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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 657 · 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 9 white balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 15 (b) 2 (c) 11 (d) 10
  2. 2.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 40 (b) 32 (c) 64 (d) 12
  3. 3.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 64 sq cm (b) 224 sq cm (c) 56 sq cm (d) 112 sq cm
  4. 4.What is the sum of the first 7 terms of the AP 4, 6, 8, …? (a) 140 (b) 16 (c) 77 (d) 70
  5. 5.Two angles of a triangle are 20° and 95°. What is the exterior angle at the third corner? (a) 85° (b) 160° (c) 115° (d) 65°
  6. 6.What is the 22nd term of the AP 4, 13, 22, 31, …? (a) 189 (b) 198 (c) 202 (d) 193
  7. 7.In a class of 38 children, 22 like mangoes, 21 like bananas and 8 like both. How many like at least one of the two? (a) 43 (b) 38 (c) 35 (d) 27
  8. 8.What is the 33rd term of the AP 13, 16, 19, 22, …? (a) 109 (b) 99 (c) 96 (d) 112
  9. 9.In a class of 52 children, 24 like mangoes, 28 like bananas and 8 like both. How many like at least one of the two? (a) 45 (b) 36 (c) 44 (d) 52
  10. 10.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
  11. 11.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
  12. 12.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 497 (c) 992 (d) 496
  13. 13.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 189 (d) 180
  14. 14.What is the 12th term of the AP 13, 21, 29, 37, …? (a) 109 (b) 101 (c) 96 (d) 88
  15. 15.What is the sum of all the whole numbers from 1 to 32? (a) 528 (b) 512 (c) 1056 (d) 496
  16. 16.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 3/8 (d) 1/4
  17. 17.What is the mode of 13, 16, 7, 4, 7, 4 and 7? (a) 7 (b) 16 (c) 4 (d) 13
  18. 18.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
  19. 19.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 55° (b) 90° (c) 125° (d) 145°
  20. 20.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 264 (c) 289 (d) 288
  21. 21.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 132 (c) 144 (d) 24
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 16 (b) 18 (c) 6 (d) 17
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
  24. 24.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 4) (c) (x + 1)(x + 6) (d) (x + 2)(x + 3)
  25. 25.What is the median of 3, 26, 16, 10 and 21? (a) 17 (b) 10 (c) 16 (d) 21
  26. 26.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 7 (d) 1
  27. 27.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  28. 28.In a class of 41 children, 20 like cricket, 27 like football and 3 like neither. How many like both? (a) 38 (b) 6 (c) 3 (d) 9
  29. 29.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 135° (b) 90° (c) 91° (d) 45°
  30. 30.What is the median of 33, 10, 37, 34 and 1? (a) 37 (b) 33 (c) 23 (d) 34
  31. 31.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
  32. 32.A bag has 2 green, 3 blue and 5 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 3/10 (c) 7/10 (d) 3/7
  33. 33.A bag has 12 blue balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 2 (c) 16 (d) 13
  34. 34.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 75° (b) 150° (c) 45° (d) 135°
  35. 35.If a + b = 18 and ab = 80, what is (a − b)²? (a) 164 (b) 324 (c) 4 (d) 2
  36. 36.What is the sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 14 (c) 16 (d) 15
  37. 37.What is the mean of 4, 19, 6, 19, 5 and 7? (a) 12 (b) 11 (c) 9 (d) 10
  38. 38.In a class of 28 children, 8 like mangoes, 21 like bananas and 2 like both. How many like neither? (a) 0 (b) 2 (c) 1 (d) 3
  39. 39.What is the sum of the first 10 terms of the AP 5, 8, 11, …? (a) 185 (b) 32 (c) 200 (d) 370
  40. 40.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm

Answer key

  1. 11
  2. 32
  3. 112 sq cm
  4. 70
  5. 115°
  6. 193
  7. 35
  8. 109
  9. 44
  10. 7
  11. 3
  12. 496
  13. 189
  14. 101
  15. 528
  16. 3/4
  17. 7
  18. 2
  19. 125°
  20. 288
  21. 132
  22. 17
  23. 18
  24. (x + 2)(x + 3)
  25. 16
  26. 7
  27. 7
  28. 9
  29. 90°
  30. 33
  31. 1/2
  32. 3/10
  33. 14
  34. 45°
  35. 4
  36. 15
  37. 10
  38. 1
  39. 185
  40. 132 cm

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