Egzamin Maturalny (Matura Poland) ยท Mathematics

Geometry, sequences and probability

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

Practise Geometry, sequences and probability now

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 tablet is 200. It is first increased by 40% and then the new price is decreased by 40%. What is the final price?
  2. 20% of a number is 12. What is the number?
  3. The mean of 7 numbers is 66. Of them, 6 are 59, 60, 66, 59, 54, 72. What is the remaining number?
  4. What is the difference between the compound interest and the simple interest on 2500 for 2 years at 6% per year (compounded annually)?
  5. A rectangle has length 10 cm and width 10 cm. A square of side 2 cm is cut from one corner. What is the area of the remaining shape, in cm?
  6. A right triangle has legs of length 20 and 48. What is the length of its hypotenuse?
  7. A box contains 3 red and 6 blue beads. Two beads are drawn at random without replacement. What is the probability that both are red?
  8. In how many ways can a team of 3 people be chosen from a group of 5 people?
  9. The equation has two roots. What is the sum of the squares of the roots?
  10. An arithmetic sequence has first term 5 and common difference 4. What is the sum of its first 14 terms?
  11. How many integers satisfy ?
  12. On a map with scale 1 : 200000, two towns are 5 cm apart. What is the real distance in kilometres?
  13. A 30 kg solution contains 25% salt. After adding 20 kg of pure water, what percentage of the new mixture is salt?
  14. A father is three times as old as his son. In 5 years the father's age will be 1 more than twice the son's age. How old is the son now?
  15. What is the median of the numbers 7, 8, 13, 8, 29, 21, 15?
  16. A line passes through the points and . What is its slope?
  17. What is the sum of the interior angles of a convex polygon with 8 sides?
  18. A cylinder has radius 5 cm and height 3 cm. What is its volume, in cm, in terms of ?
  19. A shop buys a backpack for 500, marks it up by 20% and then sells it at a 10% discount on the marked price. What is the profit (negative if a loss)?
  20. What is the least common multiple of 20 and 16?
  21. If and , what is ?
  22. How many integers from 1 to 83 are divisible by 4 or by 6 (or both)?
  23. If , what is the value of ?
  24. The price of a tablet is 200. It is first increased by 20% and then the new price is decreased by 25%. What is the final price?
  25. 15% of a number is 30. What is the number?
  26. A bonus of 55 is shared in the ratio . How much does the larger share receive?
  27. The mean of 6 numbers is 87. Of them, 5 are 76, 99, 91, 78, 85. What is the remaining number?
  28. What is the difference between the compound interest and the simple interest on 1000 for 2 years at 4% per year (compounded annually)?
  29. A rectangle has length 6 cm and width 4 cm. A square of side 1 cm is cut from one corner. What is the area of the remaining shape, in cm?
  30. A right triangle has legs of length 18 and 80. What is the length of its hypotenuse?
  31. A box contains 6 red and 4 blue beads. Two beads are drawn at random without replacement. What is the probability that both are red?
  32. In how many ways can a committee of 2 people be chosen from a group of 8 people?
  33. The equation has two roots. What is the sum of the squares of the roots?
  34. If and , what is ?
  35. An arithmetic sequence has first term 9 and common difference 3. What is the sum of its first 9 terms?
  36. How many integers satisfy ?
  37. On a map with scale 1 : 50000, two towns are 7 cm apart. What is the real distance in kilometres?
  38. A 30 kg solution contains 30% salt. After adding 15 kg of pure water, what percentage of the new mixture is salt?
  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 28, 18, 12, 23, 20, 4, 23, 11, 6?
  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 10 sides?
  43. A cylinder has radius 6 cm and height 4 cm. What is its volume, in cm, in terms of ?
  44. A shop buys a sofa for 800, marks it up by 25% and then sells it at a 10% discount on the marked price. What is the profit (negative if a loss)?
  45. What is the least common multiple of 30 and 27?

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