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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 219 · 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. 1.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 64 (b) 15 (c) 112 (d) 56
  2. 2.What is the sum of the roots of x² − 11x + 28 = 0? (a) 12 (b) 11 (c) 28 (d) 10
  3. 3.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
  4. 4.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  5. 5.What is the distance between the points (1, 17) and (9, 2)? (a) 23 (b) 289 (c) 18 (d) 17
  6. 6.A bag has 8 green balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 20 (b) 9 (c) 2 (d) 13
  7. 7.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.Which term of the AP 7, 9, 11, 13, … is 51? (a) 22nd (b) 25th (c) 24th (d) 23rd
  9. 9.What is the midpoint of the line joining (3, 10) and (5, 18)? (a) (8, 28) (b) (4, 14) (c) (1, 4) (d) (14, 4)
  10. 10.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 55° (d) 70°
  11. 11.A drawer has lots of green, black, red 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) 4 (c) 5 (d) 8
  12. 12.What is the sum of the first 8 terms of the AP 6, 8, 10, …? (a) 20 (b) 112 (c) 208 (d) 104
  13. 13.What is the distance between the points (7, 21) and (23, 9)? (a) 20 (b) 400 (c) 28 (d) 21
  14. 14.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  15. 15.Two angles of a triangle are 30° and 90°. What is the exterior angle at the third corner? (a) 150° (b) 90° (c) 120° (d) 60°
  16. 16.In a class of 31 children, 21 like cricket, 11 like football and 4 like both. How many like at least one of the two? (a) 31 (b) 24 (c) 32 (d) 28
  17. 17.What is the sum of the roots of x² − 7x + 10 = 0? (a) 10 (b) 7 (c) 6 (d) 8
  18. 18.A drawer has lots of blue, red, white 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) 5 (b) 8 (c) 4 (d) 2
  19. 19.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  20. 20.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 33 (b) 123 (c) 138 (d) 246
  21. 21.What is the smallest prime factor of 161? (a) 7 (b) 23 (c) 2 (d) 1
  22. 22.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
  23. 23.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 36 (b) 15 (c) 64 (d) 72
  24. 24.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 70 (b) 40 (c) 35 (d) 12
  25. 25.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 29 (c) 28 (d) 22
  26. 26.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 108 (c) 36 (d) 12
  27. 27.A bag has 10 red balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 11 (b) 2 (c) 18 (d) 12
  28. 28.In a class of 38 children, 20 like cricket, 24 like football and 2 like neither. How many like both? (a) 6 (b) 36 (c) 8 (d) 2
  29. 29.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 66 (d) 63
  30. 30.What is the mean of 17, 20, 2 and 5? (a) 12 (b) 13 (c) 11 (d) 10
  31. 31.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1306 (b) 1296 (c) 1584 (d) 1936
  32. 32.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 21 (c) 28 (d) 49
  33. 33.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 6 (d) 4
  34. 34.How many factors does 24 have? (a) 9 (b) 6 (c) 8 (d) 7
  35. 35.What is the 15th term of the AP 9, 18, 27, 36, …? (a) 136 (b) 126 (c) 144 (d) 135
  36. 36.Two angles of a triangle are 25° and 105°. What is the third angle? (a) 130° (b) 50° (c) 155° (d) 75°
  37. 37.In a class of 44 children, 21 like tea, 17 like coffee and 10 like neither. How many like both? (a) 5 (b) 10 (c) 4 (d) 34
  38. 38.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 9 (c) 5 (d) 6
  39. 39.What is the 20th term of the AP 3, 10, 17, 24, …? (a) 140 (b) 136 (c) 143 (d) 133
  40. 40.A bag has 5 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 2 (c) 7 (d) 6

Answer key

  1. 56
  2. 11
  3. 1/4
  4. 1/2
  5. 17
  6. 13
  7. Second quadrant
  8. 23rd
  9. (4, 14)
  10. 55°
  11. 5
  12. 104
  13. 20
  14. 2³ × 3 × 7
  15. 120°
  16. 28
  17. 7
  18. 5
  19. First quadrant
  20. 123
  21. 7
  22. 44 cm
  23. 64
  24. 35
  25. 22
  26. 36
  27. 12
  28. 8
  29. 63
  30. 11
  31. 1296
  32. 21
  33. 5
  34. 8
  35. 135
  36. 50°
  37. 4
  38. 6
  39. 136
  40. 7

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