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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 614 · 40 questions
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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.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) 135 (b) 15 (c) 48 (d) 45
  2. 2.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 15° (b) 105° (c) 75° (d) 30°
  3. 3.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 486 cu cm (c) 324 cu cm (d) 729 cu cm
  4. 4.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 2 (d) 11
  5. 5.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  6. 6.How many factors does 103 have? (a) 2 (b) 1 (c) 3 (d) 4
  7. 7.The mean of 4 numbers is 31. When the number 11 is added to them, what is the new mean? (a) 21 (b) 31 (c) 27 (d) 28
  8. 8.A bag has 8 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 10 (d) 12
  9. 9.What is the sum of the roots of x² − 11x + 24 = 0? (a) 11 (b) 24 (c) 12 (d) 10
  10. 10.A bag has 7 white balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 13 (c) 8 (d) 2
  11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 5/36 (d) 4/11
  12. 12.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 28 (c) 64 (d) 36
  13. 13.How many factors does 31 have? (a) 1 (b) 3 (c) 2 (d) 4
  14. 14.What is the mean of 19, 18, 13 and 14? (a) 15 (b) 17 (c) 16 (d) 18
  15. 15.In a class of 47 children, 22 like cricket, 27 like football and 9 like both. How many like at least one of the two? (a) 49 (b) 47 (c) 31 (d) 40
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
  17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
  18. 18.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
  19. 19.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5³
  20. 20.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 12 (d) 30
  21. 21.What is the mean of 11, 4, 17 and 8? (a) 11 (b) 9 (c) 10 (d) 8
  22. 22.In a class of 37 children, 14 like dance, 22 like music and 8 like neither. How many like both? (a) 6 (b) 29 (c) 7 (d) 8
  23. 23.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.In a class of 25 children, 9 like cricket, 16 like football and 5 like both. How many like neither? (a) 0 (b) 5 (c) 6 (d) 10
  25. 25.What is the mode of 3, 13, 3, 2, 6, 3 and 6? (a) 3 (b) 2 (c) 6 (d) 13
  26. 26.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 50° (b) 80° (c) 40° (d) 100°
  27. 27.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 812 (c) 406 (d) 784
  28. 28.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  30. 30.What is the sum of the roots of x² − 9x + 20 = 0? (a) 20 (b) 8 (c) 9 (d) 10
  31. 31.What is the median of 18, 35, 3, 30 and 37? (a) 35 (b) 30 (c) 18 (d) 3
  32. 32.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
  33. 33.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 42 (c) 35 (d) 12
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  35. 35.If a + b = 10 and ab = 9, what is a² + b²? (a) 100 (b) 118 (c) 82 (d) 91
  36. 36.Two angles of a triangle are 50° and 120°. What is the third angle? (a) 60° (b) 170° (c) 10° (d) 130°
  37. 37.Two angles of a triangle are 75° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 125° (c) 55° (d) 130°
  38. 38.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
  39. 39.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) 13 (c) 25 (d) 12
  40. 40.4 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 16 (b) 12 (c) 8 (d) 6

Answer key

  1. 45
  2. 30°
  3. 729 cu cm
  4. 11
  5. 2² × 3 × 5
  6. 2
  7. 27
  8. 10
  9. 11
  10. 13
  11. 1/9
  12. 28
  13. 2
  14. 16
  15. 40
  16. 2
  17. 1386 sq cm
  18. 176 cm
  19. 2³ × 5
  20. 15
  21. 10
  22. 7
  23. Second quadrant
  24. 5
  25. 3
  26. 40°
  27. 784
  28. 6
  29. 25
  30. 9
  31. 30
  32. 1/2
  33. 35
  34. 5
  35. 82
  36. 10°
  37. 125°
  38. 6
  39. 13
  40. 8

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