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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 930 · 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 distance between the points (5, 4) and (17, 9)? (a) 14 (b) 13 (c) 17 (d) 169
  2. 2.What is the sum of the first 9 terms of the AP 5, 9, 13, …? (a) 207 (b) 37 (c) 189 (d) 378
  3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
  4. 4.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 170° (b) 140° (c) 50° (d) 10°
  5. 5.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
  6. 6.What is the midpoint of the line joining (1, 4) and (5, 10)? (a) (6, 14) (b) (3, 7) (c) (2, 3) (d) (7, 3)
  7. 7.What is the midpoint of the line joining (10, 12) and (14, 4)? (a) (2, 4) (b) (12, 8) (c) (8, 12) (d) (24, 16)
  8. 8.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 930 (c) 900 (d) 59
  9. 9.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 15 (c) 14 (d) 21
  10. 10.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 60° (c) 300° (d) 120°
  11. 11.What is the smallest prime factor of 69? (a) 1 (b) 23 (c) 2 (d) 3
  12. 12.In a class of 37 children, 16 like maths, 29 like science and 12 like both. How many like neither? (a) 12 (b) 4 (c) 16 (d) 5
  13. 13.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 50° (c) 80° (d) 40°
  14. 14.4 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) 32 (b) 8 (c) 20 (d) 16
  15. 15.In a class of 32 children, 11 like mangoes, 16 like bananas and 3 like both. How many like at least one of the two? (a) 32 (b) 21 (c) 24 (d) 27
  16. 16.What is the mean of 12, 14, 14, 20 and 20? (a) 20 (b) 15 (c) 16 (d) 17
  17. 17.What is the sum of all the whole numbers from 1 to 11? (a) 132 (b) 67 (c) 55 (d) 66
  18. 18.If a + b = 4 and ab = 3, what is (a − b)²? (a) 16 (b) 10 (c) 4 (d) 2
  19. 19.How many factors does 44 have? (a) 6 (b) 7 (c) 5 (d) 4
  20. 20.What is the smallest prime factor of 39? (a) 1 (b) 3 (c) 13 (d) 2
  21. 21.What is the median of 5, 32, 27, 18, 31, 37 and 17? (a) 28 (b) 27 (c) 18 (d) 31
  22. 22.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 105° (b) 15° (c) 165° (d) 90°
  23. 23.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 99 (d) 36
  24. 24.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
  25. 25.A bag has 3 red, 5 green and 7 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 1/4 (c) 1/5 (d) 4/5
  26. 26.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 110° (b) 70° (c) 135° (d) 155°
  27. 27.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
  28. 28.What is the sum of the first 10 terms of the AP 6, 11, 16, …? (a) 51 (b) 285 (c) 310 (d) 570
  29. 29.In which quadrant does the point (3, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.What is the distance between the points (6, 7) and (14, 13)? (a) 10 (b) 11 (c) 100 (d) 14
  31. 31.What is the midpoint of the line joining (10, 4) and (22, 6)? (a) (16, 5) (b) (6, 1) (c) (32, 10) (d) (5, 16)
  32. 32.What is the midpoint of the line joining (0, 6) and (4, 10)? (a) (4, 16) (b) (8, 2) (c) (2, 2) (d) (2, 8)
  33. 33.Two angles of a triangle are 65° and 50°. What is the exterior angle at the third corner? (a) 245° (b) 115° (c) 65° (d) 130°
  34. 34.In a class of 42 children, 21 like mangoes, 32 like bananas and 12 like both. How many like at least one of the two? (a) 53 (b) 29 (c) 42 (d) 41
  35. 35.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 15 (c) 25 (d) 20
  36. 36.What is the mean of 17, 13, 12, 13, 4 and 19? (a) 14 (b) 13 (c) 12 (d) 15
  37. 37.The mean of 4 numbers is 31. When the number 51 is added to them, what is the new mean? (a) 41 (b) 31 (c) 36 (d) 35
  38. 38.What is the midpoint of the line joining (1, 5) and (7, 3)? (a) (8, 8) (b) (4, 4) (c) (3, 1) (d) (5, 4)
  39. 39.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 2 (d) 29
  40. 40.What is the mean of 5, 20, 20, 13, 15 and 17? (a) 16 (b) 14 (c) 18 (d) 15

Answer key

  1. 13
  2. 189
  3. 1/2
  4. 10°
  5. 3/8
  6. (3, 7)
  7. (12, 8)
  8. 900
  9. 15
  10. 120°
  11. 3
  12. 4
  13. 80°
  14. 16
  15. 24
  16. 16
  17. 66
  18. 4
  19. 6
  20. 3
  21. 27
  22. 15°
  23. 33
  24. 36
  25. 1/5
  26. 110°
  27. 55
  28. 285
  29. Fourth quadrant
  30. 10
  31. (16, 5)
  32. (2, 8)
  33. 115°
  34. 41
  35. 10
  36. 13
  37. 35
  38. (4, 4)
  39. 11
  40. 15

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