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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 619 · 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.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 182 (c) 169 (d) 25
  2. 2.A bag has 3 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 11 (c) 2 (d) 4
  3. 3.In which quadrant does the point (7, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  4. 4.A bag has 8 white balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 2 (c) 10 (d) 20
  5. 5.A drawer has lots of white, red, green, yellow and blue 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) 5 (d) 10
  6. 6.What is the median of 11, 28, 40, 22 and 1? (a) 11 (b) 22 (c) 40 (d) 28
  7. 7.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 30° (c) 15° (d) 25°
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  9. 9.What is the mean of 3, 11, 14 and 20? (a) 11 (b) 16 (c) 12 (d) 13
  10. 10.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
  11. 11.What are the roots of x² − 9x + 20 = 0? (a) 4 and 5 (b) 2 and 10 (c) 1 and 8 (d) 1 and 20
  12. 12.How many factors does 26 have? (a) 2 (b) 5 (c) 4 (d) 3
  13. 13.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
  14. 14.A drawer has lots of red 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) 2 (b) 4 (c) 5 (d) 3
  15. 15.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 18 (d) 20
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 5 (b) 4 (c) 7 (d) 6
  18. 18.How many factors does 45 have? (a) 4 (b) 6 (c) 5 (d) 7
  19. 19.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
  20. 20.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  21. 21.In a class of 35 children, 16 like mangoes, 18 like bananas and 8 like both. How many like only mangoes? (a) 17 (b) 16 (c) 8 (d) 10
  22. 22.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 24 (d) 25
  23. 23.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
  24. 24.What is the mode of 18, 7, 18, 10, 7, 7 and 14? (a) 7 (b) 14 (c) 10 (d) 18
  25. 25.A bag has 5 white balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 9 (d) 6
  26. 26.A bag has 4 yellow, 4 green and 3 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 4/11 (c) 4/7 (d) 7/11
  27. 27.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
  28. 28.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
  29. 29.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the mode of 13, 7, 13, 13, 9, 16 and 9? (a) 16 (b) 9 (c) 13 (d) 7
  31. 31.In a class of 29 children, 18 like mangoes, 12 like bananas and 1 like neither. How many like both? (a) 3 (b) 28 (c) 1 (d) 2
  32. 32.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 5 (d) 4
  33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  34. 34.Two angles of a triangle are 35° and 45°. What is the third angle? (a) 80° (b) 145° (c) 100° (d) 135°
  35. 35.What is the 11th term of the AP 16, 20, 24, 28, …? (a) 40 (b) 44 (c) 60 (d) 56
  36. 36.A bag has 4 black 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) 6 (b) 2 (c) 5 (d) 9
  37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  38. 38.What is the smallest prime factor of 341? (a) 11 (b) 31 (c) 2 (d) 1
  39. 39.What is the median of 12, 24, 2, 31 and 27? (a) 27 (b) 24 (c) 12 (d) 2
  40. 40.What is the median of 40, 39, 3, 34 and 15? (a) 39 (b) 3 (c) 34 (d) 15

Answer key

  1. 169
  2. 5
  3. Fourth quadrant
  4. 10
  5. 6
  6. 22
  7. 15°
  8. 2
  9. 12
  10. 132 cm
  11. 4 and 5
  12. 4
  13. 16 times
  14. 3
  15. First quadrant
  16. 19
  17. 6
  18. 6
  19. 25 times
  20. 3² × 5 × 7
  21. 8
  22. 25
  23. 3/4
  24. 7
  25. 6
  26. 4/11
  27. 6
  28. 35°
  29. First quadrant
  30. 13
  31. 2
  32. 4
  33. 20
  34. 100°
  35. 56
  36. 6
  37. 24
  38. 11
  39. 24
  40. 34

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