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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 569 · 40 questions
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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 circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
  2. 2.The mean of 9 numbers is 36. When the number 26 is added to them, what is the new mean? (a) 31 (b) 36 (c) 35 (d) 34
  3. 3.What is the 19th term of the AP 16, 25, 34, 43, …? (a) 171 (b) 178 (c) 162 (d) 187
  4. 4.What is the distance between the points (1, 6) and (9, 12)? (a) 14 (b) 10 (c) 100 (d) 11
  5. 5.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  6. 6.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
  7. 7.What is the median of 5, 23, 35, 21, 26, 28 and 38? (a) 26 (b) 23 (c) 28 (d) 21
  8. 8.What is the median of 11, 2, 22, 27, 37, 10 and 7? (a) 11 (b) 22 (c) 27 (d) 10
  9. 9.The mean of 8 numbers is 40. When the number 58 is added to them, what is the new mean? (a) 43 (b) 40 (c) 42 (d) 49
  10. 10.A bag has 8 red, 4 white and 7 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 8/19 (b) 12/19 (c) 1/3 (d) 11/19
  11. 11.A bag has 5 blue balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 6 (c) 7 (d) 2
  12. 12.What is the 19th term of the AP 13, 21, 29, 37, …? (a) 165 (b) 144 (c) 152 (d) 157
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  14. 14.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
  15. 15.What is the midpoint of the line joining (3, 17) and (15, 7)? (a) (12, 9) (b) (6, 5) (c) (18, 24) (d) (9, 12)
  16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
  17. 17.What is the midpoint of the line joining (1, 10) and (13, 12)? (a) (6, 1) (b) (11, 7) (c) (14, 22) (d) (7, 11)
  18. 18.What is the mode of 19, 8, 19, 19, 12, 8 and 7? (a) 8 (b) 19 (c) 12 (d) 7
  19. 19.Which term of the AP 20, 26, 32, 38, … is 134? (a) 22nd (b) 19th (c) 20th (d) 21st
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 7 (d) 5
  21. 21.How many factors does 24 have? (a) 8 (b) 6 (c) 9 (d) 7
  22. 22.What is the 21st term of the AP 17, 19, 21, 23, …? (a) 42 (b) 40 (c) 59 (d) 57
  23. 23.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
  24. 24.How many factors does 47 have? (a) 2 (b) 4 (c) 3 (d) 1
  25. 25.What is the smallest prime factor of 39? (a) 3 (b) 1 (c) 13 (d) 2
  26. 26.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 3/8 (d) 1/4
  27. 27.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
  28. 28.A drawer has lots of yellow, green, red, white and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 2 (c) 5 (d) 10
  29. 29.Which term of the AP 2, 8, 14, 20, … is 80? (a) 13th (b) 15th (c) 16th (d) 14th
  30. 30.A bag has 4 blue balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 5 (d) 9
  31. 31.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 6)(x + 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
  32. 32.In a class of 29 children, 13 like dance, 18 like music and 5 like neither. How many like both? (a) 7 (b) 5 (c) 2 (d) 24
  33. 33.A bag has 3 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 4 (c) 6 (d) 5
  34. 34.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 44 cm (d) 88 cm
  35. 35.In a class of 21 children, 7 like tea, 10 like coffee and 3 like both. How many like only tea? (a) 7 (b) 4 (c) 3 (d) 11
  36. 36.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 4 (d) 6
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 6/11 (d) 1/6
  38. 38.What is the median of 18, 25, 10, 12 and 39? (a) 18 (b) 25 (c) 10 (d) 12
  39. 39.What is the mode of 4, 1, 1, 1, 5, 5 and 7? (a) 1 (b) 4 (c) 7 (d) 5
  40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11

Answer key

  1. 176 cm
  2. 35
  3. 178
  4. 10
  5. 2 × 3 × 7
  6. 1/2
  7. 26
  8. 11
  9. 42
  10. 11/19
  11. 7
  12. 157
  13. 10
  14. 7
  15. (9, 12)
  16. 88 cm
  17. (7, 11)
  18. 19
  19. 20th
  20. 6
  21. 8
  22. 57
  23. 1/3
  24. 2
  25. 3
  26. 3/4
  27. 1/2
  28. 6
  29. 14th
  30. 6
  31. (x + 6)(x + 7)
  32. 7
  33. 5
  34. 88 cm
  35. 4
  36. 4
  37. 1/6
  38. 18
  39. 1
  40. 1/36

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