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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 412 · 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.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  2. 2.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 153 (d) 306
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 41° (c) 40° (d) 80°
  4. 4.What is the midpoint of the line joining (10, 0) and (18, 2)? (a) (4, 1) (b) (14, 1) (c) (28, 2) (d) (1, 14)
  5. 5.A fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/12 (c) 1/18 (d) 2/11
  7. 7.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 616 sq cm (c) 44 sq cm (d) 154 sq cm
  8. 8.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 155° (b) 120° (c) 85° (d) 60°
  9. 9.What is the sum of the roots of x² − 8x + 12 = 0? (a) 7 (b) 8 (c) 9 (d) 12
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 15 (d) 16
  11. 11.What is the distance between the points (8, 10) and (32, 3)? (a) 31 (b) 625 (c) 25 (d) 26
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 10 (c) 12 (d) 13
  13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  14. 14.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478
  15. 15.The mean of 7 numbers is 32. When the number 40 is added to them, what is the new mean? (a) 34 (b) 32 (c) 36 (d) 33
  16. 16.What is the median of 1, 19, 37, 25 and 32? (a) 19 (b) 32 (c) 37 (d) 25
  17. 17.How many factors does 66 have? (a) 9 (b) 7 (c) 8 (d) 6
  18. 18.What is the mean of 2, 11, 14, 9, 3 and 15? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.A bag has 7 red balls and 7 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 14 (c) 9 (d) 8
  20. 20.What is the sum of the first 12 terms of the AP 8, 9, 10, …? (a) 324 (b) 19 (c) 168 (d) 162
  21. 21.What is the sum of the first 6 terms of the AP 7, 8, 9, …? (a) 57 (b) 60 (c) 114 (d) 12
  22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 12 (c) 16 (d) 24
  23. 23.What is the distance between the points (6, 6) and (10, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 64 times (d) 8 times
  25. 25.A bag has 4 green, 3 white and 4 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 8/11 (b) 3/8 (c) 1/3 (d) 3/11
  26. 26.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 264 cm (c) 1386 cm (d) 132 cm
  27. 27.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
  28. 28.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
  29. 29.A bag has 6 green, 5 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 7/18 (b) 1/3 (c) 2/3 (d) 1/2
  30. 30.What is the missing term in the AP 18, 25, 32, ?, 46? (a) 46 (b) 38 (c) 39 (d) 40
  31. 31.There are 5 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) 60 (b) 35 (c) 11 (d) 30
  32. 32.In which quadrant does the point (4, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 15 (c) 55 (d) 54
  34. 34.In a class of 27 children, 7 like dance, 17 like music and 3 like both. How many like only dance? (a) 4 (b) 7 (c) 14 (d) 10
  35. 35.Which term of the AP 8, 11, 14, 17, … is 86? (a) 29th (b) 28th (c) 26th (d) 27th
  36. 36.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 231 (c) 462 (d) 441
  37. 37.In a class of 26 children, 13 like maths, 14 like science and 3 like both. How many like neither? (a) 3 (b) 1 (c) 5 (d) 2
  38. 38.In a class of 21 children, 17 like mangoes, 5 like bananas and 2 like both. How many like only mangoes? (a) 17 (b) 15 (c) 16 (d) 3
  39. 39.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 2464 sq cm (c) 176 sq cm (d) 1232 sq cm
  40. 40.What is the distance between the points (0, 18) and (16, 6)? (a) 21 (b) 28 (c) 400 (d) 20

Answer key

  1. 24
  2. 289
  3. 40°
  4. (14, 1)
  5. 1/2
  6. 1/18
  7. 154 sq cm
  8. 120°
  9. 8
  10. 16
  11. 25
  12. 12
  13. 15
  14. 609
  15. 33
  16. 25
  17. 8
  18. 9
  19. 9
  20. 162
  21. 57
  22. 24
  23. 5
  24. 16 times
  25. 3/11
  26. 132 cm
  27. 176 cm
  28. 4
  29. 1/3
  30. 39
  31. 30
  32. Fourth quadrant
  33. 54
  34. 4
  35. 27th
  36. 441
  37. 2
  38. 15
  39. 2464 sq cm
  40. 20

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