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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 949 · 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.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 124 (d) 114
  2. 2.Which is the correct factorisation of x² + 13x + 40? (a) (x − 5)(x − 8) (b) (x + 1)(x + 12) (c) (x + 5)(x + 8) (d) (x + 1)(x + 40)
  3. 3.What is the midpoint of the line joining (7, 2) and (13, 12)? (a) (7, 10) (b) (3, 5) (c) (10, 7) (d) (20, 14)
  4. 4.A bag has 10 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 11 (c) 16 (d) 12
  5. 5.What is the sum of the first 8 terms of the AP 8, 13, 18, …? (a) 204 (b) 43 (c) 408 (d) 224
  6. 6.A bag has 8 red balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 18 (c) 2 (d) 10
  7. 7.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 88 cm (d) 176 cm
  8. 8.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 69 (c) 66 (d) 22
  9. 9.What is the median of 15, 5, 38, 1 and 14? (a) 14 (b) 38 (c) 5 (d) 15
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 20 (d) 21
  11. 11.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/6 (c) 5/36 (d) 1/11
  13. 13.What is the distance between the points (3, 11) and (7, 8)? (a) 7 (b) 5 (c) 6 (d) 25
  14. 14.What is the mode of 12, 16, 12, 16, 10, 9 and 12? (a) 12 (b) 16 (c) 10 (d) 9
  15. 15.A bag has 8 white, 2 red and 5 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/15 (b) 2/3 (c) 1/3 (d) 11/15
  16. 16.A bag has 3 red balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 10 (c) 2 (d) 8
  17. 17.If a + b = 9 and ab = 18, what is (a − b)²? (a) 81 (b) 3 (c) 45 (d) 9
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
  19. 19.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 1 and 16 (c) 1 and 72 (d) 2 and 36
  20. 20.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  21. 21.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 7 (b) 16 (c) 12 (d) 24
  22. 22.The mean of 8 numbers is 40. When the number 49 is added to them, what is the new mean? (a) 42 (b) 43 (c) 40 (d) 41
  23. 23.What is the distance between the points (0, 21) and (12, 5)? (a) 21 (b) 28 (c) 20 (d) 400
  24. 24.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 60° (d) 121°
  25. 25.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 40° (c) 140° (d) 220°
  26. 26.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 2 (d) 7
  27. 27.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 72 (c) 17 (d) 73
  28. 28.A bag has 9 yellow balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 11 (b) 2 (c) 15 (d) 10
  29. 29.In a class of 30 children, 20 like cricket, 11 like football and 3 like both. How many like at least one of the two? (a) 25 (b) 31 (c) 28 (d) 30
  30. 30.In which quadrant does the point (2, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  31. 31.A bag has 5 blue balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 14 (c) 7 (d) 6
  32. 32.If a + b = 6 and ab = 8, what is a² + b²? (a) 52 (b) 28 (c) 20 (d) 36
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 19 (c) 20 (d) 8
  34. 34.In a class of 44 children, 27 like mangoes, 25 like bananas and 9 like both. How many like at least one of the two? (a) 43 (b) 34 (c) 52 (d) 44
  35. 35.What is the mode of 20, 17, 9, 13, 9, 13 and 9? (a) 17 (b) 9 (c) 13 (d) 20
  36. 36.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  37. 37.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/4 (c) 1/7 (d) 7/8
  38. 38.What are the roots of x² − 6x + 8 = 0? (a) 1 and 8 (b) 2 and 5 (c) 2 and 4 (d) 1 and 5
  39. 39.What is the midpoint of the line joining (1, 4) and (9, 6)? (a) (4, 1) (b) (5, 5) (c) (6, 5) (d) (10, 10)
  40. 40.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 20 (c) 25 (d) 10

Answer key

  1. 123
  2. (x + 5)(x + 8)
  3. (10, 7)
  4. 12
  5. 204
  6. 10
  7. 88 cm
  8. 66
  9. 14
  10. 20
  11. 7
  12. 5/36
  13. 5
  14. 12
  15. 2/3
  16. 8
  17. 9
  18. 5
  19. 8 and 9
  20. 120
  21. 12
  22. 41
  23. 20
  24. 120°
  25. 40°
  26. 7
  27. 72
  28. 11
  29. 28
  30. Fourth quadrant
  31. 7
  32. 20
  33. 19
  34. 43
  35. 9
  36. 24
  37. 1/8
  38. 2 and 4
  39. (5, 5)
  40. 10

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