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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 559 · 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 30° and 125°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 25°
  2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  3. 3.What is the sum of the roots of x² − 13x + 36 = 0? (a) 14 (b) 36 (c) 13 (d) 12
  4. 4.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 45 (d) 90
  5. 5.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 42 (b) 49 (c) 84 (d) 13
  6. 6.How many prime numbers are there between 70 and 90? (a) 5 (b) 6 (c) 4 (d) 7
  7. 7.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 66 (c) 132 (d) 144
  8. 8.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 45 (c) 55 (d) 100
  9. 9.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 90° (c) 91° (d) 45°
  10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  11. 11.In which quadrant does the point (4, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5² × 7
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  14. 14.Two angles of a triangle are 30° and 55°. What is the third angle? (a) 150° (b) 85° (c) 125° (d) 95°
  15. 15.Two angles of a triangle are 80° and 50°. What is the third angle? (a) 230° (b) 50° (c) 130° (d) 100°
  16. 16.Which term of the AP 4, 8, 12, 16, … is 84? (a) 22nd (b) 23rd (c) 20th (d) 21st
  17. 17.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 6 times (d) 3 times
  18. 18.In a class of 31 children, 9 like cricket, 24 like football and 4 like both. How many like neither? (a) 6 (b) 2 (c) 4 (d) 3
  19. 19.What is the distance between the points (2, 15) and (17, 7)? (a) 23 (b) 18 (c) 17 (d) 289
  20. 20.Two angles of a triangle are 60° and 100°. What is the third angle? (a) 120° (b) 20° (c) 80° (d) 160°
  21. 21.What is the distance between the points (7, 6) and (11, 9)? (a) 25 (b) 6 (c) 5 (d) 7
  22. 22.The mean of 5 numbers is 22. When the number 28 is added to them, what is the new mean? (a) 25 (b) 22 (c) 24 (d) 23
  23. 23.What is the distance between the points (4, 13) and (16, 8)? (a) 17 (b) 169 (c) 13 (d) 14
  24. 24.What is the median of 38, 23, 35, 3 and 12? (a) 35 (b) 12 (c) 23 (d) 24
  25. 25.What is the missing term in the AP 1, ?, 7, 10, 13? (a) 7 (b) 3 (c) 4 (d) 5
  26. 26.A drawer has lots of white, yellow 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) 3 (b) 6 (c) 4 (d) 2
  27. 27.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 11025 (b) 9975 (c) 9035 (d) 9025
  28. 28.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  29. 29.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
  30. 30.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x + 3)(x + 5) (c) (x − 3)(x − 5) (d) (x + 1)(x + 7)
  31. 31.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  32. 32.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 35° (b) 305° (c) 125° (d) 55°
  33. 33.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6241 (b) 6571 (c) 6401 (d) 6561
  34. 34.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
  35. 35.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 16 (c) 14 (d) 15
  36. 36.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 4624 (b) 5184 (c) 4904 (d) 5194
  37. 37.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  38. 38.Two angles of a triangle are 45° and 25°. What is the exterior angle at the third corner? (a) 70° (b) 155° (c) 135° (d) 110°
  39. 39.In a class of 27 children, 15 like tea, 20 like coffee and 12 like both. How many like at least one of the two? (a) 23 (b) 11 (c) 35 (d) 27
  40. 40.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 153 (c) 17 (d) 51

Answer key

  1. 25°
  2. 154 sq cm
  3. 13
  4. 45
  5. 42
  6. 5
  7. 66
  8. 45
  9. 90°
  10. 24
  11. Fourth quadrant
  12. 5 × 7
  13. 8
  14. 95°
  15. 50°
  16. 21st
  17. 9 times
  18. 2
  19. 17
  20. 20°
  21. 5
  22. 23
  23. 13
  24. 23
  25. 4
  26. 4
  27. 9025
  28. 24
  29. 132
  30. (x + 3)(x + 5)
  31. 120
  32. 125°
  33. 6561
  34. 3/8
  35. 15
  36. 5184
  37. 1/3
  38. 70°
  39. 23
  40. 51

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