FUVEST (University of São Paulo Entrance Exam) · Mathematics and Physics

Mathematics: Sequences and Functions

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

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All 15 questions

  1. For which value of x does f(x) = 2x - 2 equal zero?
  2. A geometric progression has first term 5 and ratio 3. What is the term in position 7?
  3. A geometric progression has first term 1 and ratio 2. What is the term in position 6?
  4. For which value of x does f(x) = 5x - 5 equal zero?
  5. What is the sum of the roots of x^2 - 7x + 10 = 0?
  6. What is the sum of the infinite series 8 + 2 + 1/2 + ... in which each term is 1/4 of the previous one?
  7. A line passes through (2, 3) and (3, 1). What is its slope?
  8. In an arithmetic progression with first term 15 and common difference 9, what is the term in position 10?
  9. What is the sum of the first 12 terms of the arithmetic progression that starts at 9 and increases by 3 each time?
  10. What is the sum of the infinite series 12 + 3 + 3/4 + ... in which each term is 1/4 of the previous one?
  11. What is the minimum value of f(x) = x^2 - 10x + 24?
  12. What is the minimum value of f(x) = x^2 - 14x + 48?
  13. A colony of 1000 bacteria doubles every 2 hours. How many bacteria are there after 8 hours?
  14. What is the sum of the infinite series 10 + 20/3 + 40/9 + ... in which each term is 2/3 of the previous one?
  15. What is the sum of the infinite series 8 + 4 + 2 + ... in which each term is 1/2 of the previous one?

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