← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 564 · 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 team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 66 (c) 24 (d) 132
  2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
  3. 3.What is the missing term in the AP 20, 23, 26, ?, 32? (a) 30 (b) 28 (c) 32 (d) 29
  4. 4.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 16° (c) 15° (d) 195°
  5. 5.In a class of 28 children, 11 like maths, 16 like science and 3 like neither. How many like both? (a) 1 (b) 25 (c) 2 (d) 3
  6. 6.A bag has 4 white, 5 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/4 (b) 1/4 (c) 13/16 (d) 1/3
  7. 7.What is the sum of the first 6 terms of the AP 6, 7, 8, …? (a) 54 (b) 102 (c) 11 (d) 51
  8. 8.How many factors does 107 have? (a) 4 (b) 1 (c) 2 (d) 3
  9. 9.A bag has 4 white balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 11 (d) 14
  10. 10.A drawer has lots of blue, red, black, white 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) 5 (b) 10 (c) 6 (d) 2
  11. 11.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 420 (b) 210 (c) 400 (d) 39
  12. 12.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
  13. 13.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 5 (b) 4 (c) 7 (d) 6
  14. 14.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 130° (c) 50° (d) 135°
  15. 15.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 21 (c) 42 (d) 24
  16. 16.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 121 (c) 122 (d) 112
  17. 17.How many factors does 12 have? (a) 4 (b) 6 (c) 7 (d) 5
  18. 18.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 17 (c) 9 (d) 25
  19. 19.Two angles of a triangle are 55° and 25°. What is the third angle? (a) 80° (b) 125° (c) 100° (d) 155°
  20. 20.A bag has 8 red balls and 4 black 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) 5 (c) 2 (d) 9
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 15 (d) 3
  22. 22.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 6375 (b) 5625 (c) 7225 (d) 5635
  23. 23.If a + b = 17 and ab = 70, what is a² + b²? (a) 149 (b) 289 (c) 429 (d) 219
  24. 24.What is the midpoint of the line joining (6, 4) and (18, 16)? (a) (12, 10) (b) (6, 6) (c) (10, 12) (d) (24, 20)
  25. 25.A bag has 7 red balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 8 (c) 17 (d) 2
  26. 26.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
  27. 27.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 7/8 (d) 1/7
  28. 28.A bag has 8 red, 9 green and 9 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 9/17 (b) 1/3 (c) 17/26 (d) 9/26
  29. 29.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 378 (b) 729 (c) 53 (d) 756
  30. 30.What is the 36th term of the AP 6, 12, 18, 24, …? (a) 217 (b) 210 (c) 216 (d) 222
  31. 31.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 130° (d) 150°
  32. 32.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 171 (c) 153 (d) 162
  33. 33.A bag has 9 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 2 (c) 17 (d) 11
  34. 34.What is the 33rd term of the AP 4, 8, 12, 16, …? (a) 132 (b) 133 (c) 128 (d) 136
  35. 35.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 84 (c) 48 (d) 13
  36. 36.What is the median of 4, 12, 18, 37 and 14? (a) 14 (b) 12 (c) 18 (d) 17
  37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  38. 38.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 225 (c) 216 (d) 222
  39. 39.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 70° (d) 110°
  40. 40.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13

Answer key

  1. 66
  2. 1/36
  3. 29
  4. 15°
  5. 2
  6. 3/4
  7. 51
  8. 2
  9. 11
  10. 6
  11. 400
  12. 3 and 5
  13. 6
  14. 130°
  15. 21
  16. 121
  17. 6
  18. 9
  19. 100°
  20. 9
  21. 14
  22. 5625
  23. 149
  24. (12, 10)
  25. 11
  26. 154 sq cm
  27. 1/8
  28. 9/26
  29. 729
  30. 216
  31. 80°
  32. 171
  33. 11
  34. 132
  35. 42
  36. 14
  37. 120
  38. 225
  39. 110°
  40. 11

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