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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 231 · 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.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 165° (b) 95° (c) 100° (d) 15°
  2. 2.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 300 (c) 301 (d) 291
  3. 3.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 5 (d) 4
  4. 4.What is the mode of 16, 5, 19, 16, 5, 9 and 16? (a) 16 (b) 19 (c) 9 (d) 5
  5. 5.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) 48 (b) 32 (c) 11 (d) 24
  6. 6.What is the distance between the points (2, 20) and (10, 5)? (a) 18 (b) 17 (c) 289 (d) 23
  7. 7.How many factors does 50 have? (a) 7 (b) 5 (c) 4 (d) 6
  8. 8.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
  9. 9.What are the roots of x² − 16x + 63 = 0? (a) 3 and 21 (b) 7 and 9 (c) 1 and 63 (d) 1 and 15
  10. 10.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 16° (b) 15° (c) 165° (d) 195°
  11. 11.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 154 cm (d) 22 cm
  12. 12.Using (a − b)² = a² − 2ab + b², what is 97²? (a) 10609 (b) 9419 (c) 9991 (d) 9409
  13. 13.What is the sum of the first 10 terms of the AP 3, 9, 15, …? (a) 600 (b) 330 (c) 57 (d) 300
  14. 14.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
  15. 15.What is the midpoint of the line joining (1, 4) and (13, 16)? (a) (7, 10) (b) (14, 20) (c) (6, 6) (d) (10, 7)
  16. 16.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  17. 17.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 16 (c) 18 (d) 7
  19. 19.What is the 17th term of the AP 2, 6, 10, 14, …? (a) 68 (b) 70 (c) 64 (d) 66
  20. 20.4 T-shirts and 4 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) 32 (c) 20 (d) 8
  21. 21.What is the median of 23, 21, 39, 19, 27, 29 and 25? (a) 19 (b) 23 (c) 25 (d) 27
  22. 22.If a + b = 11 and ab = 28, what is (a − b)²? (a) 65 (b) 3 (c) 121 (d) 9
  23. 23.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 285 (c) 294 (d) 295
  24. 24.What is the mean of 7, 5, 18, 8 and 17? (a) 13 (b) 10 (c) 11 (d) 12
  25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
  26. 26.A drawer has lots of white, yellow, red and green 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) 8 (c) 5 (d) 4
  27. 27.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 3 (d) 1
  29. 29.What is the sum of the first 9 terms of the AP 6, 10, 14, …? (a) 396 (b) 198 (c) 38 (d) 216
  30. 30.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 37 (c) 49 (d) 48
  31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  32. 32.What is the missing term in the AP 2, ?, 6, 8, 10? (a) 3 (b) 6 (c) 4 (d) 5
  33. 33.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 3850 cm (d) 220 cm
  34. 34.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
  35. 35.A bag has 11 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 19 (b) 12 (c) 13 (d) 2
  36. 36.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 110° (d) 150°
  37. 37.If a + b = 5 and ab = 4, what is (a − b)²? (a) 9 (b) 17 (c) 25 (d) 3
  38. 38.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 120° (c) 59° (d) 61°
  39. 39.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 20 (c) 11 (d) 25
  40. 40.What is the distance between the points (9, 4) and (15, 12)? (a) 11 (b) 14 (c) 10 (d) 100

Answer key

  1. 15°
  2. 300
  3. 5
  4. 16
  5. 24
  6. 17
  7. 6
  8. 44 cm
  9. 7 and 9
  10. 15°
  11. 44 cm
  12. 9409
  13. 300
  14. 90
  15. (7, 10)
  16. 1/2
  17. 88 cm
  18. 17
  19. 66
  20. 16
  21. 25
  22. 9
  23. 294
  24. 11
  25. 5/36
  26. 5
  27. 1/2
  28. 3
  29. 198
  30. 37
  31. 6
  32. 4
  33. 220 cm
  34. 2
  35. 13
  36. 150°
  37. 9
  38. 60°
  39. 10
  40. 10

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