← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 365 · 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 11 green balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 2 (c) 7 (d) 12
  2. 2.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 125 times (d) 25 times
  3. 3.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 225 (c) 210 (d) 120
  4. 4.The mean of 6 numbers is 39. When the number 60 is added to them, what is the new mean? (a) 43 (b) 39 (c) 42 (d) 41
  5. 5.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 439 (c) 429 (d) 438
  6. 6.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
  7. 7.What is the sum of the first 12 terms of the AP 10, 12, 14, …? (a) 264 (b) 252 (c) 32 (d) 504
  8. 8.What is the missing term in the AP 18, ?, 34, 42, 50? (a) 26 (b) 27 (c) 25 (d) 34
  9. 9.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 50° (b) 65° (c) 115° (d) 230°
  10. 10.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) 14 (c) 7 (d) 8
  11. 11.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
  12. 12.A bag has 4 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 2 (c) 6 (d) 13
  13. 13.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
  14. 14.What is the median of 1, 31, 5, 17, 15, 35 and 23? (a) 15 (b) 17 (c) 23 (d) 18
  15. 15.How many factors does 120 have? (a) 16 (b) 15 (c) 17 (d) 14
  16. 16.What is the sum of the roots of x² − 12x + 27 = 0? (a) 12 (b) 27 (c) 13 (d) 11
  17. 17.A bag has 7 yellow, 7 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 7/8 (b) 1/3 (c) 15/16 (d) 1/8
  18. 18.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 50° (d) 80°
  19. 19.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 90° (b) 135° (c) 46° (d) 45°
  20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 72 (d) 36
  21. 21.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 41 (b) 460 (c) 250 (d) 230
  22. 22.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 3/8 (d) 5/8
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 85° (b) 95° (c) 10° (d) 190°
  25. 25.What is the distance between the points (0, 20) and (9, 8)? (a) 15 (b) 225 (c) 21 (d) 16
  26. 26.A bag has 9 red, 3 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 7/16 (c) 5/8 (d) 9/16
  27. 27.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 20 (c) 10 (d) 15
  28. 28.What is the mode of 3, 7, 7, 3, 11, 16 and 7? (a) 3 (b) 11 (c) 7 (d) 16
  29. 29.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  30. 30.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
  31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  32. 32.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 40° (b) 140° (c) 100° (d) 120°
  33. 33.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 44 cm (d) 88 cm
  34. 34.If a + b = 13 and ab = 36, what is a² + b²? (a) 241 (b) 97 (c) 169 (d) 133
  35. 35.What is the midpoint of the line joining (5, 5) and (13, 7)? (a) (18, 12) (b) (9, 6) (c) (4, 1) (d) (6, 9)
  36. 36.What is the distance between the points (9, 7) and (17, 22)? (a) 18 (b) 17 (c) 23 (d) 289
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  38. 38.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  39. 39.In a class of 27 children, 14 like tea, 17 like coffee and 10 like both. How many like only tea? (a) 4 (b) 7 (c) 14 (d) 10
  40. 40.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 15 (c) 20 (d) 7

Answer key

  1. 12
  2. 25 times
  3. 105
  4. 42
  5. 438
  6. 2/3
  7. 252
  8. 26
  9. 115°
  10. 8
  11. 1/2
  12. 6
  13. 1386 sq cm
  14. 17
  15. 16
  16. 12
  17. 7/8
  18. 50°
  19. 45°
  20. 36
  21. 230
  22. 3/8
  23. 25
  24. 95°
  25. 15
  26. 9/16
  27. 10
  28. 7
  29. 24
  30. 37
  31. 13
  32. 40°
  33. 88 cm
  34. 97
  35. (9, 6)
  36. 17
  37. 15
  38. 78
  39. 4
  40. 10

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