1. Simplify the expression:
\( \frac{4x^2 –9}{2^2– 3x} \)
2. Solve the system of equations:
\( \begin{cases} 3x + 2y = 5 \\ x - 4y = -6 \end{cases} \)
3. Calculate the derivative of the function:
\( f(x)=x^3 –4x^2 +3x–1 \)
4. Find the antiderivative of the function: \( F' (x)=3x^2 –6x+2 \)
5. Determine the equation of the line passing through the points \((2,3)\) and \((-1,4)\).
6. Solve the quadratic equation:
\( 2x^2–5x+3=0 \)
7. Simplify the expression:
\( (2x^3 y^2 )^3 (4x^2 y^4 )^{-2} \)
8. Determine the area of a triangle with sides of lengths 7, 10, and 13.
9. Calculate the surface area of a cylinder with radius 3 and height 8.
10. Find the sum of the arithmetic series:
\( 2 + 5 + 8 +⋯ + 74 \)
11. Determine the equation of the circle with center \((3,-2)\) and radius 5.
12. Evaluate the definite integral:
\( \int_{1}^{3} (2x - 3) \, dx \)
13. Find the domain and range of the function:
\( \frac{g(x)=1}{x^2-1} \)
14. Determine the inverse function of \( f(x)=3x–7 \)
15. Solve the inequality:
\( 2x^2 –4x+3 > 0 \)
16. Calculate the distance between the points \( A(3,2) \) and \( B(-1,-4) \).
17. Find the equation of the parabola with vertex \( (1,-2) \) and focus \( (1,-1) \).
18. Evaluate the limit: \( \underset{x \to 2}{\lim} \frac{x^2 - 4}{x - 2} \)
19. Find the value of k such that the function.
\(f(x) = \begin{cases} 2x - 1, & \text{if } x < 2 \\ kx + 3, & \text{if } x \geq 2 \end{cases}\)
20. Determine the volume of a cone with base radius 4 and height 9.
21. Simplify the complex number: \( (3–4i)(2+i) \).
22. Determine the general term of the geometric sequence: \( 5, 15, 45, ... \)
23. Solve the system of inequalities graphically:
\( \begin{align*} y &\geq x + 2 \\ y &\leq -x + 4 \\ x &\geq 0 \end{align*} \)
24. Find the coordinates of the vertex of the quadratic function: \(f(x)=-x^2+6x–5\).
25. Determine the amplitude, period, and phase shift of the function: \( y=3 \sin(2x- \pi ) \).
26. Solve the logarithmic equation:
\( log_3 (x–1)+log_3 (x+2)=3 \).
27. Find the maximum value of the function:
\( f(x)=2 \cos x-\sin x \).
28. Let \( g(x)=\frac{x^3 –2x^2 +x}{x} \) be a rational function. Find the \(x\)-intercepts, \(y\)-intercepts, and any asymptotes of the function.
29. Given the function \( f(x)=x^2–6x+10 \), find the \(x\) values for which the function has a value of 7.
30. Determine the area enclosed by the curves \(y=x^2\) and \(y=x^3–x\).