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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 659 · 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 sum of the first 10 terms of the AP 5, 10, 15, …? (a) 275 (b) 300 (c) 50 (d) 550
  2. 2.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 399 (b) 441 (c) 361 (d) 371
  3. 3.What is the mode of 13, 19, 15, 15, 13, 13 and 11? (a) 19 (b) 15 (c) 13 (d) 11
  4. 4.What is the midpoint of the line joining (0, 2) and (2, 12)? (a) (1, 7) (b) (1, 5) (c) (2, 14) (d) (7, 1)
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  6. 6.The mean of 8 numbers is 22. When the number 31 is added to them, what is the new mean? (a) 24 (b) 25 (c) 23 (d) 22
  7. 7.What is the mode of 2, 2, 15, 3, 4, 2 and 4? (a) 3 (b) 15 (c) 2 (d) 4
  8. 8.In which quadrant does the point (7, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  9. 9.What is the median of 23, 39, 26, 5, 29, 35 and 18? (a) 25 (b) 5 (c) 26 (d) 29
  10. 10.What is the 15th term of the AP 20, 26, 32, 38, …? (a) 90 (b) 110 (c) 104 (d) 84
  11. 11.In a class of 33 children, 18 like mangoes, 14 like bananas and 6 like both. How many like only mangoes? (a) 18 (b) 19 (c) 12 (d) 8
  12. 12.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 9 (c) 21 (d) 14
  14. 14.How many factors does 48 have? (a) 10 (b) 11 (c) 8 (d) 9
  15. 15.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  16. 16.In a class of 36 children, 15 like mangoes, 23 like bananas and 4 like both. How many like at least one of the two? (a) 34 (b) 30 (c) 36 (d) 38
  17. 17.What is the mean of 2, 2, 4 and 4? (a) 4 (b) 3 (c) 5 (d) 2
  18. 18.A drawer has lots of red, yellow, green, 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) 10 (b) 6 (c) 2 (d) 5
  19. 19.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 140° (d) 110°
  20. 20.6 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) 48 (b) 84 (c) 42 (d) 13
  21. 21.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 6 (c) 9 (d) 3
  22. 22.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
  23. 23.How many factors does 21 have? (a) 4 (b) 3 (c) 5 (d) 2
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 6/11 (c) 1/6 (d) 7/36
  25. 25.If a + b = 20 and ab = 96, what is (a − b)²? (a) 400 (b) 4 (c) 208 (d) 16
  26. 26.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 106 (d) 105
  27. 27.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
  28. 28.A bag has 4 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 6 (d) 5
  29. 29.What is the distance between the points (0, 13) and (9, 1)? (a) 16 (b) 21 (c) 225 (d) 15
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  31. 31.Using (a + b)² = a² + 2ab + b², what is 84²? (a) 7066 (b) 7056 (c) 5776 (d) 6416
  32. 32.In a class of 25 children, 19 like cricket, 13 like football and 2 like neither. How many like both? (a) 7 (b) 23 (c) 2 (d) 9
  33. 33.Two angles of a triangle are 65° and 30°. What is the third angle? (a) 115° (b) 85° (c) 150° (d) 95°
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 3 (b) 5 (c) 2 (d) 4
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/12 (c) 2/11 (d) 1/18
  36. 36.A bag has 6 yellow balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 8 (c) 7 (d) 10
  37. 37.In a class of 24 children, 7 like dance, 16 like music and 4 like both. How many like neither? (a) 4 (b) 5 (c) 1 (d) 9
  38. 38.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
  39. 39.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 10 (b) 11 (c) 9 (d) 17
  40. 40.A cuboid is 12 cm long, 4 cm wide and 4 cm high. What is its total surface area? (a) 192 sq cm (b) 448 sq cm (c) 224 sq cm (d) 112 sq cm

Answer key

  1. 275
  2. 361
  3. 13
  4. (1, 7)
  5. 4
  6. 23
  7. 2
  8. Fourth quadrant
  9. 26
  10. 104
  11. 12
  12. Third quadrant
  13. 14
  14. 10
  15. 2 × 3² × 5
  16. 34
  17. 3
  18. 6
  19. 110°
  20. 42
  21. 6
  22. 30°
  23. 4
  24. 1/6
  25. 16
  26. 105
  27. 1/3
  28. 6
  29. 15
  30. 2
  31. 7056
  32. 9
  33. 85°
  34. 4
  35. 1/18
  36. 8
  37. 5
  38. 45
  39. 10
  40. 224 sq cm

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