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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 477 · 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.What is the mean of 15, 20, 16 and 5? (a) 15 (b) 16 (c) 13 (d) 14
  2. 2.9 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
  3. 3.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
  4. 4.What is the sum of the roots of x² − 13x + 40 = 0? (a) 12 (b) 13 (c) 40 (d) 14
  5. 5.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 5 (d) 4
  6. 6.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x − 5)(x − 8) (c) (x + 1)(x + 40) (d) (x + 5)(x + 8)
  7. 7.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
  8. 8.Two angles of a triangle are 25° and 125°. What is the third angle? (a) 155° (b) 30° (c) 150° (d) 55°
  9. 9.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 144 (c) 78 (d) 66
  10. 10.What is the median of 36, 5, 16, 14, 4, 2 and 32? (a) 16 (b) 5 (c) 15 (d) 14
  11. 11.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 27 (b) 34 (c) 29 (d) 28
  12. 12.How many factors does 57 have? (a) 2 (b) 3 (c) 4 (d) 5
  13. 13.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 32 (c) 11 (d) 28
  14. 14.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 2 (d) 11
  16. 16.A bag has 11 green balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 23 (c) 12 (d) 13
  17. 17.What is the mean of 5, 13, 20, 12, 16 and 6? (a) 14 (b) 13 (c) 11 (d) 12
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  19. 19.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 7 (d) 5
  20. 20.How many factors does 70 have? (a) 8 (b) 6 (c) 9 (d) 7
  21. 21.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 256 (b) 576 (c) 416 (d) 586
  22. 22.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x + 7)(x + 8) (c) (x − 7)(x − 8) (d) (x + 1)(x + 56)
  23. 23.A bag has 9 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 2 (c) 16 (d) 11
  24. 24.What is the mode of 4, 14, 9, 16, 9, 9 and 16? (a) 16 (b) 14 (c) 9 (d) 4
  25. 25.In a class of 33 children, 20 like mangoes, 15 like bananas and 11 like both. How many like neither? (a) 20 (b) 9 (c) 10 (d) 11
  26. 26.In a class of 24 children, 17 like tea, 11 like coffee and 3 like neither. How many like both? (a) 7 (b) 21 (c) 4 (d) 3
  27. 27.In a class of 49 children, 22 like cricket, 19 like football and 2 like both. How many like only cricket? (a) 17 (b) 22 (c) 20 (d) 30
  28. 28.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 22 (d) 15
  29. 29.In a class of 38 children, 24 like cricket, 18 like football and 1 like neither. How many like both? (a) 37 (b) 4 (c) 5 (d) 1
  30. 30.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 150° (b) 75° (c) 135° (d) 105°
  31. 31.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 3 (d) 2
  32. 32.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 127 (c) 118 (d) 136
  33. 33.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
  34. 34.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 128 (b) 144 (c) 256 (d) 30
  35. 35.Using (a + b)² = a² + 2ab + b², what is 104²? (a) 9216 (b) 10816 (c) 10826 (d) 10016
  36. 36.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
  37. 37.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 552 (c) 440 (d) 543
  38. 38.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
  39. 39.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/6 (d) 1/3
  40. 40.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 18 (c) 9 (d) 36

Answer key

  1. 14
  2. 36
  3. 1/2
  4. 13
  5. 5
  6. (x + 5)(x + 8)
  7. 2464 sq cm
  8. 30°
  9. 66
  10. 14
  11. 28
  12. 4
  13. 28
  14. Fourth quadrant
  15. 11
  16. 13
  17. 12
  18. 17
  19. 5
  20. 8
  21. 576
  22. (x + 7)(x + 8)
  23. 11
  24. 9
  25. 9
  26. 7
  27. 20
  28. 15
  29. 5
  30. 75°
  31. 3
  32. 127
  33. 5
  34. 128
  35. 10816
  36. 176 cm
  37. 552
  38. 40°
  39. 1/6
  40. 18

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