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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 264 · 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.A bag has 3 green, 6 red and 7 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 11/16 (c) 3/8 (d) 5/8
  2. 2.If a + b = 5 and ab = 6, what is a² + b²? (a) 25 (b) 37 (c) 13 (d) 19
  3. 3.The mean of 8 numbers is 19. When the number 1 is added to them, what is the new mean? (a) 10 (b) 19 (c) 18 (d) 17
  4. 4.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 20 (c) 84 (d) 150
  6. 6.The mean of 4 numbers is 25. When the number 20 is added to them, what is the new mean? (a) 24 (b) 23 (c) 26 (d) 25
  7. 7.In a class of 24 children, 12 like cricket, 9 like football and 7 like neither. How many like both? (a) 7 (b) 17 (c) 4 (d) 5
  8. 8.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
  9. 9.What is the mean of 11, 13, 2, 13 and 11? (a) 11 (b) 10 (c) 12 (d) 9
  10. 10.A bag has 12 white balls and 13 red 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) 13 (c) 25 (d) 14
  11. 11.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 40° (c) 80° (d) 50°
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  14. 14.What is the missing term in the AP 16, 25, ?, 43, 52? (a) 43 (b) 34 (c) 33 (d) 35
  15. 15.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
  16. 16.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  17. 17.What is the missing term in the AP 7, ?, 21, 28, 35? (a) 15 (b) 13 (c) 21 (d) 14
  18. 18.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 72 (c) 216 (d) 75
  19. 19.In a class of 36 children, 14 like tea, 22 like coffee and 2 like both. How many like at least one of the two? (a) 35 (b) 34 (c) 32 (d) 36
  20. 20.What is the mode of 1, 7, 12, 7, 11, 11 and 7? (a) 7 (b) 11 (c) 12 (d) 1
  21. 21.What is the mean of 19, 19, 2 and 20? (a) 16 (b) 20 (c) 12 (d) 15
  22. 22.The mean of 8 numbers is 38. When the number 74 is added to them, what is the new mean? (a) 42 (b) 38 (c) 56 (d) 43
  23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 110 cm (c) 220 cm (d) 440 cm
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  25. 25.How many factors does 67 have? (a) 4 (b) 3 (c) 2 (d) 1
  26. 26.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 352 cm (d) 2464 cm
  27. 27.What is the mean of 13, 12, 9 and 18? (a) 14 (b) 13 (c) 15 (d) 12
  28. 28.What is the distance between the points (2, 9) and (14, 14)? (a) 14 (b) 169 (c) 17 (d) 13
  29. 29.A bag has 3 green balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 6 (c) 5 (d) 4
  30. 30.In a class of 30 children, 19 like cricket, 20 like football and 3 like neither. How many like both? (a) 27 (b) 9 (c) 12 (d) 3
  31. 31.In a class of 49 children, 29 like mangoes, 28 like bananas and 9 like both. How many like only mangoes? (a) 29 (b) 21 (c) 20 (d) 19
  32. 32.In a class of 34 children, 11 like cricket, 20 like football and 4 like both. How many like at least one of the two? (a) 31 (b) 34 (c) 23 (d) 27
  33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  34. 34.Two angles of a triangle are 80° and 45°. What is the third angle? (a) 100° (b) 55° (c) 125° (d) 135°
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 7 (d) 19
  36. 36.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 250° (b) 70° (c) 110° (d) 140°
  37. 37.What is the mean of 8, 13, 10, 10, 14 and 17? (a) 13 (b) 11 (c) 12 (d) 14
  38. 38.A bag has 5 red, 3 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 9/16 (b) 1/2 (c) 1/3 (d) 1/16
  39. 39.In a class of 44 children, 18 like mangoes, 18 like bananas and 2 like both. How many like neither? (a) 8 (b) 10 (c) 2 (d) 12
  40. 40.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 600 (d) 576

Answer key

  1. 5/8
  2. 13
  3. 17
  4. First quadrant
  5. 75
  6. 24
  7. 4
  8. 30
  9. 10
  10. 14
  11. 80°
  12. 25
  13. 20
  14. 34
  15. 2
  16. 120
  17. 14
  18. 72
  19. 34
  20. 7
  21. 15
  22. 42
  23. 220 cm
  24. 6
  25. 2
  26. 176 cm
  27. 13
  28. 13
  29. 5
  30. 12
  31. 20
  32. 27
  33. 15
  34. 55°
  35. 18
  36. 110°
  37. 12
  38. 1/2
  39. 10
  40. 576

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