Sultan Qaboos University Foundation & Aptitude Test · Mathematics Reasoning

Algebra and Functions

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

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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 the linear equation for x: 4(2x - 3) - 3(x + 5) = 14.
  2. Find the solution set for the absolute value inequality: |3x - 7| <= 11.
  3. Determine the roots of the quadratic equation 2x^2 - 7x + 3 = 0 using factoring.
  4. What is the nature of the roots of the quadratic equation 3x^2 - 4x + 2 = 0?
  5. Solve the system of equations for x and y: 3x + 2y = 16 and 2x - y = 6.
  6. According to the Remainder Theorem, what is the remainder when P(x) = 2x^3 - 5x^2 + 4x - 7 is divided by (x - 2)?
  7. If f(x) = 2x + 5 and g(x) = x^2 - 3, find the composite function value f(g(4)).
  8. Find the inverse function f^(-1)(x) for the one-to-one function f(x) = (3x - 4) / 5.
  9. What is the domain of the real-valued function h(x) = sqrt(2x - 8) / (x - 6)?
  10. Solve the exponential equation for x: 9^(x - 1) = 27^(2x - 4).
  11. Evaluate the logarithmic expression: log_2(32) - log_3(81) + ln(e^5).
  12. Simplify the rational expression: (x^2 - 9) / (2x^2 + 5x - 3).
  13. Solve the logarithmic equation: log(x + 2) + log(x - 1) = 1 (where log is base 10).
  14. Find the vertex of the parabola defined by f(x) = 2x^2 - 8x + 11.
  15. If a polynomial P(x) has a degree of 4, what is the maximum number of turning points (local extrema) its graph can have?
  16. Find the value of k such that (x + 3) is a factor of P(x) = x^3 + k*x^2 - 4x + 12.
  17. Solve for x: sqrt(3x + 1) = x - 3.
  18. Simplify the complex fraction: [(1/x) - (1/y)] / [(1/x^2) - (1/y^2)].
  19. Find the vertical and horizontal asymptotes of f(x) = (3x + 6) / (x - 4).
  20. What is the range of the exponential function g(x) = 3^(x - 2) - 5?
  21. Determine the sum of the roots of the cubic polynomial 2x^3 - 8x^2 + 5x - 9 = 0 using Vieta's formulas.
  22. If log_b(2) = 0.301 and log_b(3) = 0.477, what is the value of log_b(18)?
  23. Solve the rational inequality: (x - 2) / (x + 4) >= 0.
  24. What is the period of the trigonometric function f(x) = 4 * sin(3x - pi/2)?
  25. Find the solution to the 2x2 system: 5x + 3y = 9 and 2x + 4y = 12 using Cramer's rule.
  26. If f(x) is an odd function and f(3) = 7, what is the value of f(-3) + 2*f(3)?
  27. A trader marks up an article by 40% above its production cost. During a seasonal promotion, he offers a discount of 25% off the marked price. What is his net percentage profit?
  28. Pipe A can empty a water tank in 12 hours, while Pipe B can fill it in 8 hours. If both pipes are opened simultaneously when the tank is half full, in how many hours will the tank become completely fu…
  29. If , what is the value of ?
  30. The average score of 24 boys in an aptitude test is 72, and the average score of 16 girls in the same test is 82. What is the combined average score of all 40 students?
  31. A circular swimming pool of radius 7 m is surrounded by a uniform concrete walkway of width 3.5 m. What is the area of the concrete walkway? (Use )

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