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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 974 · 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.In which quadrant does the point (4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.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) 14 (b) 7 (c) 8 (d) 15
  3. 3.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
  4. 4.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 9 (d) 6
  5. 5.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
  6. 6.How many factors does 99 have? (a) 6 (b) 4 (c) 7 (d) 5
  7. 7.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 25 (c) 15 (d) 20
  8. 8.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  9. 9.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
  10. 10.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 17 cu cm (b) 16 cu cm (c) 8 cu cm (d) 40 cu cm
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 18 (b) 9 (c) 19 (d) 16
  12. 12.In a class of 21 children, 8 like tea, 12 like coffee and 2 like both. How many like only tea? (a) 10 (b) 6 (c) 9 (d) 8
  13. 13.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 121 (c) 66 (d) 110
  14. 14.How many factors does 67 have? (a) 4 (b) 1 (c) 2 (d) 3
  15. 15.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 65° (b) 30° (c) 150° (d) 145°
  16. 16.A bag has 10 blue balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 12 (c) 15 (d) 2
  17. 17.What is the distance between the points (5, 5) and (9, 2)? (a) 25 (b) 5 (c) 7 (d) 6
  18. 18.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  19. 19.In a class of 26 children, 7 like maths, 19 like science and 3 like neither. How many like both? (a) 3 (b) 4 (c) 2 (d) 23
  20. 20.What is the sum of the first 10 terms of the AP 7, 10, 13, …? (a) 410 (b) 205 (c) 34 (d) 220
  21. 21.What is the distance between the points (4, 8) and (12, 2)? (a) 14 (b) 100 (c) 10 (d) 11
  22. 22.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
  23. 23.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 80° (c) 10° (d) 50°
  24. 24.The mean of 4 numbers is 37. When the number 32 is added to them, what is the new mean? (a) 36 (b) 35 (c) 38 (d) 37
  25. 25.What is the sum of the roots of x² − 15x + 54 = 0? (a) 54 (b) 14 (c) 16 (d) 15
  26. 26.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 50° (c) 140° (d) 170°
  27. 27.What is the sum of the first 9 terms of the AP 7, 10, 13, …? (a) 31 (b) 171 (c) 174 (d) 342
  28. 28.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
  29. 29.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
  30. 30.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 240 (c) 252 (d) 243
  31. 31.Which term of the AP 4, 10, 16, 22, … is 76? (a) 14th (b) 15th (c) 12th (d) 13th
  32. 32.What is the mode of 3, 6, 6, 6, 4, 7 and 4? (a) 3 (b) 4 (c) 7 (d) 6
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 16 (d) 17
  34. 34.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
  35. 35.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 25 (c) 120 (d) 20
  36. 36.In a class of 48 children, 20 like maths, 23 like science and 4 like both. How many like at least one of the two? (a) 43 (b) 35 (c) 48 (d) 39
  37. 37.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.A bag has 6 red balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 8 (c) 2 (d) 7
  39. 39.What is the median of 3, 26, 39, 1 and 27? (a) 39 (b) 3 (c) 27 (d) 26
  40. 40.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 150° (b) 100° (c) 110° (d) 30°

Answer key

  1. First quadrant
  2. 8
  3. 125 times
  4. 6
  5. 44 cm
  6. 6
  7. 10
  8. 5
  9. 3/4
  10. 16 cu cm
  11. 18
  12. 6
  13. 55
  14. 2
  15. 30°
  16. 12
  17. 5
  18. 120
  19. 3
  20. 205
  21. 10
  22. 9 times
  23. 50°
  24. 36
  25. 15
  26. 10°
  27. 171
  28. 4 times
  29. 1/3
  30. 252
  31. 13th
  32. 6
  33. 17
  34. 21
  35. 120
  36. 39
  37. Third quadrant
  38. 8
  39. 26
  40. 150°

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