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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 26 · 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 dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/9 (b) 4/11 (c) 5/36 (d) 1/11
  2. 2.A bag has 6 green balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 18 (d) 13
  3. 3.In a class of 26 children, 17 like maths, 8 like science and 4 like both. How many like only maths? (a) 18 (b) 13 (c) 17 (d) 4
  4. 4.There are 7 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) 42 (b) 10 (c) 21 (d) 28
  5. 5.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 529 (b) 276 (c) 552 (d) 45
  6. 6.A bag has 7 blue balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 8 (c) 9 (d) 15
  7. 7.A bag has 12 blue balls and 13 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 25 (b) 2 (c) 14 (d) 13
  8. 8.What is the smallest prime factor of 403? (a) 2 (b) 13 (c) 31 (d) 1
  9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  10. 10.4 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 40 (c) 20 (d) 9
  11. 11.What is the sum of all the whole numbers from 1 to 30? (a) 465 (b) 450 (c) 435 (d) 930
  12. 12.What is the midpoint of the line joining (9, 10) and (15, 14)? (a) (24, 24) (b) (13, 12) (c) (3, 2) (d) (12, 12)
  13. 13.The mean of 4 numbers is 14. When the number 4 is added to them, what is the new mean? (a) 9 (b) 12 (c) 13 (d) 14
  14. 14.What is the missing term in the AP 9, 18, ?, 36, 45? (a) 26 (b) 27 (c) 28 (d) 36
  15. 15.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
  16. 16.In a class of 38 children, 24 like tea, 23 like coffee and 10 like both. How many like at least one of the two? (a) 37 (b) 47 (c) 38 (d) 27
  17. 17.The mean of 3 numbers is 35. When the number 27 is added to them, what is the new mean? (a) 31 (b) 35 (c) 33 (d) 34
  18. 18.What is the 15th term of the AP 20, 25, 30, 35, …? (a) 75 (b) 90 (c) 95 (d) 70
  19. 19.How many factors does 79 have? (a) 1 (b) 4 (c) 2 (d) 3
  20. 20.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 35° (b) 140° (c) 75° (d) 145°
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  22. 22.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 784 (b) 904 (c) 1034 (d) 1024
  23. 23.What is the 37th term of the AP 10, 15, 20, 25, …? (a) 185 (b) 190 (c) 180 (d) 195
  24. 24.In a league, 15 teams each play every other team once. How many matches are played? (a) 225 (b) 210 (c) 120 (d) 105
  25. 25.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 32 (d) 11
  26. 26.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  27. 27.If a + b = 14 and ab = 45, what is a² + b²? (a) 286 (b) 106 (c) 196 (d) 151
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  29. 29.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 30 (c) 35 (d) 11
  30. 30.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 4916 (b) 4356 (c) 5486 (d) 5476
  31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
  32. 32.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its volume? (a) 24 cu cm (b) 9 cu cm (c) 6 cu cm (d) 52 cu cm
  33. 33.Using (a − b)² = a² − 2ab + b², what is 57²? (a) 3591 (b) 3969 (c) 3259 (d) 3249
  34. 34.What is the missing term in the AP 18, ?, 22, 24, 26? (a) 19 (b) 22 (c) 20 (d) 21
  35. 35.What is the 12th term of the AP 11, 16, 21, 26, …? (a) 71 (b) 60 (c) 66 (d) 55
  36. 36.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 441 (b) 371 (c) 361 (d) 399
  37. 37.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 91 (c) 156 (d) 78
  38. 38.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 228 (c) 229 (d) 224
  39. 39.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 56 (b) 64 (c) 28 (d) 16
  40. 40.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm

Answer key

  1. 1/9
  2. 13
  3. 13
  4. 21
  5. 529
  6. 9
  7. 14
  8. 13
  9. 1/2
  10. 20
  11. 465
  12. (12, 12)
  13. 12
  14. 27
  15. 9 times
  16. 37
  17. 33
  18. 90
  19. 2
  20. 35°
  21. 10
  22. 1024
  23. 190
  24. 105
  25. 24
  26. Third quadrant
  27. 106
  28. 10
  29. 30
  30. 5476
  31. 21
  32. 24 cu cm
  33. 3249
  34. 20
  35. 66
  36. 361
  37. 78
  38. 228
  39. 28
  40. 176 cm

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