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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 149 · 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.What is the sum of the first 11 terms of the AP 2, 5, 8, …? (a) 190 (b) 374 (c) 187 (d) 32
  2. 2.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  3. 3.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
  4. 4.A bag has 6 yellow balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 13 (c) 2 (d) 7
  5. 5.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
  6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  7. 7.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 24 (c) 13 (d) 25
  8. 8.A cuboid is 8 cm long, 5 cm wide and 10 cm high. What is its total surface area? (a) 340 sq cm (b) 400 sq cm (c) 680 sq cm (d) 170 sq cm
  9. 9.What is the 23rd term of the AP 11, 19, 27, 35, …? (a) 195 (b) 176 (c) 184 (d) 187
  10. 10.A bag has 5 green balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 9 (b) 7 (c) 2 (d) 6
  11. 11.Two angles of a triangle are 20° and 125°. What is the third angle? (a) 160° (b) 145° (c) 55° (d) 35°
  12. 12.A drawer has lots of black, white, yellow, red 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) 2 (b) 10 (c) 5 (d) 6
  13. 13.How many factors does 13 have? (a) 1 (b) 4 (c) 3 (d) 2
  14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  15. 15.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 5 (d) 1
  16. 16.How many factors does 54 have? (a) 9 (b) 6 (c) 8 (d) 7
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 7 (b) 6 (c) 8 (d) 5
  18. 18.If a + b = 12 and ab = 11, what is (a − b)²? (a) 100 (b) 10 (c) 122 (d) 144
  19. 19.In a class of 22 children, 10 like dance, 13 like music and 3 like both. How many like neither? (a) 5 (b) 3 (c) 1 (d) 2
  20. 20.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
  21. 21.In a class of 34 children, 19 like cricket, 21 like football and 9 like both. How many like only cricket? (a) 19 (b) 12 (c) 13 (d) 10
  22. 22.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
  23. 23.In a class of 44 children, 16 like mangoes, 30 like bananas and 9 like neither. How many like both? (a) 9 (b) 35 (c) 11 (d) 2
  24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  25. 25.If a + b = 6 and ab = 5, what is a² + b²? (a) 36 (b) 46 (c) 26 (d) 31
  26. 26.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 686 (b) 1156 (c) 676 (d) 884
  27. 27.How many factors does 75 have? (a) 6 (b) 5 (c) 4 (d) 7
  28. 28.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 72 (c) 64 (d) 15
  29. 29.A bag has 5 green balls and 12 yellow 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) 17 (c) 13 (d) 6
  30. 30.A bag has 12 yellow balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 23 (b) 13 (c) 2 (d) 12
  31. 31.A drawer has lots of red 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) 4 (b) 2 (c) 3 (d) 5
  32. 32.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3969 (b) 3249 (c) 3591 (d) 3259
  33. 33.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  34. 34.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
  35. 35.What is the 23rd term of the AP 4, 11, 18, 25, …? (a) 158 (b) 161 (c) 165 (d) 154
  36. 36.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  37. 37.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 132 (d) 78
  38. 38.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 6 (b) 7 (c) 8 (d) 9
  40. 40.What is the distance between the points (7, 22) and (15, 7)? (a) 18 (b) 17 (c) 23 (d) 289

Answer key

  1. 187
  2. 6
  3. 60°
  4. 13
  5. 7/8
  6. 17
  7. 13
  8. 340 sq cm
  9. 187
  10. 7
  11. 35°
  12. 6
  13. 2
  14. 10
  15. 5
  16. 8
  17. 7
  18. 100
  19. 2
  20. 1/3
  21. 10
  22. 154 sq cm
  23. 11
  24. 1/3
  25. 26
  26. 676
  27. 6
  28. 64
  29. 13
  30. 13
  31. 3
  32. 3249
  33. Third quadrant
  34. 90
  35. 158
  36. 1/2
  37. 66
  38. 8 times
  39. 8
  40. 17

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