Kuwait University Aptitude Tests (KUAT) · Mathematics and Quantitative Reasoning

Algebra, Equations, and Functions

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

Practise Algebra, Equations, and Functions now

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

All 31 questions

  1. Solve for x in the equation: 4^(2x - 1) = 32^(x + 1).
  2. Find the domain of the real-valued function: f(x) = sqrt(2x - 8) / (x - 7).
  3. If f(x) = 2x + 3 and g(x) = x^2 - 4, what is the value of (g o f)(-2)?
  4. Find the inverse function f^(-1)(x) for the one-to-one function: f(x) = (3x + 5) / (2x - 1), where x != 1/2.
  5. What are all real solutions to the absolute value equation: |3x - 4| = 2x + 6?
  6. Find the solution set of the quadratic inequality: x^2 - 5x - 14 <= 0.
  7. If log_3(x) + log_3(x - 2) = 1, what is the value of x?
  8. Determine the remainder when the polynomial P(x) = 2x^4 - 3x^3 + 5x - 8 is divided by (x - 2).
  9. Solve the linear system for y:
    3x + 2y = 16
    5x - 4y = 8
  10. If a polynomial equation x^3 - 6x^2 + 11x - 6 = 0 has roots r_1, r_2, and r_3, what is the sum of the squares of the roots: r_1^2 + r_2^2 + r_3^2?
  11. What is the vertical asymptote and horizontal asymptote of the rational function: g(x) = (4x - 7) / (2x + 6)?
  12. Simplify the algebraic expression: (x^3 - 8) / (x^2 - 4) for x != 2 and x != -2.
  13. Solve for x: 2^(2x) - 10 * 2^x + 16 = 0.
  14. What is the vertex of the parabola defined by the quadratic equation: y = -2x^2 + 12x - 11?
  15. For what value of k will the quadratic equation 3x^2 - 6x + k = 0 have exactly one real solution (a repeated double root)?
  16. If the arithmetic sequence has a first term a_1 = 7 and a common difference d = 4, what is the sum of the first 25 terms (S_25)?
  17. What is the sum of the infinite geometric series: 18 - 6 + 2 - 2/3 + ...?
  18. Find the value of x that satisfies the equation: ln(2x - 3) = 2.
  19. If 3^(x + 2) = 5^(x - 1), express x in terms of natural logarithms:
  20. Determine the range of the quadratic function: f(x) = 3(x - 2)^2 - 5.
  21. Find the values of x that satisfy the rational inequality: (x - 3) / (x + 4) >= 0.
  22. Simplify the complex number expression: (3 + 4i) / (1 - 2i), where i = sqrt(-1).
  23. What is the coefficient of x^3 in the binomial expansion of (2x - 1)^5?
  24. If matrix A = [[2, 3], [1, 4]], what is the determinant of matrix A and its inverse A^(-1)?
  25. A car radiator contains 10 liters of a mixture of water and antifreeze that is 20% antifreeze. How many liters of pure antifreeze must be added to increase the concentration to 40% antifreeze?
  26. If a work crew of 6 workers can complete paving a roadway in 14 days working 8 hours per day, how many days will it take 7 workers working 6 hours per day to complete the same project at the same rate…
  27. A merchant mixes 20 kg of tea worth $15/kg with 30 kg of tea worth $25/kg. At what price per kilogram must the resulting mixture be sold to realize a 20% profit on total cost?
  28. Working alone, pump A fills a reservoir in 6 hours, while pump B fills it in 8 hours. If both pumps operate together for 2 hours and pump A is then shut down, how many additional hours will pump B tak…
  29. If , what is the exact value of ?
  30. A train 150 meters long traveling at 72 km/h crosses a bridge in 25 seconds. What is the length of the bridge?
  31. The sum of the interior angles of a regular polygon is . How many diagonals does this polygon have?

Keep practising

More Kuwait University Aptitude Tests (KUAT) topics

All Kuwait University Aptitude Tests (KUAT) practice →

Ready for the full Kuwait University Aptitude Tests (KUAT) test?

Take a mock testKuwait University Aptitude Tests (KUAT) hub