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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 980 · 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.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  2. 2.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 20 (c) 25 (d) 120
  3. 3.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) 50° (d) 100°
  4. 4.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 693 sq cm
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 16 (c) 5 (d) 17
  6. 6.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 12 (d) 30
  7. 7.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 2 (d) 1
  8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 21 (b) 49 (c) 14 (d) 42
  9. 9.How many factors does 119 have? (a) 4 (b) 3 (c) 2 (d) 5
  10. 10.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 16 (c) 12 (d) 48
  11. 11.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 125 times (c) 5 times (d) 25 times
  12. 12.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  14. 14.A bag has 11 white balls and 5 blue 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) 12 (c) 16 (d) 6
  15. 15.What is the sum of the first 9 terms of the AP 7, 9, 11, …? (a) 23 (b) 135 (c) 270 (d) 144
  16. 16.What is the 35th term of the AP 14, 16, 18, 20, …? (a) 68 (b) 84 (c) 82 (d) 70
  17. 17.How many factors does 79 have? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 274 (d) 303
  19. 19.A bag has 8 blue balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 2 (c) 11 (d) 9
  20. 20.In a class of 39 children, 27 like cricket, 16 like football and 10 like both. How many like only cricket? (a) 17 (b) 6 (c) 27 (d) 23
  21. 21.What is the product of the roots of x² − 15x + 56 = 0? (a) 57 (b) 55 (c) 56 (d) 15
  22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 16 (c) 48 (d) 12
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 5 (c) 16 (d) 15
  24. 24.A drawer has lots of blue, red, black, yellow 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) 6 (b) 10 (c) 2 (d) 5
  25. 25.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 146 (c) 155 (d) 164
  26. 26.In a class of 38 children, 23 like mangoes, 19 like bananas and 5 like both. How many like only mangoes? (a) 19 (b) 14 (c) 23 (d) 18
  27. 27.Which term of the AP 5, 14, 23, 32, … is 221? (a) 25th (b) 24th (c) 26th (d) 27th
  28. 28.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 50 (b) 30 (c) 25 (d) 10
  29. 29.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/4 (d) 1/2
  30. 30.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 110° (b) 70° (c) 155° (d) 95°
  31. 31.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 5544 sq cm
  32. 32.The mean of 6 numbers is 31. When the number 52 is added to them, what is the new mean? (a) 31 (b) 33 (c) 34 (d) 35
  33. 33.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 56 (c) 96 (d) 14
  34. 34.Which is the correct factorisation of x² + 9x + 14? (a) (x + 2)(x + 7) (b) (x + 1)(x + 8) (c) (x + 1)(x + 14) (d) (x − 2)(x − 7)
  35. 35.In a class of 23 children, 9 like mangoes, 9 like bananas and 3 like both. How many like neither? (a) 11 (b) 5 (c) 3 (d) 8
  36. 36.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 10201 (b) 9801 (c) 9999 (d) 9811
  37. 37.In a class of 24 children, 9 like mangoes, 7 like bananas and 2 like both. How many like only mangoes? (a) 9 (b) 5 (c) 7 (d) 17
  38. 38.If a + b = 15 and ab = 56, what is (a − b)²? (a) 169 (b) 225 (c) 113 (d) 1
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  40. 40.What is the mean of 13, 9, 15, 10 and 8? (a) 12 (b) 10 (c) 11 (d) 13

Answer key

  1. 1/2
  2. 120
  3. 50°
  4. 1386 sq cm
  5. 16
  6. 30
  7. 11
  8. 42
  9. 4
  10. 24
  11. 25 times
  12. 88 cm
  13. 9
  14. 12
  15. 135
  16. 82
  17. 2
  18. 303
  19. 11
  20. 17
  21. 56
  22. 24
  23. 16
  24. 6
  25. 155
  26. 18
  27. 25th
  28. 25
  29. 1/2
  30. 70°
  31. 1386 sq cm
  32. 34
  33. 48
  34. (x + 2)(x + 7)
  35. 8
  36. 9801
  37. 7
  38. 1
  39. 10
  40. 11

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