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

Mathematics

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

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All 21 questions

  1. Solve the equation 3x - 7 = 11.
  2. What is the slope of the straight line through the points (1, 2) and (3, 8)?
  3. What are the roots of x^2 - 5x + 6 = 0?
  4. An arithmetic sequence has first term 3 and common difference 4. What is the sum of its first 10 terms?
  5. What is the value of log base 2 of 32 plus log base 3 of 9?
  6. Let f(x) = 2x + 1 and g(x) = x^2. What is f(g(3))?
  7. A price falls by 20% and then rises by 10%. What is the net change from the original price?
  8. Which set of values satisfies |2x - 3| < 5?
  9. What is the sum of the infinite geometric series 6 + 2 + 2/3 + 2/9 + ...?
  10. How many integers from 1 to 100 are divisible by 3 or by 5?
  11. Two fair dice are rolled. What is the probability that the sum is 7?
  12. In how many different orders can the six distinct letters of the word FUVEST be arranged?
  13. What is the area of a circle with radius 5?
  14. A triangle has sides 6, 8 and 10. What is its area?
  15. What is the area of a regular hexagon with side length 2?
  16. What is the volume of a cylinder with radius 3 and height 4?
  17. Which line passes through (0, 1) and is perpendicular to y = 2x + 3?
  18. What is the value of sin(pi/6) + cos(pi/3)?
  19. In a triangle two sides measure 5 and 7 with a 60 degree angle between them. What is the third side?
  20. What is (1 + i)^2, where i is the imaginary unit with i^2 = -1?
  21. The polynomial x^3 - 6x^2 + 11x - 6 has roots 1, 2 and 3. What is the sum of the squares of its roots?

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