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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 272 · 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 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 17 (d) 16
  2. 2.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  3. 3.A drawer has lots of white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 2 (d) 4
  4. 4.What is the midpoint of the line joining (6, 4) and (18, 8)? (a) (6, 12) (b) (24, 12) (c) (6, 2) (d) (12, 6)
  5. 5.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 56 (d) 36
  6. 6.In which quadrant does the point (8, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  8. 8.What is the median of 19, 30, 38, 32, 31, 21 and 27? (a) 31 (b) 32 (c) 30 (d) 27
  9. 9.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 29 (c) 296 (d) 148
  10. 10.What is the mean of 2, 13, 17, 15 and 3? (a) 9 (b) 12 (c) 10 (d) 11
  11. 11.A bag has 9 red balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 10 (c) 2 (d) 13
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 78? (a) 6 (b) 8 (c) 7 (d) 5
  13. 13.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 28 (d) 16
  14. 14.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 154 (c) 145 (d) 146
  15. 15.What is the median of 7, 22, 28, 31, 12, 20 and 39? (a) 31 (b) 20 (c) 28 (d) 22
  16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
  17. 17.What is the 15th term of the AP 3, 5, 7, 9, …? (a) 28 (b) 33 (c) 30 (d) 31
  18. 18.How many prime numbers are there between 10 and 40? (a) 10 (b) 9 (c) 8 (d) 7
  19. 19.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  21. 21.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
  22. 22.A drawer has lots of black, green, yellow 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) 8 (c) 5 (d) 2
  23. 23.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 25 (c) 20 (d) 120
  24. 24.How many factors does 29 have? (a) 3 (b) 1 (c) 2 (d) 4
  25. 25.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 66 (d) 121
  26. 26.What is the mean of 14, 10, 13, 3, 12 and 14? (a) 12 (b) 11 (c) 10 (d) 13
  27. 27.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) 14 (b) 15 (c) 7 (d) 8
  28. 28.What is the distance between the points (5, 4) and (13, 10)? (a) 10 (b) 100 (c) 11 (d) 14
  29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 1/9 (c) 3/11 (d) 1/12
  30. 30.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 156 (c) 169 (d) 91
  31. 31.Which term of the AP 13, 19, 25, 31, … is 55? (a) 8th (b) 10th (c) 9th (d) 7th
  32. 32.What is the midpoint of the line joining (9, 2) and (11, 8)? (a) (20, 10) (b) (5, 10) (c) (10, 5) (d) (1, 3)
  33. 33.A bag has 8 yellow balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 2 (c) 9 (d) 12
  34. 34.What is the sum of all the whole numbers from 1 to 56? (a) 1568 (b) 1540 (c) 3192 (d) 1596
  35. 35.What is the median of 39, 38, 29, 3 and 13? (a) 30 (b) 38 (c) 29 (d) 13
  36. 36.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
  37. 37.How many factors does 15 have? (a) 4 (b) 3 (c) 5 (d) 2
  38. 38.The mean of 5 numbers is 38. When the number 26 is added to them, what is the new mean? (a) 37 (b) 38 (c) 36 (d) 32
  39. 39.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 60 (d) 20
  40. 40.What is the 28th term of the AP 6, 10, 14, 18, …? (a) 108 (b) 118 (c) 114 (d) 112

Answer key

  1. 17
  2. 1/3
  3. 3
  4. (12, 6)
  5. 28
  6. Fourth quadrant
  7. 6
  8. 30
  9. 148
  10. 10
  11. 11
  12. 7
  13. 28
  14. 145
  15. 22
  16. 1/9
  17. 31
  18. 8
  19. 60°
  20. 15
  21. 220 cm
  22. 5
  23. 120
  24. 2
  25. 55
  26. 11
  27. 8
  28. 10
  29. 1/12
  30. 78
  31. 8th
  32. (10, 5)
  33. 10
  34. 1596
  35. 29
  36. 616 sq cm
  37. 4
  38. 36
  39. 60
  40. 114

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