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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 876 · 40 questions
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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.Two angles of a triangle are 20° and 60°. What is the exterior angle at the third corner? (a) 100° (b) 120° (c) 80° (d) 160°
  2. 2.What is the sum of all the whole numbers from 1 to 28? (a) 378 (b) 812 (c) 406 (d) 392
  3. 3.What is the 35th term of the AP 2, 11, 20, 29, …? (a) 315 (b) 308 (c) 317 (d) 306
  4. 4.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  5. 5.In a class of 25 children, 17 like tea, 12 like coffee and 8 like both. How many like at least one of the two? (a) 13 (b) 29 (c) 21 (d) 25
  6. 6.What is the median of 17, 8, 6, 21, 20, 26 and 35? (a) 20 (b) 19 (c) 21 (d) 17
  7. 7.A bag has 8 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 9 (b) 10 (c) 2 (d) 14
  8. 8.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  9. 9.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 15 (b) 16 (c) 19 (d) 17
  10. 10.What is the median of 27, 17, 4, 29 and 3? (a) 16 (b) 4 (c) 27 (d) 17
  11. 11.In a class of 26 children, 13 like mangoes, 7 like bananas and 4 like both. How many like only mangoes? (a) 19 (b) 9 (c) 3 (d) 13
  12. 12.What is the median of 27, 12, 39, 5 and 4? (a) 39 (b) 5 (c) 27 (d) 12
  13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
  14. 14.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
  15. 15.In a class of 42 children, 18 like mangoes, 17 like bananas and 3 like both. How many like at least one of the two? (a) 29 (b) 35 (c) 32 (d) 42
  16. 16.If a + b = 16 and ab = 48, what is a² + b²? (a) 208 (b) 256 (c) 352 (d) 160
  17. 17.What is the mean of 8, 9, 3, 6 and 9? (a) 8 (b) 9 (c) 7 (d) 6
  18. 18.In a class of 35 children, 22 like cricket, 22 like football and 11 like both. How many like at least one of the two? (a) 22 (b) 33 (c) 35 (d) 44
  19. 19.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 45 (c) 100 (d) 20
  20. 20.In a class of 32 children, 21 like dance, 19 like music and 9 like both. How many like neither? (a) 1 (b) 9 (c) 10 (d) 2
  21. 21.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  22. 22.Using (a − b)² = a² − 2ab + b², what is 47²? (a) 2209 (b) 2219 (c) 2491 (d) 2809
  23. 23.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 28 (c) 16 (d) 56
  24. 24.What is the sum of the first 11 terms of the AP 6, 11, 16, …? (a) 56 (b) 341 (c) 346 (d) 682
  25. 25.What is the mode of 2, 20, 20, 3, 3, 4 and 20? (a) 20 (b) 4 (c) 2 (d) 3
  26. 26.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 12 (c) 6 (d) 5
  27. 27.What is the median of 3, 30, 27, 31, 21, 14 and 9? (a) 31 (b) 21 (c) 27 (d) 14
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
  29. 29.A bag has 3 green, 3 white and 3 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/3 (b) 4/9 (c) 1/2 (d) 1/3
  30. 30.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 55° (b) 150° (c) 155° (d) 125°
  31. 31.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  32. 32.How many factors does 53 have? (a) 1 (b) 3 (c) 4 (d) 2
  33. 33.The mean of 4 numbers is 40. When the number 30 is added to them, what is the new mean? (a) 35 (b) 38 (c) 39 (d) 40
  34. 34.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 120° (b) 110° (c) 60° (d) 130°
  35. 35.What is the midpoint of the line joining (1, 16) and (9, 8)? (a) (5, 12) (b) (4, 4) (c) (12, 5) (d) (10, 24)
  36. 36.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 69 (c) 78 (d) 70
  37. 37.A bag has 5 white, 4 yellow and 8 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 13/17 (b) 12/17 (c) 5/17 (d) 1/3
  38. 38.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
  39. 39.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 4 times (d) 5 times
  40. 40.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465

Answer key

  1. 80°
  2. 406
  3. 308
  4. 7
  5. 21
  6. 20
  7. 10
  8. 13
  9. 16
  10. 17
  11. 9
  12. 12
  13. 616 sq cm
  14. 1/6
  15. 32
  16. 160
  17. 7
  18. 33
  19. 45
  20. 1
  21. 24
  22. 2209
  23. 28
  24. 341
  25. 20
  26. 6
  27. 21
  28. 19
  29. 1/3
  30. 125°
  31. 2² × 3 × 7
  32. 2
  33. 38
  34. 120°
  35. (5, 12)
  36. 69
  37. 12/17
  38. 176 cm
  39. 4 times
  40. 900

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