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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 748 · 40 questions
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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 distance between the points (0, 5) and (12, 21)? (a) 20 (b) 400 (c) 21 (d) 28
  2. 2.What is the 32nd term of the AP 13, 22, 31, 40, …? (a) 279 (b) 292 (c) 288 (d) 301
  3. 3.The mean of 3 numbers is 31. When the number 43 is added to them, what is the new mean? (a) 35 (b) 37 (c) 31 (d) 34
  4. 4.What is the sum of the first 8 terms of the AP 6, 9, 12, …? (a) 144 (b) 27 (c) 264 (d) 132
  5. 5.A cuboid is 9 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 168 cu cm (b) 54 cu cm (c) 108 cu cm (d) 17 cu cm
  6. 6.What is the mean of 3, 4, 14, 11 and 13? (a) 8 (b) 10 (c) 9 (d) 11
  7. 7.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 6 (d) 7
  8. 8.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 21 (d) 42
  9. 9.A drawer has lots of black, blue, red, yellow and white 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) 5 (c) 10 (d) 6
  10. 10.What is the sum of the first 7 terms of the AP 8, 10, 12, …? (a) 98 (b) 105 (c) 196 (d) 20
  11. 11.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 155° (b) 130° (c) 310° (d) 25°
  12. 12.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 36 (c) 24 (d) 25
  14. 14.What is the mean of 15, 4, 3 and 18? (a) 8 (b) 11 (c) 9 (d) 10
  15. 15.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) 28 (c) 22 (d) 21
  16. 16.A drawer has lots of black 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) 5 (c) 3 (d) 4
  17. 17.What is the sum of all the whole numbers from 1 to 23? (a) 253 (b) 276 (c) 277 (d) 552
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  19. 19.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2² × 3² × 5
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 7 (b) 16 (c) 17 (d) 18
  21. 21.In a class of 39 children, 17 like mangoes, 20 like bananas and 4 like neither. How many like both? (a) 2 (b) 4 (c) 3 (d) 35
  22. 22.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 72 (c) 18 (d) 17
  23. 23.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 70 (c) 78 (d) 69
  24. 24.What is the median of 11, 2, 8, 28 and 36? (a) 17 (b) 8 (c) 11 (d) 28
  25. 25.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 7 (d) 6
  26. 26.Which is the correct factorisation of x² + 12x + 27? (a) (x − 3)(x − 9) (b) (x + 1)(x + 27) (c) (x + 3)(x + 9) (d) (x + 1)(x + 11)
  27. 27.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 36 (b) 12 (c) 72 (d) 42
  28. 28.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 739 (b) 1089 (c) 891 (d) 729
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 5 (d) 2
  30. 30.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  31. 31.What is the distance between the points (3, 5) and (11, 20)? (a) 18 (b) 23 (c) 17 (d) 289
  32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
  33. 33.What is the mode of 3, 18, 18, 14, 14, 2 and 18? (a) 14 (b) 18 (c) 2 (d) 3
  34. 34.A cuboid is 8 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 424 sq cm (b) 106 sq cm (c) 212 sq cm (d) 144 sq cm
  35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  36. 36.What is the distance between the points (0, 3) and (5, 15)? (a) 14 (b) 169 (c) 13 (d) 17
  37. 37.If a + b = 17 and ab = 72, what is a² + b²? (a) 145 (b) 289 (c) 217 (d) 433
  38. 38.What is the median of 13, 30, 1, 3 and 6? (a) 1 (b) 3 (c) 6 (d) 13
  39. 39.What is the distance between the points (6, 5) and (30, 12)? (a) 25 (b) 31 (c) 625 (d) 26
  40. 40.A bag has 8 white balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 20 (b) 2 (c) 9 (d) 10

Answer key

  1. 20
  2. 292
  3. 34
  4. 132
  5. 108 cu cm
  6. 9
  7. 5
  8. 21
  9. 6
  10. 98
  11. 155°
  12. Second quadrant
  13. 25
  14. 10
  15. 22
  16. 3
  17. 276
  18. 15
  19. 2² × 3² × 5
  20. 17
  21. 2
  22. 17
  23. 69
  24. 11
  25. 6
  26. (x + 3)(x + 9)
  27. 36
  28. 729
  29. 4
  30. 6
  31. 17
  32. 1/9
  33. 18
  34. 212 sq cm
  35. 25
  36. 13
  37. 145
  38. 6
  39. 25
  40. 10

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