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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 924 · 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.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
  2. 2.The mean of 9 numbers is 40. When the number 50 is added to them, what is the new mean? (a) 41 (b) 45 (c) 42 (d) 40
  3. 3.How many factors does 32 have? (a) 5 (b) 6 (c) 7 (d) 4
  4. 4.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  5. 5.What is the product of the roots of x² − 16x + 63 = 0? (a) 62 (b) 16 (c) 63 (d) 64
  6. 6.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 12 (c) 36 (d) 30
  7. 7.What is the midpoint of the line joining (5, 5) and (17, 1)? (a) (11, 3) (b) (3, 11) (c) (6, 2) (d) (22, 6)
  8. 8.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  9. 9.What is the sum of the first 10 terms of the AP 10, 11, 12, …? (a) 145 (b) 290 (c) 150 (d) 19
  10. 10.What is the mode of 19, 19, 3, 19, 11, 17 and 17? (a) 3 (b) 19 (c) 17 (d) 11
  11. 11.What is the midpoint of the line joining (5, 3) and (11, 1)? (a) (8, 2) (b) (3, 1) (c) (2, 8) (d) (16, 4)
  12. 12.A bag has 11 red balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 2 (c) 12 (d) 6
  13. 13.What is the product of the roots of x² − 11x + 24 = 0? (a) 23 (b) 25 (c) 24 (d) 11
  14. 14.What is the 21st term of the AP 9, 16, 23, 30, …? (a) 156 (b) 140 (c) 149 (d) 147
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 2/11 (d) 1/18
  16. 16.In a class of 32 children, 26 like tea, 11 like coffee and 8 like both. How many like neither? (a) 8 (b) 11 (c) 3 (d) 4
  17. 17.What is the mean of 16, 2, 16, 19 and 7? (a) 10 (b) 15 (c) 12 (d) 13
  18. 18.A bag has 6 blue, 4 yellow and 7 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 6/11 (b) 1/3 (c) 6/17 (d) 11/17
  19. 19.Which term of the AP 4, 6, 8, 10, … is 46? (a) 22nd (b) 23rd (c) 21st (d) 24th
  20. 20.5 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) 60 (b) 11 (c) 35 (d) 30
  21. 21.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  22. 22.In a class of 34 children, 19 like dance, 15 like music and 3 like neither. How many like both? (a) 2 (b) 3 (c) 4 (d) 31
  23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
  24. 24.What is the sum of the first 8 terms of the AP 2, 5, 8, …? (a) 100 (b) 23 (c) 200 (d) 112
  25. 25.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 130° (b) 85° (c) 95° (d) 145°
  26. 26.A drawer has lots of red, white, blue, 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) 2 (b) 6 (c) 10 (d) 5
  27. 27.A bag has 4 red, 4 green and 8 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/4 (b) 13/16 (c) 1/3 (d) 3/4
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 17 (d) 15
  29. 29.A bag has 8 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 16 (c) 9 (d) 2
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  31. 31.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 21 cu cm (c) 196 cu cm (d) 343 cu cm
  32. 32.A bag has 8 black balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 2 (c) 9 (d) 10
  33. 33.If a + b = 12 and ab = 27, what is a² + b²? (a) 144 (b) 117 (c) 198 (d) 90
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  35. 35.In a class of 36 children, 15 like tea, 23 like coffee and 6 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 26 (d) 32
  36. 36.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/4 (c) 1/8 (d) 1/7
  37. 37.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 3 times (c) 9 times (d) 6 times
  38. 38.In which quadrant does the point (8, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  39. 39.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 15 (c) 21 (d) 22
  40. 40.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) 12 (b) 25 (c) 24 (d) 13

Answer key

  1. 3/4
  2. 41
  3. 6
  4. 7
  5. 63
  6. 30
  7. (11, 3)
  8. 120
  9. 145
  10. 19
  11. (8, 2)
  12. 12
  13. 24
  14. 149
  15. 1/18
  16. 3
  17. 12
  18. 6/17
  19. 22nd
  20. 30
  21. 120
  22. 3
  23. 220 cm
  24. 100
  25. 85°
  26. 6
  27. 3/4
  28. 16
  29. 10
  30. 7
  31. 343 cu cm
  32. 10
  33. 90
  34. 5
  35. 32
  36. 1/8
  37. 9 times
  38. Fourth quadrant
  39. 15
  40. 13

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