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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 251 · 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 36th term of the AP 19, 25, 31, 37, …? (a) 235 (b) 216 (c) 229 (d) 210
  2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/9 (c) 5/36 (d) 1/11
  6. 6.How many factors does 63 have? (a) 6 (b) 7 (c) 4 (d) 5
  7. 7.What is the 27th term of the AP 15, 20, 25, 30, …? (a) 130 (b) 145 (c) 135 (d) 150
  8. 8.What is the missing term in the AP 6, 12, 18, ?, 30? (a) 23 (b) 25 (c) 30 (d) 24
  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) 15 (b) 21 (c) 14 (d) 22
  10. 10.How many factors does 66 have? (a) 8 (b) 9 (c) 7 (d) 6
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/11 (d) 1/9
  12. 12.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/8 (d) 1/4
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 17 (d) 19
  14. 14.The mean of 3 numbers is 14. When the number 6 is added to them, what is the new mean? (a) 13 (b) 12 (c) 10 (d) 14
  15. 15.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
  16. 16.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 13 (c) 15 (d) 4
  18. 18.Using (a − b)² = a² − 2ab + b², what is 56²? (a) 3146 (b) 3584 (c) 3136 (d) 4096
  19. 19.How many factors does 75 have? (a) 7 (b) 6 (c) 5 (d) 4
  20. 20.A bag has 10 blue balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 11 (c) 21 (d) 12
  21. 21.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 12 (d) 24
  22. 22.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  23. 23.What is the distance between the points (0, 9) and (12, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  24. 24.A bag has 3 black balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 4 (c) 10 (d) 2
  25. 25.What is the mean of 20, 4, 12 and 4? (a) 11 (b) 8 (c) 9 (d) 10
  26. 26.What is the mean of 12, 8, 10 and 14? (a) 13 (b) 12 (c) 10 (d) 11
  27. 27.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 170° (c) 130° (d) 10°
  28. 28.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 126 (d) 135
  29. 29.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 3 times (c) 9 times (d) 27 times
  30. 30.What is the sum of the first 5 terms of the AP 7, 10, 13, …? (a) 68 (b) 65 (c) 130 (d) 19
  31. 31.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 132 (c) 66 (d) 78
  32. 32.What is the midpoint of the line joining (0, 8) and (8, 2)? (a) (5, 4) (b) (8, 10) (c) (4, 5) (d) (4, 3)
  33. 33.3 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) 9 (b) 6 (c) 12 (d) 5
  34. 34.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 139 (d) 148
  35. 35.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 11 (b) 20 (c) 25 (d) 10
  36. 36.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 48 (c) 66 (d) 58
  37. 37.6 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) 48 (b) 24 (c) 10 (d) 30
  38. 38.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 110 (c) 121 (d) 55
  39. 39.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1849 (b) 1591 (c) 1379 (d) 1369
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 9 (d) 11

Answer key

  1. 229
  2. 88 cm
  3. 3
  4. 10
  5. 1/9
  6. 6
  7. 145
  8. 24
  9. 15
  10. 8
  11. 1/12
  12. 7/8
  13. 18
  14. 12
  15. 1/8
  16. 1/2
  17. 14
  18. 3136
  19. 6
  20. 12
  21. 24
  22. 1/3
  23. 15
  24. 5
  25. 10
  26. 11
  27. 10°
  28. 135
  29. 9 times
  30. 65
  31. 66
  32. (4, 5)
  33. 6
  34. 139
  35. 10
  36. 57
  37. 24
  38. 55
  39. 1369
  40. 9

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