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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 18 · 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 10 black balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 19 (b) 12 (c) 2 (d) 11
  2. 2.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 165° (b) 195° (c) 16° (d) 15°
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  4. 4.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 340 (c) 330 (d) 298
  5. 5.How many factors does 24 have? (a) 6 (b) 8 (c) 7 (d) 9
  6. 6.In a class of 42 children, 16 like dance, 31 like music and 12 like both. How many like neither? (a) 7 (b) 8 (c) 12 (d) 19
  7. 7.A bag has 11 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 23 (c) 2 (d) 12
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
  9. 9.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  10. 10.In a class of 44 children, 29 like cricket, 16 like football and 9 like both. How many like only cricket? (a) 29 (b) 28 (c) 7 (d) 20
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  12. 12.What is the mode of 9, 19, 19, 19, 5, 2 and 2? (a) 2 (b) 19 (c) 9 (d) 5
  13. 13.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 90 (c) 20 (d) 45
  14. 14.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 42 (c) 49 (d) 21
  15. 15.What is the mean of 14, 6, 8, 10, 18 and 22? (a) 15 (b) 12 (c) 14 (d) 13
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
  17. 17.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 45 (c) 90 (d) 55
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  19. 19.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
  20. 20.If a + b = 17 and ab = 70, what is a² + b²? (a) 429 (b) 289 (c) 219 (d) 149
  21. 21.How many factors does 120 have? (a) 14 (b) 15 (c) 17 (d) 16
  22. 22.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 61°
  23. 23.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 48 (c) 135 (d) 15
  24. 24.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 7310 (c) 3655 (d) 3656
  25. 25.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  26. 26.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 170 (b) 155 (c) 29 (d) 310
  27. 27.Which term of the AP 18, 21, 24, 27, … is 96? (a) 26th (b) 28th (c) 32nd (d) 27th
  28. 28.What is the distance between the points (5, 5) and (21, 17)? (a) 21 (b) 400 (c) 28 (d) 20
  29. 29.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
  30. 30.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 1 (d) 3
  31. 31.A bag has 8 blue, 8 white and 7 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/23 (b) 7/16 (c) 16/23 (d) 1/3
  32. 32.A drawer has lots of black, yellow, blue, red 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) 10 (b) 6 (c) 5 (d) 2
  33. 33.If a + b = 20 and ab = 96, what is (a − b)²? (a) 208 (b) 4 (c) 16 (d) 400
  34. 34.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 36 (c) 48 (d) 37
  35. 35.What is the distance between the points (1, 6) and (13, 22)? (a) 21 (b) 400 (c) 28 (d) 20
  36. 36.What is the missing term in the AP 1, 9, 17, ?, 33? (a) 26 (b) 24 (c) 25 (d) 33
  37. 37.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
  38. 38.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 154 sq cm (d) 77 sq cm
  39. 39.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/4 (c) 7/8 (d) 1/8
  40. 40.What is the mode of 19, 9, 19, 19, 2, 10 and 10? (a) 2 (b) 9 (c) 10 (d) 19

Answer key

  1. 12
  2. 15°
  3. 9
  4. 339
  5. 8
  6. 7
  7. 13
  8. 18
  9. 6
  10. 20
  11. 3
  12. 19
  13. 45
  14. 21
  15. 13
  16. 9
  17. 45
  18. 17
  19. 16 times
  20. 149
  21. 16
  22. 60°
  23. 45
  24. 3655
  25. 3² × 5 × 7
  26. 155
  27. 27th
  28. 20
  29. 15
  30. 3
  31. 7/23
  32. 6
  33. 16
  34. 37
  35. 20
  36. 25
  37. 1/4
  38. 154 sq cm
  39. 7/8
  40. 19

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