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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 920 · 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 a class of 15 children, 10 like cricket, 9 like football and 1 like neither. How many like both? (a) 14 (b) 1 (c) 5 (d) 4
  2. 2.What are the roots of x² − 6x + 8 = 0? (a) 2 and 4 (b) 1 and 5 (c) 2 and 5 (d) 1 and 8
  3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  4. 4.If a + b = 10 and ab = 16, what is a² + b²? (a) 132 (b) 68 (c) 84 (d) 100
  5. 5.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the 31st term of the AP 3, 11, 19, 27, …? (a) 240 (b) 248 (c) 251 (d) 243
  7. 7.The mean of 9 numbers is 12. When the number 52 is added to them, what is the new mean? (a) 17 (b) 12 (c) 16 (d) 32
  8. 8.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 1/8 (d) 7/8
  9. 9.What is the distance between the points (2, 7) and (6, 4)? (a) 6 (b) 5 (c) 25 (d) 7
  10. 10.Which is the correct factorisation of x² + 9x + 14? (a) (x + 1)(x + 8) (b) (x + 2)(x + 7) (c) (x − 2)(x − 7) (d) (x + 1)(x + 14)
  11. 11.In a class of 13 children, 9 like mangoes, 5 like bananas and 2 like both. How many like at least one of the two? (a) 12 (b) 10 (c) 13 (d) 14
  12. 12.A bag has 3 green, 7 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/10 (b) 3/13 (c) 1/3 (d) 10/13
  13. 13.What is the mean of 13, 6, 5, 11, 10 and 21? (a) 12 (b) 10 (c) 11 (d) 13
  14. 14.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 1 and 72 (c) 8 and 9 (d) 2 and 36
  15. 15.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 1 (d) 11
  16. 16.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2² × 7
  17. 17.A cube has edges of 10 cm. What is its total surface area? (a) 400 sq cm (b) 600 sq cm (c) 1000 sq cm (d) 100 sq cm
  18. 18.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  19. 19.What is the 14th term of the AP 12, 21, 30, 39, …? (a) 126 (b) 138 (c) 129 (d) 117
  20. 20.What is the midpoint of the line joining (1, 21) and (3, 9)? (a) (2, 15) (b) (4, 30) (c) (15, 2) (d) (1, 6)
  21. 21.In a class of 33 children, 19 like cricket, 10 like football and 3 like both. How many like only cricket? (a) 23 (b) 16 (c) 19 (d) 7
  22. 22.A bag has 10 black balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 11 (c) 2 (d) 8
  23. 23.If a + b = 9 and ab = 14, what is a² + b²? (a) 67 (b) 81 (c) 53 (d) 109
  24. 24.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  25. 25.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
  26. 26.A drawer has lots of black and green 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) 3 (c) 5 (d) 2
  27. 27.What is the sum of the first 6 terms of the AP 2, 8, 14, …? (a) 102 (b) 32 (c) 120 (d) 204
  28. 28.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the sum of the roots of x² − 10x + 21 = 0? (a) 11 (b) 9 (c) 21 (d) 10
  30. 30.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  32. 32.In which quadrant does the point (6, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 36 (d) 30
  34. 34.In a class of 48 children, 25 like cricket, 30 like football and 10 like both. How many like neither? (a) 10 (b) 3 (c) 4 (d) 13
  35. 35.A drawer has lots of blue and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 5 (c) 2 (d) 4
  36. 36.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 204 (c) 198 (d) 189
  37. 37.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 115° (c) 100° (d) 145°
  38. 38.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  39. 39.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 385 (c) 375 (d) 384
  40. 40.Using (a − b)² = a² − 2ab + b², what is 86²? (a) 8084 (b) 7406 (c) 7396 (d) 8836

Answer key

  1. 5
  2. 2 and 4
  3. 1/3
  4. 68
  5. Third quadrant
  6. 243
  7. 16
  8. 7/8
  9. 5
  10. (x + 2)(x + 7)
  11. 12
  12. 3/13
  13. 11
  14. 8 and 9
  15. 11
  16. 2³ × 7
  17. 600 sq cm
  18. 120
  19. 129
  20. (2, 15)
  21. 16
  22. 11
  23. 53
  24. 1/2
  25. 2³ × 5 × 7
  26. 3
  27. 102
  28. First quadrant
  29. 10
  30. First quadrant
  31. 2
  32. First quadrant
  33. 15
  34. 3
  35. 3
  36. 198
  37. 145°
  38. 17
  39. 384
  40. 7396

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