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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 842 · 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 prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
  2. 2.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 123 (b) 246 (c) 138 (d) 33
  3. 3.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 7 (d) 15
  4. 4.What is the mode of 10, 5, 17, 10, 5, 14 and 10? (a) 10 (b) 5 (c) 17 (d) 14
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
  6. 6.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 32 (c) 11 (d) 48
  7. 7.How many prime numbers are there between 70 and 80? (a) 3 (b) 4 (c) 2 (d) 5
  8. 8.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  9. 9.How many factors does 55 have? (a) 3 (b) 2 (c) 4 (d) 5
  10. 10.In a class of 26 children, 12 like dance, 16 like music and 7 like both. How many like neither? (a) 5 (b) 12 (c) 6 (d) 7
  11. 11.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  12. 12.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 15) (b) (x − 3)(x − 5) (c) (x + 1)(x + 7) (d) (x + 3)(x + 5)
  13. 13.What is the midpoint of the line joining (5, 6) and (7, 8)? (a) (7, 6) (b) (12, 14) (c) (1, 1) (d) (6, 7)
  14. 14.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
  15. 15.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 209 (b) 220 (c) 418 (d) 29
  16. 16.Which term of the AP 20, 28, 36, 44, … is 180? (a) 22nd (b) 21st (c) 23rd (d) 20th
  17. 17.A bag has 6 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 2 (c) 7 (d) 8
  18. 18.What is the sum of the first 5 terms of the AP 1, 2, 3, …? (a) 16 (b) 5 (c) 15 (d) 30
  19. 19.What is the sum of the roots of x² − 6x + 8 = 0? (a) 8 (b) 7 (c) 5 (d) 6
  20. 20.A bag has 3 red, 3 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/5 (b) 1/4 (c) 1/5 (d) 1/3
  21. 21.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 110 (b) 55 (c) 60 (d) 15
  22. 22.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 20° (c) 160° (d) 80°
  23. 23.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) 15 (b) 14 (c) 21 (d) 22
  24. 24.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
  25. 25.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 30 (c) 8 (d) 15
  26. 26.In a class of 26 children, 14 like tea, 15 like coffee and 8 like both. How many like neither? (a) 13 (b) 5 (c) 8 (d) 6
  27. 27.What is the mode of 13, 1, 1, 9, 3, 13 and 13? (a) 9 (b) 3 (c) 1 (d) 13
  28. 28.What is the median of 21, 39, 20, 35 and 32? (a) 21 (b) 35 (c) 32 (d) 20
  29. 29.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 120° (c) 95° (d) 145°
  30. 30.A bag has 6 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 16 (c) 2 (d) 11
  31. 31.A drawer has lots of yellow and red 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) 2 (c) 5 (d) 3
  32. 32.Which is the correct factorisation of x² + 14x + 45? (a) (x + 5)(x + 9) (b) (x + 1)(x + 45) (c) (x − 5)(x − 9) (d) (x + 1)(x + 13)
  33. 33.In a class of 31 children, 21 like cricket, 14 like football and 10 like both. How many like at least one of the two? (a) 25 (b) 15 (c) 35 (d) 31
  34. 34.What is the distance between the points (1, 25) and (13, 9)? (a) 20 (b) 28 (c) 21 (d) 400
  35. 35.What is the product of the roots of x² − 9x + 18 = 0? (a) 9 (b) 18 (c) 17 (d) 19
  36. 36.What is the sum of the roots of x² − 11x + 28 = 0? (a) 28 (b) 10 (c) 11 (d) 12
  37. 37.What is the mean of 13, 7, 20 and 4? (a) 13 (b) 12 (c) 11 (d) 10
  38. 38.Which term of the AP 7, 13, 19, 25, … is 67? (a) 10th (b) 12th (c) 13th (d) 11th
  39. 39.What is the midpoint of the line joining (5, 0) and (9, 4)? (a) (14, 4) (b) (7, 2) (c) (2, 2) (d) (2, 7)
  40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/9 (d) 1/12

Answer key

  1. 2⁴ × 3 × 5
  2. 123
  3. 8
  4. 10
  5. 13
  6. 24
  7. 3
  8. 7
  9. 4
  10. 5
  11. 6
  12. (x + 3)(x + 5)
  13. (6, 7)
  14. 7
  15. 209
  16. 21st
  17. 8
  18. 15
  19. 6
  20. 1/5
  21. 55
  22. 80°
  23. 15
  24. 2
  25. 15
  26. 5
  27. 13
  28. 32
  29. 95°
  30. 11
  31. 3
  32. (x + 5)(x + 9)
  33. 25
  34. 20
  35. 18
  36. 11
  37. 11
  38. 11th
  39. (7, 2)
  40. 1/12

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