← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 362 · 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.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 6 (d) 5
  2. 2.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
  3. 3.What is the mean of 5, 4, 5, 5 and 16? (a) 6 (b) 9 (c) 8 (d) 7
  4. 4.A cube has edges of 8 cm. What is its volume? (a) 384 cu cm (b) 24 cu cm (c) 512 cu cm (d) 256 cu cm
  5. 5.What is the median of 20, 32, 30, 18, 3, 4 and 7? (a) 7 (b) 18 (c) 19 (d) 20
  6. 6.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
  7. 7.Two angles of a triangle are 60° and 85°. What is the third angle? (a) 145° (b) 120° (c) 95° (d) 35°
  8. 8.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
  9. 9.What is the 12th term of the AP 20, 28, 36, 44, …? (a) 116 (b) 96 (c) 108 (d) 88
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  11. 11.Two angles of a triangle are 40° and 25°. What is the third angle? (a) 65° (b) 140° (c) 155° (d) 115°
  12. 12.What is the product of the roots of x² − 17x + 72 = 0? (a) 73 (b) 17 (c) 72 (d) 71
  13. 13.What is the 37th term of the AP 12, 15, 18, 21, …? (a) 123 (b) 108 (c) 111 (d) 120
  14. 14.7 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 56 (c) 11 (d) 35
  15. 15.What is the midpoint of the line joining (4, 10) and (6, 16)? (a) (5, 13) (b) (10, 26) (c) (1, 3) (d) (13, 5)
  16. 16.In a class of 35 children, 22 like cricket, 15 like football and 3 like both. How many like only cricket? (a) 20 (b) 12 (c) 22 (d) 19
  17. 17.If a + b = 14 and ab = 45, what is a² + b²? (a) 286 (b) 196 (c) 151 (d) 106
  18. 18.In a class of 21 children, 16 like tea, 9 like coffee and 2 like neither. How many like both? (a) 4 (b) 19 (c) 2 (d) 6
  19. 19.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  20. 20.What is the mode of 13, 20, 20, 20, 5, 13 and 15? (a) 20 (b) 13 (c) 5 (d) 15
  21. 21.A bag has 12 red balls and 10 white 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) 2 (c) 22 (d) 13
  22. 22.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 135° (c) 145° (d) 100°
  23. 23.In a class of 29 children, 20 like tea, 18 like coffee and 12 like both. How many like at least one of the two? (a) 14 (b) 26 (c) 29 (d) 38
  24. 24.What is the mode of 18, 18, 12, 12, 13, 12 and 17? (a) 17 (b) 13 (c) 18 (d) 12
  25. 25.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2499 (b) 2601 (c) 2401 (d) 2411
  26. 26.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 27 (c) 9 (d) 30
  27. 27.In a class of 41 children, 24 like tea, 14 like coffee and 6 like both. How many like neither? (a) 15 (b) 3 (c) 6 (d) 9
  28. 28.Using (a − b)² = a² − 2ab + b², what is 77²? (a) 5939 (b) 6889 (c) 6391 (d) 5929
  29. 29.Two angles of a triangle are 30° and 70°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 100° (d) 110°
  30. 30.What is the 21st term of the AP 11, 15, 19, 23, …? (a) 84 (b) 95 (c) 91 (d) 80
  31. 31.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 31 (d) 2
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
  33. 33.The mean of 8 numbers is 18. When the number 45 is added to them, what is the new mean? (a) 22 (b) 21 (c) 20 (d) 18
  34. 34.A cuboid is 7 cm long, 3 cm wide and 10 cm high. What is its total surface area? (a) 242 sq cm (b) 121 sq cm (c) 210 sq cm (d) 484 sq cm
  35. 35.What is the distance between the points (6, 32) and (13, 8)? (a) 31 (b) 625 (c) 25 (d) 26
  36. 36.What is the sum of the first 6 terms of the AP 2, 3, 4, …? (a) 30 (b) 54 (c) 27 (d) 7
  37. 37.In a class of 28 children, 6 like mangoes, 17 like bananas and 2 like both. How many like only mangoes? (a) 4 (b) 11 (c) 15 (d) 6
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 100 (d) 45
  39. 39.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
  40. 40.What is the midpoint of the line joining (6, 2) and (18, 14)? (a) (6, 6) (b) (12, 8) (c) (24, 16) (d) (8, 12)

Answer key

  1. 5
  2. 1/2
  3. 7
  4. 512 cu cm
  5. 18
  6. 9 times
  7. 35°
  8. 5/36
  9. 108
  10. 17
  11. 115°
  12. 72
  13. 120
  14. 28
  15. (5, 13)
  16. 19
  17. 106
  18. 6
  19. 2² × 3 × 5 × 7
  20. 20
  21. 13
  22. 100°
  23. 26
  24. 12
  25. 2401
  26. 27
  27. 9
  28. 5929
  29. 100°
  30. 91
  31. 3
  32. 1/36
  33. 21
  34. 242 sq cm
  35. 25
  36. 27
  37. 4
  38. 45
  39. 2
  40. (12, 8)

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