General Education Diploma (GED Oman) · Pure Mathematics

Calculus and Mathematical Analysis

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

Practise Calculus and Mathematical Analysis 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. Evaluate the trigonometric limit: lim (x -> 0) [sin(7x) / (2x)].
  2. Find the derivative of the rational function f(x) = (3x - 5) / (2x + 1) for x != -1/2.
  3. What is the slope of the tangent line to the curve y = 2x^3 - 5x^2 + 4 at x = 2?
  4. Determine the indefinite integral: integral of (6x^2 - 4x + 5) dx.
  5. Evaluate the definite integral: integral from 0 to 3 of (4x + 1) dx.
  6. Find the local maximum of the polynomial function f(x) = -x^3 + 3x + 2.
  7. Evaluate the limit using L'Hopital's rule: lim (x -> 1) [(x^3 - 1) / (x^2 + 2x - 3)].
  8. Find the derivative of the composite exponential function g(x) = e^(4x^2 - 3).
  9. Calculate the derivative of the logarithmic function h(x) = ln(x^2 + 5x).
  10. Evaluate the integral by substitution: integral of [2x / (x^2 + 9)] dx.
  11. Find the total area enclosed between the parabola y = 4 - x^2 and the line y = 0.
  12. A particle moves along a straight line such that its velocity is v(t) = 3t^2 - 12 m/s. What is its acceleration at t = 4 seconds?
  13. Find the inflection point of the cubic curve f(x) = 2x^3 - 6x^2 + 5x - 1.
  14. Evaluate the definite integral: integral from 0 to pi/2 of [cos(x) * sin^3(x)] dx.
  15. What is the equation of the normal line to y = x^2 at the point (2, 4)?
  16. Evaluate the limit: lim (x -> infinity) [(5x^3 - 2x + 1) / (3x^3 + 4x^2 - 7)].
  17. Find the derivative of f(x) = tan(3x).
  18. If the marginal cost function is MC(q) = 3q^2 - 8q + 10 and fixed costs are 50 OMR, find the total cost function C(q).
  19. Determine the interval where f(x) = x^3 - 6x^2 + 9x + 1 is strictly increasing.
  20. Evaluate the integral using integration by parts: integral of [x * e^(2x)] dx.
  21. Find dy/dx by implicit differentiation for x^2 + y^2 = 25 at the point (3, 4).
  22. What is the average value of the function f(x) = 6x on the closed interval [1, 4]?
  23. Find the critical points of f(x) = x^4 - 4x^3 + 10.
  24. Evaluate the limit: lim (x -> 0) [(e^(3x) - 1) / x].
  25. Find the volume of the solid generated by revolving the region bounded by y = sqrt(x), y = 0, and x = 4 about the x-axis.
  26. Determine the concavity of f(x) = x^4 - 6x^2 on the interval (-1, 1).
  27. What is the area of the finite region enclosed by the parabola and the line ?
  28. Evaluate the limit: .
  29. Find the particular solution to the differential equation passing through . What is the value of ?
  30. What is the angle between the two 3D vectors and ?
  31. A cylindrical can with an open top has a volume of . What radius minimizes the total surface area of sheet metal required?

Keep practising

More General Education Diploma (GED Oman) topics

All General Education Diploma (GED Oman) practice →

Calculus and Mathematical Analysis in other exams

Ready for the full General Education Diploma (GED Oman) test?

Take a mock testGeneral Education Diploma (GED Oman) hub
Calculus and Mathematical Analysis practice questions | GetMyMockTest