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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 325 · 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.Two angles of a triangle are 60° and 25°. What is the third angle? (a) 120° (b) 155° (c) 85° (d) 95°
  2. 2.What is the smallest prime factor of 93? (a) 31 (b) 1 (c) 2 (d) 3
  3. 3.What is the missing term in the AP 19, 21, 23, ?, 27? (a) 24 (b) 27 (c) 25 (d) 26
  4. 4.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 105 (d) 225
  5. 5.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 250° (c) 140° (d) 70°
  6. 6.In a class of 23 children, 16 like mangoes, 6 like bananas and 3 like both. How many like at least one of the two? (a) 16 (b) 19 (c) 22 (d) 23
  7. 7.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
  8. 8.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 66 (d) 144
  9. 9.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  10. 10.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
  11. 11.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 100° (d) 110°
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
  13. 13.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  14. 14.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2 × 3³ (d) 2² × 3²
  15. 15.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 30 cu cm (c) 600 cu cm (d) 1000 cu cm
  16. 16.Two angles of a triangle are 60° and 65°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 120° (d) 115°
  17. 17.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
  18. 18.What is the 12th term of the AP 19, 28, 37, 46, …? (a) 108 (b) 99 (c) 127 (d) 118
  19. 19.What is the 30th term of the AP 5, 8, 11, 14, …? (a) 87 (b) 90 (c) 95 (d) 92
  20. 20.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  21. 21.In a league, 11 teams each play every other team once. How many matches are played? (a) 55 (b) 66 (c) 121 (d) 110
  22. 22.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  23. 23.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
  24. 24.What is the distance between the points (9, 6) and (17, 21)? (a) 18 (b) 23 (c) 289 (d) 17
  25. 25.What is the midpoint of the line joining (4, 8) and (6, 2)? (a) (1, 3) (b) (5, 5) (c) (10, 10) (d) (6, 5)
  26. 26.What is the 20th term of the AP 14, 21, 28, 35, …? (a) 147 (b) 133 (c) 140 (d) 154
  27. 27.What is the midpoint of the line joining (1, 0) and (5, 2)? (a) (6, 2) (b) (2, 1) (c) (1, 3) (d) (3, 1)
  28. 28.A bag has 7 green, 4 white and 5 yellow balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 1/4 (c) 5/16 (d) 3/4
  29. 29.What is the distance between the points (2, 3) and (14, 19)? (a) 28 (b) 20 (c) 400 (d) 21
  30. 30.In a class of 27 children, 11 like maths, 18 like science and 3 like both. How many like at least one of the two? (a) 26 (b) 23 (c) 27 (d) 29
  31. 31.7 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) 11 (b) 35 (c) 28 (d) 56
  32. 32.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 334 (c) 384 (d) 393
  33. 33.What is the mean of 7, 9, 17 and 7? (a) 8 (b) 11 (c) 9 (d) 10
  34. 34.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
  35. 35.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 48) (c) (x + 6)(x + 8) (d) (x + 1)(x + 13)
  36. 36.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 15° (c) 285° (d) 105°
  37. 37.Two angles of a triangle are 40° and 35°. What is the third angle? (a) 140° (b) 105° (c) 145° (d) 75°
  38. 38.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 20° (d) 30°
  39. 39.How many factors does 90 have? (a) 11 (b) 12 (c) 13 (d) 10
  40. 40.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 4 (b) 5 (c) 6 (d) 3

Answer key

  1. 95°
  2. 3
  3. 25
  4. 105
  5. 70°
  6. 19
  7. 72
  8. 66
  9. 120
  10. 220 cm
  11. 100°
  12. 1/12
  13. 1/2
  14. 2 × 3²
  15. 1000 cu cm
  16. 125°
  17. (x + 8)(x + 9)
  18. 118
  19. 92
  20. First quadrant
  21. 55
  22. 2
  23. 1/3
  24. 17
  25. (5, 5)
  26. 147
  27. (3, 1)
  28. 1/4
  29. 20
  30. 26
  31. 28
  32. 393
  33. 10
  34. 220 cm
  35. (x + 6)(x + 8)
  36. 105°
  37. 105°
  38. 20°
  39. 12
  40. 4

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