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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 80 · 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.Two angles of a triangle are 80° and 25°. What is the third angle? (a) 105° (b) 75° (c) 155° (d) 100°
  2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
  3. 3.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10211 (b) 10001 (c) 9801 (d) 10201
  4. 4.Two angles of a triangle are 60° and 40°. What is the third angle? (a) 120° (b) 140° (c) 80° (d) 100°
  5. 5.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 15 (b) 14 (c) 16 (d) 21
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
  7. 7.The mean of 6 numbers is 30. When the number 23 is added to them, what is the new mean? (a) 28 (b) 30 (c) 31 (d) 29
  8. 8.What is the mean of 15, 14, 5 and 14? (a) 16 (b) 12 (c) 11 (d) 13
  9. 9.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  10. 10.In which quadrant does the point (3, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  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) 1/3 (c) 1/4 (d) 1/2
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/36 (d) 1/12
  13. 13.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the missing term in the AP 17, ?, 21, 23, 25? (a) 20 (b) 19 (c) 21 (d) 18
  15. 15.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 88 (c) 97 (d) 106
  16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 154 sq cm (d) 616 sq cm
  17. 17.A bag has 7 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 2 (c) 6 (d) 8
  18. 18.Two angles of a triangle are 45° and 90°. What is the third angle? (a) 90° (b) 45° (c) 225° (d) 135°
  19. 19.In a class of 40 children, 19 like tea, 27 like coffee and 9 like both. How many like neither? (a) 3 (b) 4 (c) 9 (d) 12
  20. 20.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
  21. 21.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 110 (c) 22 (d) 55
  22. 22.A cuboid is 12 cm long, 10 cm wide and 9 cm high. What is its volume? (a) 120 cu cm (b) 31 cu cm (c) 636 cu cm (d) 1080 cu cm
  23. 23.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  24. 24.What is the sum of the first 8 terms of the AP 3, 5, 7, …? (a) 80 (b) 160 (c) 88 (d) 17
  25. 25.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
  26. 26.If a + b = 18 and ab = 77, what is a² + b²? (a) 247 (b) 170 (c) 478 (d) 324
  27. 27.In a class of 23 children, 13 like dance, 10 like music and 7 like both. How many like neither? (a) 7 (b) 0 (c) 8 (d) 14
  28. 28.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.In a class of 38 children, 20 like cricket, 27 like football and 10 like both. How many like neither? (a) 10 (b) 2 (c) 11 (d) 1
  30. 30.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
  31. 31.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 4 (d) 6
  32. 32.A drawer has lots of green, blue 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) 6 (b) 2 (c) 4 (d) 3
  33. 33.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 4901 (b) 4761 (c) 5051 (d) 5041
  34. 34.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) 11 (b) 24 (c) 32 (d) 48
  35. 35.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  36. 36.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 28 (d) 42
  37. 37.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 90 (d) 100
  38. 38.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 81 (d) 90
  39. 39.13 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
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 3 (b) 12 (c) 13 (d) 14

Answer key

  1. 75°
  2. 1/12
  3. 10201
  4. 80°
  5. 15
  6. 7
  7. 29
  8. 12
  9. 5
  10. First quadrant
  11. 1/2
  12. 1/36
  13. Third quadrant
  14. 19
  15. 97
  16. 154 sq cm
  17. 8
  18. 45°
  19. 3
  20. 8 times
  21. 55
  22. 1080 cu cm
  23. 1/3
  24. 80
  25. 72
  26. 170
  27. 7
  28. First quadrant
  29. 1
  30. 5 × 7
  31. 4
  32. 4
  33. 5041
  34. 24
  35. 10
  36. 21
  37. 90
  38. 81
  39. 78
  40. 13

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