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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 712 · 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 90 and 100? (a) 3 (b) 2 (c) 1 (d) 0
  2. 2.If a + b = 11 and ab = 30, what is a² + b²? (a) 91 (b) 181 (c) 61 (d) 121
  3. 3.If a + b = 7 and ab = 6, what is a² + b²? (a) 61 (b) 49 (c) 37 (d) 43
  4. 4.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 42 (d) 28
  5. 5.What is the 12th term of the AP 10, 14, 18, 22, …? (a) 58 (b) 44 (c) 54 (d) 48
  6. 6.In a class of 31 children, 14 like tea, 20 like coffee and 8 like both. How many like only tea? (a) 6 (b) 14 (c) 12 (d) 11
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  8. 8.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
  9. 9.How many factors does 72 have? (a) 10 (b) 13 (c) 12 (d) 11
  10. 10.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
  11. 11.What is the distance between the points (4, 8) and (8, 11)? (a) 25 (b) 5 (c) 6 (d) 7
  12. 12.What is the median of 19, 3, 22, 29, 10, 5 and 11? (a) 29 (b) 10 (c) 19 (d) 11
  13. 13.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 60 (b) 120 (c) 16 (d) 65
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 7 (b) 5 (c) 6 (d) 8
  16. 16.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 79 (d) 80
  17. 17.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3146 (b) 4096 (c) 3584 (d) 3136
  18. 18.What is the 10th term of the AP 20, 26, 32, 38, …? (a) 60 (b) 54 (c) 74 (d) 80
  19. 19.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3721 (b) 3481 (c) 3731 (d) 3601
  20. 20.A bag has 5 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 7 (b) 6 (c) 2 (d) 8
  21. 21.What is the sum of the first 10 terms of the AP 8, 10, 12, …? (a) 26 (b) 340 (c) 180 (d) 170
  22. 22.What is the midpoint of the line joining (7, 8) and (15, 18)? (a) (13, 11) (b) (4, 5) (c) (22, 26) (d) (11, 13)
  23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 21 (d) 28
  24. 24.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 85° (c) 95° (d) 5°
  25. 25.What is the median of 31, 35, 38, 16 and 23? (a) 38 (b) 35 (c) 23 (d) 31
  26. 26.What is the mode of 3, 9, 16, 16, 3, 4 and 16? (a) 16 (b) 3 (c) 4 (d) 9
  27. 27.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  29. 29.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 125° (c) 25° (d) 155°
  30. 30.What is the smallest prime factor of 187? (a) 17 (b) 11 (c) 1 (d) 2
  31. 31.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 589 (c) 579 (d) 588
  32. 32.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  34. 34.What is the midpoint of the line joining (2, 9) and (4, 19)? (a) (6, 28) (b) (1, 5) (c) (14, 3) (d) (3, 14)
  35. 35.If a + b = 15 and ab = 54, what is a² + b²? (a) 171 (b) 225 (c) 117 (d) 333
  36. 36.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 15 (c) 7 (d) 10
  37. 37.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 33 (c) 11 (d) 99
  38. 38.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 21 (d) 42
  39. 39.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
  40. 40.In a class of 36 children, 25 like cricket, 19 like football and 12 like both. How many like neither? (a) 5 (b) 4 (c) 16 (d) 12

Answer key

  1. 1
  2. 61
  3. 37
  4. 21
  5. 54
  6. 6
  7. 5
  8. 44 cm
  9. 12
  10. 2
  11. 5
  12. 11
  13. Second quadrant
  14. 60
  15. 7
  16. 79
  17. 3136
  18. 74
  19. 3721
  20. 7
  21. 170
  22. (11, 13)
  23. 22
  24. 95°
  25. 31
  26. 16
  27. 20°
  28. 25
  29. 25°
  30. 11
  31. 588
  32. 96 sq cm
  33. 20
  34. (3, 14)
  35. 117
  36. 10
  37. 33
  38. 21
  39. 110
  40. 4

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