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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 625 · 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 mode of 17, 5, 17, 7, 17, 7 and 6? (a) 6 (b) 5 (c) 7 (d) 17
  2. 2.In a class of 44 children, 21 like cricket, 17 like football and 4 like both. How many like at least one of the two? (a) 44 (b) 34 (c) 38 (d) 30
  3. 3.What is the midpoint of the line joining (8, 14) and (16, 2)? (a) (24, 16) (b) (8, 12) (c) (12, 8) (d) (4, 6)
  4. 4.In a class of 42 children, 24 like mangoes, 12 like bananas and 10 like neither. How many like both? (a) 10 (b) 32 (c) 5 (d) 4
  5. 5.What is the 11th term of the AP 2, 4, 6, 8, …? (a) 24 (b) 20 (c) 22 (d) 23
  6. 6.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
  7. 7.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 150° (b) 115° (c) 145° (d) 65°
  8. 8.In a class of 23 children, 19 like mangoes, 11 like bananas and 8 like both. How many like at least one of the two? (a) 23 (b) 30 (c) 14 (d) 22
  9. 9.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 3/8 (d) 7/8
  10. 10.How many factors does 116 have? (a) 5 (b) 7 (c) 4 (d) 6
  11. 11.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 8659 (b) 8109 (c) 8649 (d) 7569
  12. 12.In which quadrant does the point (−5, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the sum of the first 7 terms of the AP 1, 6, 11, …? (a) 31 (b) 224 (c) 112 (d) 117
  14. 14.A bag has 8 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 6 (d) 13
  15. 15.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 40° (c) 70° (d) 140°
  16. 16.In a class of 45 children, 17 like tea, 22 like coffee and 2 like both. How many like neither? (a) 10 (b) 2 (c) 6 (d) 8
  17. 17.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) 15 (b) 48 (c) 135 (d) 45
  18. 18.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) 15 (b) 14 (c) 7 (d) 8
  19. 19.A bag has 7 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 8 (c) 2 (d) 15
  20. 20.Two angles of a triangle are 45° and 65°. What is the third angle? (a) 135° (b) 110° (c) 115° (d) 70°
  21. 21.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) 24 (b) 25 (c) 12 (d) 13
  22. 22.The mean of 7 numbers is 11. When the number 3 is added to them, what is the new mean? (a) 7 (b) 10 (c) 9 (d) 11
  23. 23.In a class of 41 children, 17 like mangoes, 26 like bananas and 6 like both. How many like only mangoes? (a) 11 (b) 20 (c) 15 (d) 17
  24. 24.The mean of 3 numbers is 32. When the number 40 is added to them, what is the new mean? (a) 36 (b) 35 (c) 34 (d) 32
  25. 25.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
  26. 26.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 11) (b) (x + 3)(x + 9) (c) (x + 1)(x + 27) (d) (x − 3)(x − 9)
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  28. 28.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 50° (c) 65° (d) 115°
  29. 29.How many factors does 37 have? (a) 1 (b) 4 (c) 2 (d) 3
  30. 30.What is the sum of the first 8 terms of the AP 2, 8, 14, …? (a) 368 (b) 208 (c) 184 (d) 44
  31. 31.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 40° (b) 70° (c) 20° (d) 110°
  32. 32.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 245° (b) 130° (c) 115° (d) 65°
  33. 33.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 5 (d) 7
  34. 34.What is the median of 6, 37, 28, 30 and 21? (a) 29 (b) 21 (c) 30 (d) 28
  35. 35.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
  36. 36.What is the mode of 11, 13, 18, 6, 6, 6 and 18? (a) 11 (b) 6 (c) 18 (d) 13
  37. 37.What is the median of 23, 39, 24, 15 and 8? (a) 15 (b) 22 (c) 24 (d) 23
  38. 38.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 496 (b) 248 (c) 272 (d) 52
  39. 39.In a league, 6 teams each play every other team once. How many matches are played? (a) 30 (b) 15 (c) 36 (d) 21
  40. 40.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 130° (b) 105° (c) 55° (d) 125°

Answer key

  1. 17
  2. 34
  3. (12, 8)
  4. 4
  5. 22
  6. 30°
  7. 115°
  8. 22
  9. 7/8
  10. 6
  11. 8649
  12. Second quadrant
  13. 112
  14. 9
  15. 70°
  16. 8
  17. 45
  18. 8
  19. 9
  20. 70°
  21. 13
  22. 10
  23. 11
  24. 34
  25. 3² × 7
  26. (x + 3)(x + 9)
  27. 5
  28. 50°
  29. 2
  30. 184
  31. 40°
  32. 65°
  33. 5
  34. 28
  35. 216 sq cm
  36. 6
  37. 23
  38. 248
  39. 15
  40. 55°

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