https://file.aiquickdraw.com/mathbot/file/1724901122098zyuj4yy4.jpg

I want you to act as a Professor of Mathematics and create 30 random college-level math problems with small equation numbers suitable for a test. Please label the test as "[Subject] Test 1" with a subtitle indicating the range of topics covered.

To begin, let's analyze the uploaded image to understand the style and complexity of the problems. Then, I'll generate a set of 30 random college-level math problems suitable for a test based on the format shown.

### Analysis of Uploaded Image
The given problem is:
\[
2x^2 + 4x = 0
\]

This is a quadratic equation, and it seems to be part of a set of algebra problems that involve solving for \(x\). Given this, I will create a set of 30 problems that span a range of topics typically covered in college-level mathematics, such as algebra, calculus, linear algebra, and differential equations.

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### [Algebra and Calculus] Test 1
**Topics Covered:** Quadratic Equations, Derivatives, Integrals, Limits, Linear Algebra, Differential Equations, Sequences and Series.

#### Section 1: Algebra (Quadratic Equations, Systems of Equations)

1. Solve for \(x\): \(3x^2 - 5x - 2 = 0\)
2. Solve for \(x\): \(x^2 + 6x + 9 = 0\)
3. Solve for \(x\) and \(y\): 
   \[
   \begin{cases}
   2x + 3y = 6 \\
   4x - y = 5
   \end{cases}
   \]
4. Solve for \(x\): \(x^3 - 2x^2 - x + 2 = 0\)
5. Find the inverse of the matrix: 
   \[
   A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}
   \]

#### Section 2: Calculus (Derivatives, Integrals, Limits)

6. Compute the derivative of \(f(x) = 3x^2 + 5x - 7\).
7. Find the integral of \(f(x) = 4x^3 - 2x + 1\) with respect to \(x\).
8. Evaluate the limit: \(\lim_{{x \to 0}} \frac{\sin(x)}{x}\).


Practice solving algebraic and calculus problems with this test. Includes quadratic equations, systems of equations, derivatives, integrals, limits, linear algebra, differential equations, and sequences and series. Test your understanding of key mathematical concepts at the college level.

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