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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 497 · 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 circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 176 cm (d) 616 cm
  2. 2.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
  3. 3.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  4. 4.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) 21 (d) 22
  5. 5.What is the median of 9, 37, 6, 22 and 38? (a) 6 (b) 9 (c) 22 (d) 37
  6. 6.What is the sum of all the whole numbers from 1 to 62? (a) 1922 (b) 1953 (c) 1891 (d) 3906
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 51° (b) 130° (c) 100° (d) 50°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 90° (d) 55°
  9. 9.Using (a + b)² = a² + 2ab + b², what is 62²? (a) 3844 (b) 3364 (c) 3854 (d) 3604
  10. 10.The mean of 6 numbers is 36. When the number 15 is added to them, what is the new mean? (a) 32 (b) 34 (c) 36 (d) 33
  11. 11.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)
  12. 12.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 86 (c) 96 (d) 104
  13. 13.Using (a + b)² = a² + 2ab + b², what is 103²? (a) 9409 (b) 10609 (c) 10009 (d) 10619
  14. 14.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 60° (b) 150° (c) 30° (d) 120°
  15. 15.The mean of 9 numbers is 29. When the number 49 is added to them, what is the new mean? (a) 39 (b) 29 (c) 31 (d) 32
  16. 16.In a class of 30 children, 21 like cricket, 17 like football and 11 like both. How many like neither? (a) 3 (b) 14 (c) 4 (d) 11
  17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
  18. 18.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 36 (d) 11
  19. 19.The mean of 3 numbers is 11. When the number 3 is added to them, what is the new mean? (a) 9 (b) 10 (c) 7 (d) 11
  20. 20.What are the roots of x² − 17x + 72 = 0? (a) 8 and 9 (b) 2 and 36 (c) 1 and 16 (d) 1 and 72
  21. 21.Which is the correct factorisation of x² + 11x + 24? (a) (x − 3)(x − 8) (b) (x + 3)(x + 8) (c) (x + 1)(x + 10) (d) (x + 1)(x + 24)
  22. 22.A bag has 8 yellow, 8 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 5/16 (b) 1/3 (c) 16/21 (d) 5/21
  23. 23.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 55 (d) 110
  24. 24.What is the sum of the first 23 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 552 (c) 529 (d) 276
  25. 25.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 2 (d) 1
  26. 26.What is the sum of all the whole numbers from 1 to 10? (a) 50 (b) 110 (c) 45 (d) 55
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 5 (d) 15
  28. 28.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 15 (d) 7
  29. 29.Which term of the AP 3, 11, 19, 27, … is 283? (a) 36th (b) 35th (c) 37th (d) 38th
  30. 30.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 80° (d) 50°
  31. 31.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
  33. 33.In a class of 55 children, 31 like tea, 29 like coffee and 6 like neither. How many like both? (a) 5 (b) 11 (c) 49 (d) 6
  34. 34.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
  35. 35.What is the mode of 15, 17, 3, 15, 10, 17 and 17? (a) 15 (b) 3 (c) 17 (d) 10
  36. 36.What is the mode of 9, 19, 15, 15, 9, 15 and 13? (a) 19 (b) 13 (c) 9 (d) 15
  37. 37.A drawer has lots of yellow, blue 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) 4 (b) 2 (c) 6 (d) 3
  38. 38.If a + b = 18 and ab = 77, what is (a − b)²? (a) 170 (b) 4 (c) 324 (d) 16
  39. 39.In a class of 31 children, 18 like tea, 22 like coffee and 12 like both. How many like only tea? (a) 10 (b) 18 (c) 9 (d) 6
  40. 40.In how many different ways can the letters of the word MATHS be arranged? (a) 240 (b) 25 (c) 20 (d) 120

Answer key

  1. 88 cm
  2. 2464 sq cm
  3. Third quadrant
  4. 22
  5. 22
  6. 1953
  7. 50°
  8. 45°
  9. 3844
  10. 33
  11. (x + 8)(x + 9)
  12. 95
  13. 10609
  14. 120°
  15. 31
  16. 3
  17. 125 times
  18. 33
  19. 9
  20. 8 and 9
  21. (x + 3)(x + 8)
  22. 5/21
  23. 55
  24. 529
  25. 2
  26. 55
  27. 16
  28. 8
  29. 36th
  30. 80°
  31. Second quadrant
  32. 616 sq cm
  33. 11
  34. 1386 sq cm
  35. 17
  36. 15
  37. 4
  38. 16
  39. 6
  40. 120

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