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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 872 · 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.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 20° (b) 10° (c) 160° (d) 11°
  2. 2.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 130° (b) 80° (c) 40° (d) 50°
  3. 3.If a + b = 17 and ab = 66, what is (a − b)²? (a) 157 (b) 25 (c) 5 (d) 289
  4. 4.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 125° (b) 100° (c) 80° (d) 135°
  5. 5.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10211 (b) 9801 (c) 10201 (d) 10001
  7. 7.In a class of 33 children, 23 like cricket, 12 like football and 6 like both. How many like at least one of the two? (a) 23 (b) 33 (c) 29 (d) 35
  8. 8.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
  9. 9.A cuboid is 6 cm long, 4 cm wide and 2 cm high. What is its total surface area? (a) 176 sq cm (b) 48 sq cm (c) 44 sq cm (d) 88 sq cm
  10. 10.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 1/11 (d) 7/36
  11. 11.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  12. 12.In a class of 35 children, 8 like mangoes, 20 like bananas and 3 like both. How many like at least one of the two? (a) 28 (b) 25 (c) 22 (d) 35
  13. 13.How many prime numbers are there between 30 and 50? (a) 6 (b) 5 (c) 4 (d) 7
  14. 14.What is the sum of the roots of x² − 13x + 42 = 0? (a) 12 (b) 42 (c) 13 (d) 14
  15. 15.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
  16. 16.What is the distance between the points (1, 12) and (5, 9)? (a) 5 (b) 6 (c) 7 (d) 25
  17. 17.What is the distance between the points (9, 4) and (17, 10)? (a) 10 (b) 11 (c) 100 (d) 14
  18. 18.What is the mean of 17, 13, 9 and 5? (a) 12 (b) 11 (c) 10 (d) 13
  19. 19.What is the distance between the points (3, 2) and (8, 14)? (a) 14 (b) 169 (c) 17 (d) 13
  20. 20.In a class of 30 children, 20 like tea, 12 like coffee and 5 like neither. How many like both? (a) 2 (b) 5 (c) 7 (d) 25
  21. 21.A bag has 5 black balls and 6 green 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) 7 (c) 6 (d) 11
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 2 (d) 18
  23. 23.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 35 (c) 12 (d) 42
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/18 (d) 1/11
  25. 25.A bag has 9 blue balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 11 (c) 2 (d) 19
  26. 26.What is the 33rd term of the AP 11, 14, 17, 20, …? (a) 99 (b) 96 (c) 107 (d) 110
  27. 27.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6399 (b) 6241 (c) 6251 (d) 6561
  28. 28.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 50° (c) 130° (d) 25°
  29. 29.What is the mode of 16, 16, 19, 5, 16, 5 and 20? (a) 5 (b) 20 (c) 16 (d) 19
  30. 30.Which is the correct factorisation of x² + 14x + 45? (a) (x + 5)(x + 9) (b) (x + 1)(x + 45) (c) (x − 5)(x − 9) (d) (x + 1)(x + 13)
  31. 31.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 140 (c) 149 (d) 158
  32. 32.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  33. 33.In a class of 49 children, 21 like maths, 22 like science and 4 like both. How many like at least one of the two? (a) 43 (b) 49 (c) 35 (d) 39
  34. 34.In a class of 29 children, 10 like tea, 22 like coffee and 6 like both. How many like only tea? (a) 4 (b) 7 (c) 16 (d) 10
  35. 35.What is the midpoint of the line joining (9, 10) and (15, 14)? (a) (24, 24) (b) (3, 2) (c) (13, 12) (d) (12, 12)
  36. 36.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 56 (c) 28 (d) 16
  37. 37.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 105° (d) 135°
  38. 38.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 60° (c) 30° (d) 61°
  39. 39.What is the 31st term of the AP 9, 12, 15, 18, …? (a) 102 (b) 90 (c) 99 (d) 93
  40. 40.What is the 29th term of the AP 16, 20, 24, 28, …? (a) 128 (b) 116 (c) 112 (d) 132

Answer key

  1. 10°
  2. 80°
  3. 25
  4. 100°
  5. Third quadrant
  6. 10201
  7. 29
  8. 1/3
  9. 88 sq cm
  10. 1/6
  11. 120
  12. 25
  13. 5
  14. 13
  15. 64 times
  16. 5
  17. 10
  18. 11
  19. 13
  20. 7
  21. 7
  22. 2
  23. 35
  24. 1/18
  25. 11
  26. 107
  27. 6241
  28. 25°
  29. 16
  30. (x + 5)(x + 9)
  31. 149
  32. 1/2
  33. 39
  34. 4
  35. (12, 12)
  36. 56
  37. 75°
  38. 60°
  39. 99
  40. 128

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