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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 485 · 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 times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16
  2. 2.The mean of 6 numbers is 38. When the number 10 is added to them, what is the new mean? (a) 24 (b) 35 (c) 38 (d) 34
  3. 3.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 56 (b) 28 (c) 13 (d) 49
  4. 4.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 110 (c) 100 (d) 19
  5. 5.In a class of 21 children, 12 like tea, 12 like coffee and 8 like both. How many like only tea? (a) 9 (b) 8 (c) 12 (d) 4
  6. 6.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 400 (c) 390 (d) 399
  7. 7.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 105° (b) 15° (c) 75° (d) 285°
  8. 8.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  9. 9.What is the sum of all the whole numbers from 1 to 18? (a) 171 (b) 162 (c) 153 (d) 342
  10. 10.What is the distance between the points (9, 1) and (16, 25)? (a) 31 (b) 25 (c) 26 (d) 625
  11. 11.In which quadrant does the point (4, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  12. 12.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 81 (d) 18
  13. 13.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
  14. 14.What is the 40th term of the AP 2, 9, 16, 23, …? (a) 273 (b) 280 (c) 282 (d) 275
  15. 15.In a class of 27 children, 8 like maths, 19 like science and 4 like both. How many like neither? (a) 0 (b) 4 (c) 8 (d) 5
  16. 16.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 85° (b) 150° (c) 125° (d) 95°
  17. 17.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
  18. 18.What is the distance between the points (5, 1) and (8, 5)? (a) 5 (b) 7 (c) 25 (d) 6
  19. 19.What is the sum of the first 11 terms of the AP 8, 13, 18, …? (a) 368 (b) 363 (c) 726 (d) 58
  20. 20.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  21. 21.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  22. 22.What is the 12th term of the AP 11, 18, 25, 32, …? (a) 95 (b) 88 (c) 77 (d) 84
  23. 23.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  24. 24.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 20 (d) 240
  25. 25.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6724 (b) 6734 (c) 6404 (d) 6084
  26. 26.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) 8 (c) 14 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  28. 28.What is the mean of 11, 7, 19, 19 and 19? (a) 15 (b) 14 (c) 17 (d) 16
  29. 29.How many factors does 89 have? (a) 2 (b) 4 (c) 3 (d) 1
  30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  31. 31.What is the sum of all the whole numbers from 1 to 31? (a) 497 (b) 496 (c) 992 (d) 465
  32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
  33. 33.If a + b = 15 and ab = 56, what is a² + b²? (a) 169 (b) 113 (c) 225 (d) 337
  34. 34.A bag has 3 green, 9 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/9 (b) 1/3 (c) 9/17 (d) 8/17
  35. 35.What is the 39th term of the AP 12, 17, 22, 27, …? (a) 202 (b) 195 (c) 207 (d) 190
  36. 36.A bag has 7 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 2 (c) 8 (d) 9
  37. 37.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
  38. 38.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 36 (c) 30 (d) 12
  39. 39.What is the smallest prime factor of 33? (a) 2 (b) 11 (c) 3 (d) 1
  40. 40.In a class of 37 children, 23 like dance, 18 like music and 6 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 35 (d) 29

Answer key

  1. 17
  2. 34
  3. 49
  4. 100
  5. 4
  6. 399
  7. 105°
  8. 1/3
  9. 171
  10. 25
  11. Fourth quadrant
  12. 36
  13. 4 times
  14. 275
  15. 4
  16. 85°
  17. 1/6
  18. 5
  19. 363
  20. 21
  21. 24
  22. 88
  23. 2² × 3 × 5 × 7
  24. 120
  25. 6724
  26. 8
  27. 8
  28. 15
  29. 2
  30. 13
  31. 496
  32. 3/8
  33. 113
  34. 8/17
  35. 202
  36. 9
  37. 25 times
  38. 15
  39. 3
  40. 35

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