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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 121 · 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 bag has 10 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 4 (c) 2 (d) 11
  2. 2.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 7 (c) 14 (d) 8
  3. 3.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2025 (b) 2525 (c) 3025 (d) 3035
  4. 4.What is the distance between the points (1, 4) and (8, 28)? (a) 26 (b) 625 (c) 25 (d) 31
  5. 5.What is the sum of the roots of x² − 9x + 20 = 0? (a) 10 (b) 8 (c) 9 (d) 20
  6. 6.How many factors does 45 have? (a) 7 (b) 4 (c) 6 (d) 5
  7. 7.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 15 (c) 10 (d) 20
  8. 8.What is the sum of the first 9 terms of the AP 2, 8, 14, …? (a) 261 (b) 468 (c) 50 (d) 234
  9. 9.What is the distance between the points (8, 15) and (13, 3)? (a) 14 (b) 169 (c) 13 (d) 17
  10. 10.What is the mean of 10, 3, 17 and 6? (a) 12 (b) 8 (c) 10 (d) 9
  11. 11.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 125° (b) 170° (c) 10° (d) 65°
  12. 12.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 12 (d) 3
  13. 13.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 10 (b) 25 (c) 21 (d) 20
  14. 14.A cuboid is 9 cm long, 2 cm wide and 5 cm high. What is its total surface area? (a) 292 sq cm (b) 146 sq cm (c) 73 sq cm (d) 90 sq cm
  15. 15.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 3/8 (d) 1/4
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 20° (b) 200° (c) 80° (d) 100°
  17. 17.A drawer has lots of white, green, yellow, black and red 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) 2 (c) 6 (d) 10
  18. 18.How many prime numbers are there between 50 and 60? (a) 4 (b) 3 (c) 1 (d) 2
  19. 19.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  20. 20.How many factors does 75 have? (a) 6 (b) 7 (c) 4 (d) 5
  21. 21.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2³ × 7 (d) 2 × 7²
  22. 22.What is the median of 37, 6, 38, 20, 4, 10 and 9? (a) 20 (b) 10 (c) 9 (d) 11
  23. 23.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
  24. 24.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 10 (c) 20 (d) 25
  25. 25.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 220° (c) 40° (d) 140°
  26. 26.A drawer has lots of black and red 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) 5 (c) 4 (d) 2
  27. 27.In which quadrant does the point (−2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
  29. 29.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 650 (b) 49 (c) 325 (d) 625
  30. 30.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 27 (c) 8 (d) 72
  31. 31.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 90 (d) 100
  32. 32.A drawer has lots of blue 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) 2 (b) 4 (c) 3 (d) 5
  33. 33.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 180 (c) 162 (d) 171
  34. 34.How many factors does 18 have? (a) 4 (b) 5 (c) 6 (d) 7
  35. 35.What is the mean of 5, 2, 8 and 17? (a) 7 (b) 10 (c) 8 (d) 9
  36. 36.In a class of 48 children, 26 like dance, 24 like music and 9 like both. How many like at least one of the two? (a) 41 (b) 32 (c) 50 (d) 48
  37. 37.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 5 (d) 1
  38. 38.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 290° (b) 110° (c) 70° (d) 145°
  39. 39.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 8)(x + 9) (c) (x − 8)(x − 9) (d) (x + 1)(x + 16)
  40. 40.A bag has 12 white balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 13 (c) 14 (d) 16

Answer key

  1. 11
  2. 8
  3. 3025
  4. 25
  5. 9
  6. 6
  7. 10
  8. 234
  9. 13
  10. 9
  11. 10°
  12. 6
  13. 20
  14. 146 sq cm
  15. 3/8
  16. 100°
  17. 6
  18. 2
  19. 2² × 3² × 5
  20. 6
  21. 2 × 7
  22. 10
  23. 1/3
  24. 10
  25. 40°
  26. 3
  27. Third quadrant
  28. 1/9
  29. 625
  30. 24
  31. 45
  32. 3
  33. 171
  34. 6
  35. 8
  36. 41
  37. 5
  38. 110°
  39. (x + 8)(x + 9)
  40. 14

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