Egzamin Maturalny (Matura Poland) ยท Mathematics

Applied arithmetic and algebra

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 backpack is 200. It is first increased by 25% and then the new price is decreased by 50%. What is the final price?
  2. 45% of a number is 36. What is the number?
  3. A bonus of 98 is shared in the ratio . How much does the larger share receive?
  4. The mean of 5 numbers is 69. Of them, 4 are 63, 57, 62, 76. What is the remaining number?
  5. One pipe fills a barrel in 4 hours and another pipe fills it in 12 hours. How many hours does it take to fill the barrel when both pipes are open?
  6. What is the difference between the compound interest and the simple interest on 4000 for 3 years at 5% per year (compounded annually)?
  7. A rectangle has length 10 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?
  8. A right triangle has legs of length 12 and 16. What is the length of its hypotenuse?
  9. A pouch contains 5 red and 8 blue tokens. Two tokens are drawn at random without replacement. What is the probability that both are red?
  10. In how many ways can a panel of 4 people be chosen from a group of 5 people?
  11. The equation has two roots. What is the sum of the squares of the roots?
  12. An arithmetic sequence has first term 6 and common difference 6. What is the sum of its first 14 terms?
  13. How many integers satisfy ?
  14. On a map with scale 1 : 200000, two towns are 11 cm apart. What is the real distance in kilometres?
  15. A 50 kg solution contains 30% salt. After adding 25 kg of pure water, what percentage of the new mixture is salt?
  16. A father is three times as old as his son. In 4 years the father's age will be 9 more than twice the son's age. How old is the son now?
  17. What is the median of the numbers 3, 20, 8, 5, 23, 8, 28, 16, 19?
  18. A line passes through the points and . What is its slope?
  19. What is the sum of the interior angles of a convex polygon with 5 sides?
  20. A cylinder has radius 8 cm and height 11 cm. What is its volume, in cm, in terms of ?
  21. A shop buys a watch for 200, marks it up by 30% and then sells it at a 25% discount on the marked price. What is the profit (negative if a loss)?
  22. What is the least common multiple of 18 and 9?
  23. If and , what is ?
  24. How many integers from 1 to 33 are divisible by 6 or by 6 (or both)?
  25. If , what is the value of ?
  26. The price of a guitar is 200. It is first increased by 25% and then the new price is decreased by 40%. What is the final price?
  27. 75% of a number is 60. What is the number?
  28. A prize of 120 is shared in the ratio . How much does the larger share receive?
  29. The mean of 7 numbers is 82. Of them, 6 are 91, 85, 79, 92, 75, 92. What is the remaining number?
  30. What is the difference between the compound interest and the simple interest on 1000 for 2 years at 8% per year (compounded annually)?
  31. A rectangle has length 6 cm and width 12 cm. A square of side 3 cm is cut from one corner. What is the area of the remaining shape, in cm?
  32. A right triangle has legs of length 14 and 48. What is the length of its hypotenuse?
  33. A pouch contains 3 red and 4 blue tokens. Two tokens are drawn at random without replacement. What is the probability that both are red?
  34. In how many ways can a panel of 2 people be chosen from a group of 8 people?
  35. The equation has two roots. What is the sum of the squares of the roots?
  36. If and , what is ?
  37. An arithmetic sequence has first term 3 and common difference 6. What is the sum of its first 15 terms?
  38. How many integers satisfy ?
  39. On a map with scale 1 : 100000, two towns are 10 cm apart. What is the real distance in kilometres?
  40. A 30 kg solution contains 40% salt. After adding 20 kg of pure water, what percentage of the new mixture is salt?
  41. A father is three times as old as his son. In 5 years the father's age will be 3 more than twice the son's age. How old is the son now?
  42. What is the median of the numbers 4, 10, 16, 10, 23?
  43. A line passes through the points and . What is its slope?
  44. What is the sum of the interior angles of a convex polygon with 7 sides?
  45. A cylinder has radius 7 cm and height 9 cm. What is its volume, in cm, in terms of ?

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