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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 583 · 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.Using (a + b)² = a² + 2ab + b², what is 33²? (a) 1089 (b) 1099 (c) 909 (d) 729
  2. 2.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 145° (c) 36° (d) 35°
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  4. 4.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 10 (c) 20 (d) 15
  5. 5.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 20° (d) 100°
  6. 6.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 5/6 (c) 1/3 (d) 1/5
  7. 7.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 2 (c) 3 (d) 4
  8. 8.The mean of 5 numbers is 38. When the number 44 is added to them, what is the new mean? (a) 41 (b) 38 (c) 39 (d) 40
  9. 9.What are the roots of x² − 15x + 54 = 0? (a) 1 and 14 (b) 1 and 54 (c) 6 and 9 (d) 2 and 27
  10. 10.If a + b = 17 and ab = 72, what is a² + b²? (a) 433 (b) 145 (c) 217 (d) 289
  11. 11.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 21 (d) 28
  12. 12.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
  13. 13.What is the distance between the points (1, 2) and (7, 10)? (a) 11 (b) 14 (c) 100 (d) 10
  14. 14.What is the distance between the points (0, 13) and (6, 5)? (a) 10 (b) 11 (c) 14 (d) 100
  15. 15.What is the mean of 12, 5, 12, 8, 12 and 5? (a) 10 (b) 11 (c) 9 (d) 8
  16. 16.What is the 30th term of the AP 15, 21, 27, 33, …? (a) 180 (b) 195 (c) 174 (d) 189
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 40° (b) 21° (c) 160° (d) 20°
  18. 18.How many factors does 17 have? (a) 3 (b) 1 (c) 4 (d) 2
  19. 19.In a class of 27 children, 21 like maths, 9 like science and 1 like neither. How many like both? (a) 1 (b) 3 (c) 26 (d) 4
  20. 20.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) 8 (c) 15 (d) 7
  21. 21.What is the mean of 9, 7, 2, 6 and 6? (a) 7 (b) 8 (c) 6 (d) 5
  22. 22.A drawer has lots of blue, white 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) 2 (b) 3 (c) 4 (d) 6
  23. 23.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 160° (b) 65° (c) 115° (d) 135°
  24. 24.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
  25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 13 (b) 16 (c) 8 (d) 15
  27. 27.A bag has 10 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 14 (b) 12 (c) 11 (d) 2
  28. 28.In a class of 26 children, 7 like maths, 19 like science and 3 like both. How many like at least one of the two? (a) 24 (b) 20 (c) 26 (d) 23
  29. 29.What is the 10th term of the AP 8, 16, 24, 32, …? (a) 72 (b) 88 (c) 81 (d) 80
  30. 30.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 350 (d) 417
  31. 31.How many factors does 119 have? (a) 3 (b) 4 (c) 5 (d) 2
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  33. 33.What is the distance between the points (0, 18) and (9, 6)? (a) 225 (b) 16 (c) 15 (d) 21
  34. 34.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 55 (d) 45
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 9 (c) 8 (d) 6
  36. 36.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
  37. 37.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 7/8 (d) 1/4
  38. 38.In a class of 47 children, 25 like tea, 25 like coffee and 2 like neither. How many like both? (a) 3 (b) 45 (c) 2 (d) 5
  39. 39.What is the mean of 7, 7, 18, 18, 2 and 14? (a) 12 (b) 10 (c) 13 (d) 11
  40. 40.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 616 cm (d) 44 cm

Answer key

  1. 1089
  2. 35°
  3. 10
  4. 10
  5. 20°
  6. 5/6
  7. 3
  8. 39
  9. 6 and 9
  10. 145
  11. 22
  12. 105
  13. 10
  14. 10
  15. 9
  16. 189
  17. 20°
  18. 2
  19. 4
  20. 8
  21. 6
  22. 4
  23. 115°
  24. 25 times
  25. 20
  26. 15
  27. 12
  28. 23
  29. 80
  30. 417
  31. 4
  32. 3
  33. 15
  34. 45
  35. 8
  36. 1386 sq cm
  37. 1/8
  38. 5
  39. 11
  40. 88 cm

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