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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 439 · 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.How many factors does 12 have? (a) 7 (b) 5 (c) 4 (d) 6
  2. 2.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  3. 3.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 496 (b) 637 (c) 627 (d) 636
  4. 4.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 11 (d) 3
  5. 5.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 1/5 (d) 5/6
  6. 6.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 70° (c) 105° (d) 145°
  7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
  8. 8.What is the midpoint of the line joining (2, 9) and (4, 1)? (a) (6, 10) (b) (5, 3) (c) (1, 4) (d) (3, 5)
  9. 9.What is the 34th term of the AP 18, 21, 24, 27, …? (a) 99 (b) 102 (c) 120 (d) 117
  10. 10.There are 8 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 32 (c) 11 (d) 48
  11. 11.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 72 (c) 36 (d) 64
  12. 12.If a + b = 17 and ab = 72, what is a² + b²? (a) 433 (b) 145 (c) 289 (d) 217
  13. 13.A bag has 9 green, 9 yellow and 8 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 17/26 (b) 1/3 (c) 9/17 (d) 9/26
  14. 14.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 132 (c) 144 (d) 66
  15. 15.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  16. 16.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
  17. 17.What is the distance between the points (1, 28) and (8, 4)? (a) 625 (b) 31 (c) 26 (d) 25
  18. 18.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 21° (b) 40° (c) 160° (d) 20°
  19. 19.A bag has 3 white, 2 green and 2 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 5/7 (b) 2/5 (c) 1/3 (d) 2/7
  20. 20.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 46° (b) 45° (c) 135° (d) 90°
  21. 21.A bag has 3 red, 3 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 6/7 (b) 11/14 (c) 1/3 (d) 3/14
  22. 22.What is the mode of 16, 4, 16, 4, 14, 3 and 16? (a) 3 (b) 14 (c) 4 (d) 16
  23. 23.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 99 (c) 108 (d) 90
  24. 24.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
  25. 25.What is the mean of 4, 6, 16 and 6? (a) 10 (b) 7 (c) 9 (d) 8
  26. 26.What is the mean of 10, 3, 12, 5, 13 and 23? (a) 12 (b) 10 (c) 11 (d) 13
  27. 27.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 160° (c) 20° (d) 340°
  28. 28.A bag has 2 red, 9 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 11/19 (c) 10/19 (d) 9/19
  29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 156 (b) 78 (c) 169 (d) 91
  30. 30.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 8 times (c) 16 times (d) 64 times
  31. 31.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 100°
  32. 32.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 70° (b) 40° (c) 110° (d) 220°
  33. 33.If a + b = 15 and ab = 50, what is (a − b)²? (a) 125 (b) 225 (c) 25 (d) 5
  34. 34.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 135° (c) 90° (d) 91°
  35. 35.How many factors does 106 have? (a) 2 (b) 5 (c) 4 (d) 3
  36. 36.How many factors does 49 have? (a) 4 (b) 2 (c) 3 (d) 1
  37. 37.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 909 (b) 729 (c) 1099 (d) 1089
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
  39. 39.A bag has 3 white, 6 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 10/17 (b) 8/17 (c) 1/3 (d) 9/17
  40. 40.A bag has 4 white balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 14 (c) 11 (d) 2

Answer key

  1. 6
  2. First quadrant
  3. 636
  4. 3
  5. 5/6
  6. 70°
  7. 176 cm
  8. (3, 5)
  9. 117
  10. 24
  11. 64
  12. 145
  13. 9/26
  14. 132
  15. 6
  16. 1/2
  17. 25
  18. 20°
  19. 2/7
  20. 45°
  21. 11/14
  22. 16
  23. 99
  24. 2³ × 3 × 7
  25. 8
  26. 11
  27. 160°
  28. 10/19
  29. 78
  30. 16 times
  31. 80°
  32. 110°
  33. 25
  34. 90°
  35. 4
  36. 3
  37. 1089
  38. 15
  39. 9/17
  40. 11

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