← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 283 · 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.What is the distance between the points (2, 7) and (17, 15)? (a) 17 (b) 23 (c) 289 (d) 18
  2. 2.What is the missing term in the AP 16, ?, 24, 28, 32? (a) 19 (b) 20 (c) 24 (d) 21
  3. 3.How many prime numbers are there between 60 and 80? (a) 4 (b) 5 (c) 6 (d) 7
  4. 4.What is the mode of 3, 11, 4, 11, 10, 4 and 4? (a) 11 (b) 3 (c) 4 (d) 10
  5. 5.What is the sum of all the whole numbers from 1 to 64? (a) 4160 (b) 2016 (c) 2048 (d) 2080
  6. 6.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 40° (d) 20°
  7. 7.What is the prime factorisation of 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2³ × 5 (d) 2 × 5³
  8. 8.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  9. 9.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 22 (c) 15 (d) 14
  10. 10.The mean of 6 numbers is 17. When the number 45 is added to them, what is the new mean? (a) 31 (b) 22 (c) 17 (d) 21
  11. 11.In a class of 26 children, 11 like mangoes, 18 like bananas and 3 like neither. How many like both? (a) 3 (b) 6 (c) 23 (d) 7
  12. 12.In a class of 43 children, 20 like cricket, 26 like football and 9 like neither. How many like both? (a) 3 (b) 9 (c) 34 (d) 12
  13. 13.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 56 (d) 16
  14. 14.What is the 32nd term of the AP 19, 25, 31, 37, …? (a) 186 (b) 192 (c) 211 (d) 205
  15. 15.Two angles of a triangle are 35° and 25°. What is the exterior angle at the third corner? (a) 145° (b) 155° (c) 120° (d) 60°
  16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 1/12 (c) 2/11 (d) 1/11
  17. 17.A drawer has lots of black and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 3 (d) 2
  18. 18.The mean of 4 numbers is 40. When the number 20 is added to them, what is the new mean? (a) 30 (b) 40 (c) 36 (d) 37
  19. 19.What is the product of the roots of x² − 16x + 63 = 0? (a) 16 (b) 64 (c) 62 (d) 63
  20. 20.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 235° (b) 55° (c) 110° (d) 125°
  21. 21.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3
  22. 22.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
  23. 23.In a class of 28 children, 19 like tea, 11 like coffee and 5 like both. How many like neither? (a) 8 (b) 5 (c) 4 (d) 3
  24. 24.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
  25. 25.The mean of 7 numbers is 19. When the number 51 is added to them, what is the new mean? (a) 19 (b) 23 (c) 24 (d) 35
  26. 26.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 5 (d) 2
  27. 27.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 70° (c) 20° (d) 80°
  28. 28.In a class of 25 children, 12 like dance, 12 like music and 8 like neither. How many like both? (a) 8 (b) 17 (c) 6 (d) 7
  29. 29.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
  30. 30.How many factors does 28 have? (a) 6 (b) 7 (c) 5 (d) 4
  31. 31.In a class of 39 children, 13 like mangoes, 24 like bananas and 4 like both. How many like at least one of the two? (a) 39 (b) 37 (c) 29 (d) 33
  32. 32.In a class of 31 children, 14 like tea, 26 like coffee and 11 like both. How many like only tea? (a) 3 (b) 15 (c) 5 (d) 14
  33. 33.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 156 (d) 169
  34. 34.What is the distance between the points (5, 9) and (8, 5)? (a) 7 (b) 6 (c) 25 (d) 5
  35. 35.What is the mean of 19, 15, 13 and 5? (a) 12 (b) 14 (c) 13 (d) 15
  36. 36.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 110° (c) 150° (d) 70°
  37. 37.What is the mean of 2, 7, 17 and 18? (a) 12 (b) 13 (c) 11 (d) 10
  38. 38.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 120 (c) 20 (d) 25
  39. 39.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 90° (b) 160° (c) 110° (d) 20°
  40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 5/36 (d) 1/11

Answer key

  1. 17
  2. 20
  3. 5
  4. 4
  5. 2080
  6. 20°
  7. 2³ × 5
  8. 2
  9. 15
  10. 21
  11. 6
  12. 12
  13. 56
  14. 205
  15. 60°
  16. 1/18
  17. 3
  18. 36
  19. 63
  20. 125°
  21. 1/2
  22. 25 times
  23. 3
  24. 44 cm
  25. 23
  26. 5
  27. 80°
  28. 7
  29. 51
  30. 6
  31. 33
  32. 3
  33. 78
  34. 5
  35. 13
  36. 70°
  37. 11
  38. 120
  39. 20°
  40. 5/36

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