← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 988 · 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. 1.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
  2. 2.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 55° (c) 120° (d) 115°
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  4. 4.What is the sum of the first 7 terms of the AP 10, 13, 16, …? (a) 133 (b) 136 (c) 28 (d) 266
  5. 5.A bag has 10 blue balls and 8 white 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) 18 (c) 11 (d) 9
  6. 6.A bag has 10 green balls and 8 red 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) 18 (c) 9 (d) 11
  7. 7.What is the mean of 7, 8, 11, 6, 10 and 12? (a) 9 (b) 10 (c) 8 (d) 11
  8. 8.In a class of 23 children, 16 like tea, 16 like coffee and 1 like neither. How many like both? (a) 1 (b) 10 (c) 9 (d) 22
  9. 9.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 10 (d) 25
  10. 10.What is the 11th term of the AP 1, 7, 13, 19, …? (a) 61 (b) 60 (c) 67 (d) 66
  11. 11.In a class of 35 children, 13 like tea, 24 like coffee and 5 like both. How many like only tea? (a) 8 (b) 13 (c) 11 (d) 19
  12. 12.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 30° (b) 75° (c) 60° (d) 150°
  13. 13.What is the sum of the roots of x² − 17x + 72 = 0? (a) 17 (b) 16 (c) 18 (d) 72
  14. 14.Two angles of a triangle are 40° and 20°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 140° (d) 160°
  15. 15.What are the roots of x² − 8x + 15 = 0? (a) 1 and 15 (b) 2 and 6 (c) 1 and 7 (d) 3 and 5
  16. 16.How many factors does 81 have? (a) 3 (b) 5 (c) 4 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  18. 18.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2² × 3² (c) 2³ × 3² (d) 2⁴ × 3²
  19. 19.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) 8 (b) 15 (c) 7 (d) 14
  20. 20.What is the mean of 9, 11, 16 and 4? (a) 10 (b) 9 (c) 11 (d) 8
  21. 21.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
  22. 22.If a + b = 12 and ab = 11, what is a² + b²? (a) 122 (b) 166 (c) 133 (d) 144
  23. 23.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
  24. 24.What is the smallest prime factor of 119? (a) 7 (b) 17 (c) 1 (d) 2
  25. 25.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 10 (d) 20
  26. 26.How many factors does 98 have? (a) 4 (b) 7 (c) 6 (d) 5
  27. 27.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 30° (c) 60° (d) 120°
  28. 28.What is the 29th term of the AP 20, 29, 38, 47, …? (a) 261 (b) 272 (c) 281 (d) 252
  29. 29.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  30. 30.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 8464 (b) 8104 (c) 7744 (d) 8474
  31. 31.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 70° (c) 71° (d) 110°
  32. 32.The mean of 4 numbers is 19. When the number 24 is added to them, what is the new mean? (a) 21 (b) 19 (c) 20 (d) 22
  33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  34. 34.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 105° (b) 75° (c) 125° (d) 130°
  35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  36. 36.A drawer has lots of green and yellow 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) 5 (c) 3 (d) 4
  37. 37.If a + b = 15 and ab = 36, what is (a − b)²? (a) 153 (b) 9 (c) 225 (d) 81
  38. 38.What is the 24th term of the AP 15, 24, 33, 42, …? (a) 222 (b) 216 (c) 207 (d) 231
  39. 39.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 140° (d) 80°
  40. 40.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 65° (b) 35° (c) 150° (d) 145°

Answer key

  1. 28
  2. 55°
  3. 15
  4. 133
  5. 11
  6. 11
  7. 9
  8. 10
  9. 10
  10. 61
  11. 8
  12. 75°
  13. 17
  14. 60°
  15. 3 and 5
  16. 5
  17. 6
  18. 2³ × 3²
  19. 8
  20. 10
  21. 42
  22. 122
  23. 1/4
  24. 7
  25. 10
  26. 6
  27. 120°
  28. 272
  29. 4
  30. 8464
  31. 70°
  32. 20
  33. 20
  34. 75°
  35. 5
  36. 3
  37. 81
  38. 222
  39. 100°
  40. 35°

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad