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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 958 · 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 10, 14, 20, 10, 10, 14 and 16? (a) 10 (b) 16 (c) 20 (d) 14
  2. 2.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 1 (d) 3
  3. 3.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 29 (d) 7
  4. 4.A bag has 8 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 15 (c) 2 (d) 10
  5. 5.What is the mean of 10, 4, 6, 13 and 12? (a) 11 (b) 10 (c) 9 (d) 8
  6. 6.Two angles of a triangle are 25° and 130°. What is the third angle? (a) 50° (b) 205° (c) 155° (d) 25°
  7. 7.Two angles of a triangle are 35° and 55°. What is the third angle? (a) 125° (b) 145° (c) 90° (d) 270°
  8. 8.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 3 times (c) 6 times (d) 27 times
  9. 9.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 196 (b) 182 (c) 105 (d) 91
  10. 10.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 351 (b) 51 (c) 702 (d) 676
  11. 11.In a class of 25 children, 7 like maths, 11 like science and 9 like neither. How many like both? (a) 16 (b) 9 (c) 2 (d) 3
  12. 12.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
  13. 13.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
  14. 14.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 25° (b) 155° (c) 130° (d) 65°
  15. 15.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 15 (c) 20 (d) 10
  16. 16.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 15 (d) 30
  17. 17.A cuboid is 5 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 20 cu cm (b) 48 cu cm (c) 9 cu cm (d) 10 cu cm
  18. 18.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 111 (b) 220 (c) 110 (d) 15
  19. 19.In a class of 31 children, 15 like dance, 19 like music and 12 like both. How many like only dance? (a) 15 (b) 12 (c) 3 (d) 7
  20. 20.A drawer has lots of blue, green, red and yellow 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) 5 (c) 2 (d) 8
  21. 21.What is the smallest prime factor of 49? (a) 3 (b) 7 (c) 2 (d) 1
  22. 22.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
  23. 23.In which quadrant does the point (−3, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
  25. 25.In a class of 29 children, 8 like dance, 21 like music and 2 like both. How many like at least one of the two? (a) 25 (b) 28 (c) 27 (d) 29
  26. 26.How many factors does 17 have? (a) 3 (b) 4 (c) 1 (d) 2
  27. 27.What is the distance between the points (8, 0) and (12, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  28. 28.In a class of 50 children, 26 like maths, 24 like science and 6 like both. How many like neither? (a) 0 (b) 7 (c) 6 (d) 12
  29. 29.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 72 (b) 64 (c) 15 (d) 36
  30. 30.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 45 (d) 81
  31. 31.What is the median of 23, 40, 33, 34, 24, 30 and 38? (a) 34 (b) 30 (c) 33 (d) 32
  32. 32.7 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) 14 (b) 9 (c) 21 (d) 28
  33. 33.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
  34. 34.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  35. 35.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 250° (c) 110° (d) 71°
  36. 36.What is the sum of the first 6 terms of the AP 8, 14, 20, …? (a) 138 (b) 38 (c) 156 (d) 276
  37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
  38. 38.What is the mean of 4, 20, 16 and 20? (a) 16 (b) 15 (c) 20 (d) 12
  39. 39.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 180 (b) 13 (c) 96 (d) 90
  40. 40.What are the roots of x² − 13x + 36 = 0? (a) 1 and 12 (b) 2 and 18 (c) 1 and 36 (d) 4 and 9

Answer key

  1. 10
  2. 1
  3. 7
  4. 10
  5. 9
  6. 25°
  7. 90°
  8. 9 times
  9. 91
  10. 676
  11. 2
  12. 24
  13. 65°
  14. 130°
  15. 10
  16. 15
  17. 20 cu cm
  18. 110
  19. 3
  20. 5
  21. 7
  22. 1/2
  23. Second quadrant
  24. 157
  25. 27
  26. 2
  27. 5
  28. 6
  29. 64
  30. 36
  31. 33
  32. 14
  33. 1/2
  34. 2³ × 5 × 7
  35. 70°
  36. 138
  37. 220 cm
  38. 15
  39. 90
  40. 4 and 9

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