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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 374 · 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.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 130° (b) 135° (c) 95° (d) 85°
  2. 2.What is the distance between the points (1, 4) and (5, 1)? (a) 7 (b) 6 (c) 25 (d) 5
  3. 3.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  4. 4.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  5. 5.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 150° (c) 160° (d) 20°
  6. 6.Two angles of a triangle are 55° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 125° (c) 270° (d) 90°
  7. 7.A drawer has lots of green, black 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) 4 (b) 2 (c) 3 (d) 6
  8. 8.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 160° (c) 70° (d) 80°
  9. 9.In a class of 23 children, 8 like maths, 9 like science and 9 like neither. How many like both? (a) 4 (b) 14 (c) 9 (d) 3
  10. 10.The mean of 7 numbers is 37. When the number 45 is added to them, what is the new mean? (a) 39 (b) 37 (c) 38 (d) 41
  11. 11.Two angles of a triangle are 60° and 25°. What is the exterior angle at the third corner? (a) 120° (b) 85° (c) 155° (d) 95°
  12. 12.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 8 (d) 9
  13. 13.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 318 (c) 369 (d) 370
  14. 14.In a class of 20 children, 11 like mangoes, 9 like bananas and 3 like neither. How many like both? (a) 4 (b) 3 (c) 17 (d) 2
  15. 15.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 90 (c) 45 (d) 100
  16. 16.What is the 10th term of the AP 12, 19, 26, 33, …? (a) 82 (b) 63 (c) 70 (d) 75
  17. 17.What is the product of the roots of x² − 15x + 54 = 0? (a) 55 (b) 54 (c) 53 (d) 15
  18. 18.What is the distance between the points (7, 0) and (15, 15)? (a) 289 (b) 17 (c) 18 (d) 23
  19. 19.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
  20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/4 (d) 1/3
  21. 21.In a class of 29 children, 14 like mangoes, 15 like bananas and 6 like both. How many like neither? (a) 12 (b) 6 (c) 7 (d) 0
  22. 22.In a class of 14 children, 7 like maths, 8 like science and 2 like both. How many like neither? (a) 3 (b) 0 (c) 2 (d) 1
  23. 23.A bag has 12 black balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 17 (d) 13
  24. 24.5 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) 12 (b) 70 (c) 40 (d) 35
  25. 25.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
  26. 26.What is the mode of 14, 14, 11, 7, 11, 14 and 8? (a) 7 (b) 8 (c) 11 (d) 14
  27. 27.What is the mean of 8, 14, 11, 7 and 15? (a) 11 (b) 12 (c) 10 (d) 13
  28. 28.A bag has 8 green balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 9 (d) 13
  29. 29.A bag has 10 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 12 (b) 2 (c) 13 (d) 11
  30. 30.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 160° (b) 145° (c) 125° (d) 55°
  31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  32. 32.What is the distance between the points (3, 9) and (11, 24)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.What is the mode of 14, 14, 1, 13, 14, 6 and 6? (a) 14 (b) 1 (c) 13 (d) 6
  34. 34.What is the 14th term of the AP 8, 17, 26, 35, …? (a) 125 (b) 126 (c) 117 (d) 134
  35. 35.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 5 (d) 7
  36. 36.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  37. 37.What is the median of 5, 9, 38, 40, 12, 18 and 22? (a) 40 (b) 18 (c) 12 (d) 22
  38. 38.A cuboid is 6 cm long, 3 cm wide and 9 cm high. What is its volume? (a) 198 cu cm (b) 18 cu cm (c) 163 cu cm (d) 162 cu cm
  39. 39.Two angles of a triangle are 25° and 30°. What is the third angle? (a) 55° (b) 125° (c) 150° (d) 155°
  40. 40.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 7225 (b) 6425 (c) 5625 (d) 7235

Answer key

  1. 85°
  2. 5
  3. Third quadrant
  4. 3
  5. 20°
  6. 90°
  7. 4
  8. 80°
  9. 3
  10. 38
  11. 85°
  12. 7
  13. 369
  14. 3
  15. 45
  16. 75
  17. 54
  18. 17
  19. 2/3
  20. 1/4
  21. 6
  22. 1
  23. 13
  24. 35
  25. 1/2
  26. 14
  27. 11
  28. 9
  29. 12
  30. 125°
  31. 6
  32. 17
  33. 14
  34. 125
  35. 5
  36. 120
  37. 18
  38. 162 cu cm
  39. 125°
  40. 7225

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