SEE (Secondary Education Examination, Nepal) ยท Mathematics

Applied arithmetic and geometry

45 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 45 questions

  1. The price of a camera is 400. It is first increased by 20% and then the new price is decreased by 30%. What is the final price?
  2. 35% of a number is 28. What is the number?
  3. The mean of 6 numbers is 60. Of them, 5 are 53, 52, 68, 69, 48. What is the remaining number?
  4. A train travels from A to B at 60 km/h and returns along the same road at 30 km/h. What is the average speed for the whole trip, in km/h?
  5. One pipe fills a pool in 3 hours and another pipe fills it in 6 hours. How many hours does it take to fill the pool when both pipes are open?
  6. What is the difference between the compound interest and the simple interest on 1000 for 3 years at 4% per year (compounded annually)?
  7. A rectangle has length 12 cm and width 4 cm. A square of side 3 cm is cut from one corner. What is the area of the remaining shape, in cm?
  8. A right triangle has legs of length 80 and 84. What is the length of its hypotenuse?
  9. A bag contains 8 red and 7 blue marbles. Two marbles are drawn at random without replacement. What is the probability that both are red?
  10. In how many ways can a delegation of 2 people be chosen from a group of 7 people?
  11. The equation has two roots. What is the sum of the squares of the roots?
  12. If and , what is ?
  13. An arithmetic sequence has first term 7 and common difference 2. What is the sum of its first 19 terms?
  14. How many integers satisfy ?
  15. On a map with scale 1 : 100000, two towns are 9 cm apart. What is the real distance in kilometres?
  16. A father is three times as old as his son. In 3 years the father's age will be 8 more than twice the son's age. How old is the son now?
  17. What is the median of the numbers 9, 21, 26, 15, 8?
  18. What is the sum of the interior angles of a convex polygon with 10 sides?
  19. A cylinder has radius 5 cm and height 11 cm. What is its volume, in cm, in terms of ?
  20. A shop buys a watch for 400, marks it up by 20% and then sells it at a 25% discount on the marked price. What is the profit (negative if a loss)?
  21. What is the least common multiple of 24 and 27?
  22. If and , what is ?
  23. How many integers from 1 to 59 are divisible by 4 or by 5 (or both)?
  24. If , what is the value of ?
  25. The price of a coat is 500. It is first increased by 50% and then the new price is decreased by 10%. What is the final price?
  26. If 75% of a certain number is 225, find that number.
  27. A bonus of 143 is shared in the ratio . How much does the larger share receive?
  28. The mean of 4 numbers is 74. Of them, 3 are 62, 62, 71. What is the remaining number?
  29. What is the difference between the compound interest and the simple interest on 5000 for 2 years at 10% per year (compounded annually)?
  30. A rectangle has length 9 cm and width 11 cm. A square of side 2 cm is cut from one corner. What is the area of the remaining shape, in cm?
  31. A right triangle has legs of length 18 and 80. What is the length of its hypotenuse?
  32. A bag contains 6 red and 3 blue marbles. Two marbles are drawn at random without replacement. What is the probability that both are red?
  33. In how many ways can a committee of 2 people be chosen from a group of 8 people?
  34. The equation has two roots. What is the sum of the squares of the roots?
  35. If and , what is ?
  36. An arithmetic sequence has first term 2 and common difference 3. What is the sum of its first 14 terms?
  37. How many integers satisfy ?
  38. On a map drawn to a scale of 1 : 50000, two towns are 3 cm apart. What is their real distance in kilometres?
  39. A father is three times as old as his son. In 4 years the father's age will be 6 more than twice the son's age. How old is the son now?
  40. What is the median of the numbers 8, 29, 27, 14, 25, 21, 21?
  41. A line passes through the points and . What is its slope?
  42. What is the sum of the interior angles of a convex polygon with 6 sides?
  43. A shop buys a coat for 200, marks it up by 30% and then sells it at a 15% discount on the marked price. What is the profit (negative if a loss)?
  44. What is the least common multiple of 12 and 28?
  45. If and , what is ?

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