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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 679 · 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 bag has 10 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 13 (c) 4 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  3. 3.A drawer has lots of white, yellow, green 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) 4 (b) 2 (c) 8 (d) 5
  4. 4.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 1/3 (c) 1/6 (d) 5/6
  5. 5.What is the mode of 2, 14, 11, 7, 7, 7 and 14? (a) 7 (b) 14 (c) 2 (d) 11
  6. 6.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 110 (d) 66
  7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 176 sq cm
  8. 8.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 120 (b) 32 (c) 204 (d) 102
  9. 9.The mean of 3 numbers is 35. When the number 47 is added to them, what is the new mean? (a) 41 (b) 39 (c) 35 (d) 38
  10. 10.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 5/8 (d) 1/4
  11. 11.What is the median of 7, 37, 11, 4, 21, 40 and 19? (a) 4 (b) 21 (c) 11 (d) 19
  12. 12.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 2 (d) 1
  13. 13.In a class of 23 children, 12 like cricket, 11 like football and 8 like both. How many like only cricket? (a) 3 (b) 12 (c) 8 (d) 4
  14. 14.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 72 (c) 18 (d) 36
  15. 15.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
  16. 16.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 2 (c) 400 (d) 4
  17. 17.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 418 (c) 510 (d) 519
  18. 18.A canteen sells 7 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 35 (c) 28 (d) 56
  19. 19.In a class of 43 children, 21 like mangoes, 24 like bananas and 5 like neither. How many like both? (a) 38 (b) 5 (c) 7 (d) 2
  20. 20.A bag has 4 blue balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 5 (b) 7 (c) 6 (d) 2
  21. 21.A bag has 10 black balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 5 (d) 14
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 14 (d) 4
  23. 23.What is the mode of 19, 5, 19, 13, 13, 16 and 13? (a) 16 (b) 19 (c) 5 (d) 13
  24. 24.What is the distance between the points (1, 5) and (4, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  25. 25.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 66 (c) 48 (d) 57
  26. 26.Which is the correct factorisation of x² + 6x + 8? (a) (x + 1)(x + 8) (b) (x − 2)(x − 4) (c) (x + 2)(x + 4) (d) (x + 1)(x + 5)
  27. 27.In which quadrant does the point (4, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.In a class of 31 children, 22 like maths, 12 like science and 9 like both. How many like only maths? (a) 19 (b) 3 (c) 22 (d) 13
  29. 29.Which is the correct factorisation of x² + 7x + 12? (a) (x − 3)(x − 4) (b) (x + 1)(x + 12) (c) (x + 1)(x + 6) (d) (x + 3)(x + 4)
  30. 30.What is the missing term in the AP 20, 26, ?, 38, 44? (a) 31 (b) 38 (c) 32 (d) 33
  31. 31.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 441 (d) 3
  32. 32.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x + 1)(x + 56) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
  33. 33.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 20° (c) 160° (d) 340°
  34. 34.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 36 (c) 72 (d) 45
  35. 35.Two angles of a triangle are 75° and 40°. What is the third angle? (a) 115° (b) 140° (c) 65° (d) 105°
  36. 36.What is the distance between the points (3, 0) and (11, 6)? (a) 100 (b) 11 (c) 10 (d) 14
  37. 37.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  38. 38.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
  39. 39.What is the median of 23, 27, 22, 31 and 32? (a) 22 (b) 23 (c) 27 (d) 31
  40. 40.What is the mean of 10, 6, 13 and 7? (a) 10 (b) 12 (c) 8 (d) 9

Answer key

  1. 11
  2. 6
  3. 5
  4. 5/6
  5. 7
  6. 55
  7. 2464 sq cm
  8. 102
  9. 38
  10. 3/8
  11. 19
  12. 3
  13. 4
  14. 36
  15. 44 cm
  16. 4
  17. 519
  18. 28
  19. 7
  20. 6
  21. 11
  22. 15
  23. 13
  24. 5
  25. 57
  26. (x + 2)(x + 4)
  27. Fourth quadrant
  28. 13
  29. (x + 3)(x + 4)
  30. 32
  31. 9
  32. (x + 7)(x + 8)
  33. 160°
  34. 36
  35. 65°
  36. 10
  37. 1/2
  38. 2
  39. 27
  40. 9

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