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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 765 · 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 6, 8, 16, 2 and 8? (a) 10 (b) 9 (c) 7 (d) 8
  2. 2.Which term of the AP 7, 15, 23, 31, … is 231? (a) 30th (b) 28th (c) 29th (d) 31st
  3. 3.What is the 26th term of the AP 1, 8, 15, 22, …? (a) 183 (b) 176 (c) 175 (d) 182
  4. 4.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 61° (b) 120° (c) 240° (d) 60°
  5. 5.What is the smallest prime factor of 95? (a) 19 (b) 1 (c) 2 (d) 5
  6. 6.In a league, 15 teams each play every other team once. How many matches are played? (a) 120 (b) 105 (c) 225 (d) 210
  7. 7.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 35° (c) 145° (d) 55°
  8. 8.A cuboid is 9 cm long, 3 cm wide and 8 cm high. What is its total surface area? (a) 123 sq cm (b) 246 sq cm (c) 492 sq cm (d) 216 sq cm
  9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  10. 10.What are the roots of x² − 8x + 15 = 0? (a) 3 and 5 (b) 1 and 15 (c) 2 and 6 (d) 1 and 7
  11. 11.If a + b = 16 and ab = 60, what is (a − b)²? (a) 136 (b) 16 (c) 256 (d) 4
  12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 308 sq cm (c) 88 sq cm (d) 616 sq cm
  13. 13.What is the median of 5, 34, 32, 12 and 4? (a) 5 (b) 12 (c) 32 (d) 13
  14. 14.The mean of 4 numbers is 18. When the number 8 is added to them, what is the new mean? (a) 16 (b) 17 (c) 18 (d) 13
  15. 15.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 3 (d) 2
  16. 16.What is the median of 5, 2, 23, 39, 21, 32 and 34? (a) 32 (b) 39 (c) 21 (d) 23
  17. 17.A cube has edges of 11 cm. What is its total surface area? (a) 484 sq cm (b) 726 sq cm (c) 121 sq cm (d) 1331 sq cm
  18. 18.The mean of 9 numbers is 37. When the number 77 is added to them, what is the new mean? (a) 57 (b) 41 (c) 42 (d) 37
  19. 19.How many factors does 44 have? (a) 4 (b) 6 (c) 7 (d) 5
  20. 20.What is the median of 14, 1, 36, 29 and 17? (a) 29 (b) 14 (c) 36 (d) 17
  21. 21.A drawer has lots of blue, white, 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) 8 (b) 4 (c) 5 (d) 2
  22. 22.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 40° (b) 220° (c) 140° (d) 41°
  23. 23.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  24. 24.If a + b = 15 and ab = 50, what is a² + b²? (a) 125 (b) 325 (c) 225 (d) 175
  25. 25.What is the mode of 3, 9, 3, 15, 3, 9 and 12? (a) 9 (b) 12 (c) 15 (d) 3
  26. 26.What is the sum of the first 7 terms of the AP 7, 12, 17, …? (a) 308 (b) 154 (c) 37 (d) 159
  27. 27.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
  28. 28.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 1 (d) 2
  29. 29.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 140° (b) 280° (c) 40° (d) 100°
  30. 30.In which quadrant does the point (8, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (8, 10) and (12, 7)? (a) 25 (b) 6 (c) 5 (d) 7
  32. 32.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 125° (c) 55° (d) 135°
  33. 33.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 442 (c) 441 (d) 366
  34. 34.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 110 (c) 102 (d) 101
  35. 35.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 6 (c) 12 (d) 3
  36. 36.A bag has 8 green, 9 red and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/17 (b) 1/3 (c) 3/20 (d) 17/20
  37. 37.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 3/8 (d) 5/8
  38. 38.In which quadrant does the point (−4, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.The mean of 3 numbers is 30. When the number 22 is added to them, what is the new mean? (a) 30 (b) 29 (c) 26 (d) 28
  40. 40.In a class of 44 children, 21 like tea, 19 like coffee and 3 like both. How many like neither? (a) 4 (b) 7 (c) 3 (d) 10

Answer key

  1. 8
  2. 29th
  3. 176
  4. 60°
  5. 5
  6. 105
  7. 110°
  8. 246 sq cm
  9. 9
  10. 3 and 5
  11. 16
  12. 616 sq cm
  13. 12
  14. 16
  15. 2
  16. 23
  17. 726 sq cm
  18. 41
  19. 6
  20. 17
  21. 5
  22. 40°
  23. 91
  24. 125
  25. 3
  26. 154
  27. 1/2
  28. 3
  29. 140°
  30. First quadrant
  31. 5
  32. 55°
  33. 441
  34. 101
  35. 6
  36. 3/20
  37. 3/8
  38. Second quadrant
  39. 28
  40. 7

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