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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 768 · 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.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
  3. 3.A bag has 5 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 7 (c) 6 (d) 2
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 17 (d) 8
  5. 5.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 8 cu cm (c) 6 cu cm (d) 24 cu cm
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/9 (c) 1/11 (d) 5/36
  7. 7.What is the sum of the roots of x² − 12x + 35 = 0? (a) 12 (b) 11 (c) 35 (d) 13
  8. 8.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  9. 9.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.What is the sum of the first 5 terms of the AP 4, 5, 6, …? (a) 8 (b) 60 (c) 31 (d) 30
  11. 11.How many factors does 104 have? (a) 6 (b) 9 (c) 8 (d) 7
  12. 12.8 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 64 (b) 12 (c) 32 (d) 40
  13. 13.A drawer has lots of blue and red 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) 5 (c) 4 (d) 2
  14. 14.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
  15. 15.In a class of 39 children, 24 like maths, 24 like science and 11 like both. How many like neither? (a) 2 (b) 11 (c) 13 (d) 3
  16. 16.What is the smallest prime factor of 121? (a) 3 (b) 1 (c) 2 (d) 11
  17. 17.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 75° (d) 30°
  18. 18.If a + b = 13 and ab = 30, what is a² + b²? (a) 139 (b) 169 (c) 109 (d) 229
  19. 19.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
  20. 20.How many factors does 16 have? (a) 5 (b) 3 (c) 6 (d) 4
  21. 21.A bag has 11 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 17 (b) 2 (c) 13 (d) 12
  22. 22.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 153 (c) 289 (d) 306
  23. 23.What is the midpoint of the line joining (6, 1) and (12, 3)? (a) (9, 2) (b) (3, 1) (c) (2, 9) (d) (18, 4)
  24. 24.What is the product of the roots of x² − 17x + 72 = 0? (a) 73 (b) 72 (c) 71 (d) 17
  25. 25.What is the missing term in the AP 14, 23, 32, ?, 50? (a) 42 (b) 41 (c) 50 (d) 40
  26. 26.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 34 (b) 35 (c) 36 (d) 43
  27. 27.If a + b = 15 and ab = 50, what is (a − b)²? (a) 225 (b) 25 (c) 125 (d) 5
  28. 28.A bag has 9 red, 7 white and 9 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 19/25 (b) 18/25 (c) 7/25 (d) 1/3
  29. 29.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  30. 30.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 120° (c) 150° (d) 30°
  31. 31.Using (a − b)² = a² − 2ab + b², what is 97²? (a) 9419 (b) 9409 (c) 9991 (d) 10609
  32. 32.What is the sum of all the whole numbers from 1 to 28? (a) 392 (b) 378 (c) 406 (d) 812
  33. 33.A bag has 3 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 5 (c) 2 (d) 6
  34. 34.How many factors does 116 have? (a) 7 (b) 5 (c) 6 (d) 4
  35. 35.What is the product of the roots of x² − 10x + 21 = 0? (a) 21 (b) 20 (c) 22 (d) 10
  36. 36.What is the prime factorisation of 36? (a) 2² × 3² (b) 2 × 3² (c) 2² × 3³ (d) 2³ × 3²
  37. 37.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 20 (c) 120 (d) 25
  38. 38.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
  39. 39.A drawer has lots of blue, red, yellow, 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) 2 (b) 10 (c) 5 (d) 6
  40. 40.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7 (c) 3 × 7² (d) 3³ × 7

Answer key

  1. Fourth quadrant
  2. 5
  3. 7
  4. 18
  5. 8 cu cm
  6. 1/9
  7. 12
  8. 20
  9. Third quadrant
  10. 30
  11. 8
  12. 32
  13. 3
  14. 154 sq cm
  15. 2
  16. 11
  17. 30°
  18. 109
  19. 60°
  20. 5
  21. 13
  22. 289
  23. (9, 2)
  24. 72
  25. 41
  26. 35
  27. 25
  28. 18/25
  29. 1/2
  30. 120°
  31. 9409
  32. 406
  33. 5
  34. 6
  35. 21
  36. 2² × 3²
  37. 120
  38. 2² × 5 × 7
  39. 6
  40. 3 × 7

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