Egzamin Maturalny (Matura Poland) · Mathematics

Functions and counting

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

Practise Functions and counting now

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

All 25 questions

  1. The price of a coat is 800. It is first increased by 50% and then the new price is decreased by 50%. What is the final price?
  2. 45% of a number is 135. What is the number?
  3. The mean of 7 numbers is 68. Of them, 6 are 63, 62, 73, 57, 70, 76. 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. What is the difference between the compound interest and the simple interest on 2000 for 2 years at 5% per year (compounded annually)?
  6. A rectangle has length 7 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?
  7. A right triangle has legs of length 24 and 45. What is the length of its hypotenuse?
  8. A pouch contains 8 red and 8 blue tokens. Two tokens are drawn at random without replacement. What is the probability that both are red?
  9. In how many ways can a team of 2 people be chosen from a group of 6 people?
  10. The equation has two roots. What is the sum of the squares of the roots?
  11. An arithmetic sequence has first term 3 and common difference 7. What is the sum of its first 18 terms?
  12. How many integers satisfy ?
  13. On a map with scale 1 : 50000, two towns are 4 cm apart. What is the real distance in kilometres?
  14. A father is three times as old as his son. In 5 years the father's age will be 9 more than twice the son's age. How old is the son now?
  15. What is the median of the numbers 21, 6, 13, 21, 22, 22, 14?
  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 6 sides?
  18. A shop buys a guitar for 800, marks it up by 25% and then sells it at a 20% discount on the marked price. What is the profit (negative if a loss)?
  19. What is the least common multiple of 12 and 21?
  20. If and , what is ?
  21. How many integers from 1 to 61 are divisible by 3 or by 5 (or both)?
  22. If , what is the value of ?
  23. The price of a tablet is 200. It is first increased by 50% and then the new price is decreased by 20%. What is the final price?
  24. 20% of a number is 60. What is the number?
  25. The mean of 5 numbers is 75. Of them, 4 are 70, 72, 86, 64. What is the remaining number?

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