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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 667 · 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.What is the midpoint of the line joining (6, 13) and (18, 5)? (a) (9, 12) (b) (6, 4) (c) (24, 18) (d) (12, 9)
  2. 2.What is the median of 2, 39, 8, 1 and 24? (a) 9 (b) 2 (c) 24 (d) 8
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 4 (d) 15
  4. 4.What is the median of 22, 9, 3, 11, 25, 36 and 7? (a) 12 (b) 9 (c) 11 (d) 22
  5. 5.What is the sum of the first 5 terms of the AP 10, 13, 16, …? (a) 83 (b) 22 (c) 80 (d) 160
  6. 6.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 16 sq cm (c) 96 sq cm (d) 64 sq cm
  7. 7.What is the sum of the first 10 terms of the AP 8, 12, 16, …? (a) 520 (b) 280 (c) 260 (d) 44
  8. 8.What is the missing term in the AP 3, ?, 13, 18, 23? (a) 8 (b) 13 (c) 7 (d) 9
  9. 9.How many factors does 95 have? (a) 2 (b) 3 (c) 4 (d) 5
  10. 10.In a class of 30 children, 14 like mangoes, 17 like bananas and 5 like both. How many like neither? (a) 3 (b) 4 (c) 5 (d) 9
  11. 11.What is the smallest prime factor of 299? (a) 23 (b) 13 (c) 1 (d) 2
  12. 12.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
  13. 13.How many factors does 91 have? (a) 2 (b) 5 (c) 4 (d) 3
  14. 14.What is the distance between the points (9, 8) and (24, 16)? (a) 289 (b) 23 (c) 17 (d) 18
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/12 (c) 1/36 (d) 1/18
  16. 16.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  17. 17.Using (a − b)² = a² − 2ab + b², what is 16²? (a) 256 (b) 576 (c) 266 (d) 384
  18. 18.There are 3 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) 12 (b) 9 (c) 6 (d) 18
  19. 19.Two angles of a triangle are 25° and 60°. What is the exterior angle at the third corner? (a) 85° (b) 155° (c) 95° (d) 120°
  20. 20.What is the distance between the points (2, 6) and (8, 14)? (a) 100 (b) 11 (c) 10 (d) 14
  21. 21.In a class of 30 children, 15 like tea, 13 like coffee and 5 like both. How many like neither? (a) 12 (b) 5 (c) 2 (d) 7
  22. 22.In a class of 45 children, 29 like mangoes, 25 like bananas and 12 like both. How many like only mangoes? (a) 20 (b) 29 (c) 17 (d) 13
  23. 23.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
  24. 24.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 81 (c) 30 (d) 9
  25. 25.A bag has 7 white balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 8 (c) 11 (d) 9
  26. 26.A bag has 3 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 4 (b) 5 (c) 2 (d) 8
  27. 27.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 96 (c) 78 (d) 88
  28. 28.The mean of 5 numbers is 16. When the number 34 is added to them, what is the new mean? (a) 25 (b) 19 (c) 16 (d) 20
  29. 29.A bag has 9 yellow balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 10 (d) 6
  30. 30.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 144 (c) 66 (d) 78
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
  32. 32.What is the sum of the first 5 terms of the AP 3, 8, 13, …? (a) 23 (b) 65 (c) 130 (d) 70
  33. 33.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
  34. 34.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 189 (c) 66 (d) 21
  35. 35.What is the median of 21, 32, 22, 33 and 3? (a) 32 (b) 23 (c) 22 (d) 21
  36. 36.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  37. 37.What is the prime factorisation of 14? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
  38. 38.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1369 (b) 1849 (c) 1609 (d) 1859
  39. 39.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 40° (b) 145° (c) 75° (d) 140°
  40. 40.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 240 (d) 25

Answer key

  1. (12, 9)
  2. 8
  3. 14
  4. 11
  5. 80
  6. 96 sq cm
  7. 260
  8. 8
  9. 4
  10. 4
  11. 13
  12. 176 cm
  13. 4
  14. 17
  15. 1/36
  16. 10
  17. 256
  18. 9
  19. 85°
  20. 10
  21. 7
  22. 17
  23. 25 times
  24. 27
  25. 9
  26. 5
  27. 87
  28. 19
  29. 10
  30. 66
  31. 125°
  32. 65
  33. 616 sq cm
  34. 63
  35. 22
  36. 5
  37. 2 × 7
  38. 1849
  39. 140°
  40. 120

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