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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 426 · 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 straight lines cross. Two vertically opposite angles add up to 300°. What is each of the other two angles? (a) 31° (b) 150° (c) 30° (d) 60°
  2. 2.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) 66 (b) 189 (c) 21 (d) 63
  3. 3.What is the sum of all the whole numbers from 1 to 48? (a) 2352 (b) 1152 (c) 1176 (d) 1128
  4. 4.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 9856 sq cm
  5. 5.In a class of 35 children, 16 like cricket, 26 like football and 1 like neither. How many like both? (a) 7 (b) 8 (c) 34 (d) 1
  6. 6.What is the median of 23, 6, 12, 9, 18, 34 and 2? (a) 18 (b) 13 (c) 9 (d) 12
  7. 7.A drawer has lots of 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) 3 (b) 4 (c) 5 (d) 2
  8. 8.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
  9. 9.What is the sum of the first 5 terms of the AP 7, 9, 11, …? (a) 55 (b) 60 (c) 15 (d) 110
  10. 10.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 144 (c) 48 (d) 16
  11. 11.What is the sum of the roots of x² − 6x + 8 = 0? (a) 7 (b) 5 (c) 6 (d) 8
  12. 12.What is the mode of 2, 15, 4, 13, 15, 4 and 4? (a) 4 (b) 13 (c) 2 (d) 15
  13. 13.If a + b = 20 and ab = 96, what is a² + b²? (a) 592 (b) 400 (c) 208 (d) 304
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 270°. What is each of the other two angles? (a) 45° (b) 135° (c) 46° (d) 90°
  15. 15.Two angles of a triangle are 70° and 80°. What is the third angle? (a) 150° (b) 30° (c) 110° (d) 100°
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 2 (c) 3 (d) 5
  17. 17.A drawer has lots of white, blue, yellow and red 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) 8 (d) 4
  18. 18.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  19. 19.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 55 (b) 45 (c) 17 (d) 90
  20. 20.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 64 (b) 36 (c) 28 (d) 56
  21. 21.What is the mode of 19, 19, 19, 11, 5, 11 and 7? (a) 19 (b) 5 (c) 7 (d) 11
  22. 22.What is the 39th term of the AP 4, 9, 14, 19, …? (a) 195 (b) 190 (c) 194 (d) 199
  23. 23.If a + b = 15 and ab = 54, what is a² + b²? (a) 225 (b) 333 (c) 171 (d) 117
  24. 24.In a class of 33 children, 25 like maths, 18 like science and 11 like both. How many like neither? (a) 1 (b) 11 (c) 2 (d) 12
  25. 25.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 15 (d) 30
  26. 26.A bag has 3 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 4 (d) 7
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 5 (b) 3 (c) 2 (d) 4
  28. 28.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 1/4 (c) 1/3 (d) 2/3
  29. 29.What is the median of 29, 25, 27, 36 and 22? (a) 25 (b) 29 (c) 27 (d) 28
  30. 30.What is the sum of the first 9 terms of the AP 4, 8, 12, …? (a) 360 (b) 198 (c) 36 (d) 180
  31. 31.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
  32. 32.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1235 (b) 1225 (c) 1575 (d) 2025
  33. 33.What is the midpoint of the line joining (4, 7) and (14, 17)? (a) (9, 12) (b) (12, 9) (c) (18, 24) (d) (5, 5)
  34. 34.In which quadrant does the point (4, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the missing term in the AP 18, 24, ?, 36, 42? (a) 36 (b) 29 (c) 30 (d) 31
  36. 36.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.A bag has 6 blue balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 17 (c) 12 (d) 2
  38. 38.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 441 (b) 399 (c) 371 (d) 361
  39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
  40. 40.What is the sum of the roots of x² − 7x + 10 = 0? (a) 8 (b) 7 (c) 10 (d) 6

Answer key

  1. 30°
  2. 63
  3. 1176
  4. 2464 sq cm
  5. 8
  6. 12
  7. 3
  8. 1/2
  9. 55
  10. 48
  11. 6
  12. 4
  13. 208
  14. 45°
  15. 30°
  16. 4
  17. 5
  18. 7
  19. 45
  20. 28
  21. 19
  22. 194
  23. 117
  24. 1
  25. 25
  26. 5
  27. 4
  28. 2/3
  29. 27
  30. 180
  31. 1/3
  32. 1225
  33. (9, 12)
  34. Fourth quadrant
  35. 30
  36. Fourth quadrant
  37. 12
  38. 361
  39. 6
  40. 7

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