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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 241 · 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 factors does 78 have? (a) 9 (b) 7 (c) 8 (d) 6
  2. 2.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2⁴ × 7 (d) 2 × 7³
  3. 3.In a class of 51 children, 30 like mangoes, 28 like bananas and 4 like neither. How many like both? (a) 11 (b) 47 (c) 7 (d) 4
  4. 4.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 9 sq cm (d) 36 sq cm
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/12 (c) 1/18 (d) 1/36
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 4 (d) 15
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  9. 9.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 91° (c) 90° (d) 45°
  10. 10.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 20° (b) 160° (c) 45° (d) 155°
  11. 11.What is the mean of 3, 15, 2 and 4? (a) 5 (b) 6 (c) 8 (d) 7
  12. 12.What is the mode of 8, 7, 8, 8, 12, 15 and 12? (a) 12 (b) 15 (c) 7 (d) 8
  13. 13.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  14. 14.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  15. 15.What is the 11th term of the AP 19, 23, 27, 31, …? (a) 44 (b) 40 (c) 63 (d) 59
  16. 16.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
  17. 17.A drawer has lots of yellow, red, white, green and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
  18. 18.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 42 (d) 21
  19. 19.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
  20. 20.What is the mode of 10, 4, 3, 10, 4, 4 and 19? (a) 3 (b) 19 (c) 4 (d) 10
  21. 21.How many factors does 19 have? (a) 1 (b) 2 (c) 4 (d) 3
  22. 22.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 297 (d) 276
  23. 23.A bag has 7 black balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 17 (b) 2 (c) 9 (d) 8
  24. 24.What is the 23rd term of the AP 5, 8, 11, 14, …? (a) 74 (b) 66 (c) 69 (d) 71
  25. 25.A bag has 3 yellow balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 4 (b) 5 (c) 2 (d) 6
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  27. 27.What is the 18th term of the AP 18, 25, 32, 39, …? (a) 119 (b) 144 (c) 137 (d) 126
  28. 28.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 252 (b) 272 (c) 279 (d) 259
  29. 29.In a class of 34 children, 19 like mangoes, 15 like bananas and 3 like both. How many like at least one of the two? (a) 28 (b) 32 (c) 31 (d) 34
  30. 30.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 120° (d) 100°
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  32. 32.What is the 34th term of the AP 11, 19, 27, 35, …? (a) 275 (b) 272 (c) 283 (d) 264
  33. 33.What is the mode of 17, 17, 8, 8, 3, 10 and 17? (a) 10 (b) 3 (c) 17 (d) 8
  34. 34.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  35. 35.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
  36. 36.How many factors does 60 have? (a) 10 (b) 12 (c) 11 (d) 13
  37. 37.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 55 (c) 66 (d) 110
  38. 38.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
  39. 39.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 49 (c) 84 (d) 42
  40. 40.A drawer has lots of black 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) 2 (c) 5 (d) 4

Answer key

  1. 8
  2. 2³ × 7
  3. 11
  4. 54 sq cm
  5. 1/36
  6. 10
  7. 5
  8. 13
  9. 90°
  10. 20°
  11. 6
  12. 8
  13. 1/2
  14. 1/2
  15. 59
  16. 25
  17. 6
  18. 21
  19. 154 sq cm
  20. 4
  21. 2
  22. 306
  23. 9
  24. 71
  25. 5
  26. 5
  27. 137
  28. 272
  29. 31
  30. 80°
  31. 5
  32. 275
  33. 17
  34. 60°
  35. 1/2
  36. 12
  37. 55
  38. 8 times
  39. 42
  40. 3

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