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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 302 · 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 4 green, 5 yellow and 7 red balls. One ball is taken out without looking. What is the probability that it is green? (a) 5/16 (b) 3/4 (c) 1/3 (d) 1/4
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  3. 3.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  4. 4.A bag has 11 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 22 (b) 2 (c) 12 (d) 13
  5. 5.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 13 (d) 12
  6. 6.If a + b = 11 and ab = 30, what is (a − b)²? (a) 121 (b) 61 (c) 1 (d) 91
  7. 7.Which is the correct factorisation of x² + 8x + 12? (a) (x − 2)(x − 6) (b) (x + 2)(x + 6) (c) (x + 1)(x + 12) (d) (x + 1)(x + 7)
  8. 8.In a class of 33 children, 16 like cricket, 13 like football and 3 like both. How many like at least one of the two? (a) 33 (b) 29 (c) 23 (d) 26
  9. 9.What is the 12th term of the AP 14, 19, 24, 29, …? (a) 55 (b) 74 (c) 69 (d) 60
  10. 10.In a class of 37 children, 27 like cricket, 12 like football and 8 like both. How many like at least one of the two? (a) 31 (b) 23 (c) 37 (d) 39
  11. 11.How many factors does 20 have? (a) 6 (b) 7 (c) 4 (d) 5
  12. 12.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  13. 13.A bag has 4 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 5 (c) 9 (d) 2
  14. 14.What is the distance between the points (2, 1) and (7, 13)? (a) 17 (b) 14 (c) 169 (d) 13
  15. 15.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 11 (d) 7
  16. 16.What is the 36th term of the AP 7, 16, 25, 34, …? (a) 315 (b) 324 (c) 322 (d) 331
  17. 17.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 4 (d) 2
  18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
  19. 19.Which is the correct factorisation of x² + 12x + 27? (a) (x − 3)(x − 9) (b) (x + 3)(x + 9) (c) (x + 1)(x + 27) (d) (x + 1)(x + 11)
  20. 20.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 8 (d) 7
  21. 21.In a class of 25 children, 7 like cricket, 20 like football and 2 like neither. How many like both? (a) 2 (b) 23 (c) 5 (d) 4
  22. 22.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 68 (d) 77
  23. 23.What is the sum of the roots of x² − 7x + 10 = 0? (a) 10 (b) 6 (c) 7 (d) 8
  24. 24.What is the midpoint of the line joining (4, 12) and (8, 2)? (a) (2, 5) (b) (7, 6) (c) (6, 7) (d) (12, 14)
  25. 25.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
  26. 26.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 66 (c) 132 (d) 24
  27. 27.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the missing term in the AP 3, 11, ?, 27, 35? (a) 19 (b) 20 (c) 27 (d) 18
  29. 29.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 6 times (c) 2 times (d) 8 times
  30. 30.In a class of 37 children, 20 like tea, 17 like coffee and 2 like both. How many like at least one of the two? (a) 36 (b) 35 (c) 33 (d) 37
  31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 2/3 (c) 5/6 (d) 1/3
  32. 32.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/12 (c) 1/9 (d) 3/11
  34. 34.What is the midpoint of the line joining (6, 8) and (18, 4)? (a) (6, 12) (b) (6, 2) (c) (24, 12) (d) (12, 6)
  35. 35.Two angles of a triangle are 55° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 135° (c) 125° (d) 100°
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 17 (d) 16
  37. 37.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
  38. 38.A bag has 3 blue balls and 9 yellow 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) 4 (c) 10 (d) 12
  39. 39.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 13 (b) 42 (c) 84 (d) 49
  40. 40.In a class of 28 children, 15 like maths, 22 like science and 12 like both. How many like at least one of the two? (a) 28 (b) 25 (c) 13 (d) 37

Answer key

  1. 1/4
  2. 6
  3. First quadrant
  4. 13
  5. 13
  6. 1
  7. (x + 2)(x + 6)
  8. 26
  9. 69
  10. 31
  11. 6
  12. 130°
  13. 6
  14. 13
  15. 7
  16. 322
  17. 2
  18. 4
  19. (x + 3)(x + 9)
  20. 7
  21. 4
  22. 77
  23. 7
  24. (6, 7)
  25. 2
  26. 132
  27. Third quadrant
  28. 19
  29. 8 times
  30. 35
  31. 2/3
  32. 4
  33. 1/12
  34. (12, 6)
  35. 100°
  36. 16
  37. 1386 sq cm
  38. 10
  39. 42
  40. 25

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