? (a) 60 (b) 58 (c) 62 (d) 56
  38. 38.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 60° (b) 120° (c) 130° (d) 110°
  39. 39.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
  40. 40.If a + b = 10 and ab = 9, what is (a − b)²? (a) 64 (b) 100 (c) 82 (d) 8

Answer key

  1. 1/8
  2. 12
  3. 1/18
  4. 1/36
  5. 7
  6. 3
  7. 13
  8. 4
  9. 48
  10. 7
  11. 28
  12. 10
  13. 36
  14. 10
  15. 21
  16. 20
  17. (x + 2)(x + 3)
  18. 1/6
  19. 4
  20. 24
  21. 616 sq cm
  22. 39th
  23. 40°
  24. 3321
  25. 2
  26. 110°
  27. 70°
  28. 13
  29. 7
  30. 30
  31. 9
  32. 154 sq cm
  33. 12
  34. 13
  35. 55
  36. 25
  37. 58
  38. 60°
  39. 1/2
  40. 64

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