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The document you uploaded is a selection test from the Universidad de Los Andes, focusing on mathematical, logical reasoning, and physics problems. Below are examples of the types of problems included:

1. **Logical Reasoning**: "If two days after yesterday is Sunday, what day was two days before tomorrow?"
2. **Algebra**: "Determine the quotient and remainder of the division of \( x^3 - x^2 + 2x - 2 \) by \( x + 1 \)."
3. **Geometry**: "Calculate the area of the triangle with vertices at points \( A(1,1), B(6,5), C(3,5) \)."
4. **Trigonometry**: "If \( \sin\alpha \cdot \cos\alpha = \frac{1}{2} \), what is \( \tan\alpha \cdot \cot\alpha \)?"
5. **Physics**: "A ball is thrown upward and reaches a maximum height of 20 meters. What is the net force on the ball when it is 10 meters above its initial position?"

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Here are 5 questions to expand on these ideas:
1. How is logical reasoning commonly used in mathematical problems?
2. What is the process for solving polynomial divisions?
3. How can the area of a triangle be determined using coordinates?
4. What are the properties of trigonometric identities like \( \sin \alpha \) and \( \tan \alpha \)?
5. How does the force on an object change at different points during free fall?

**Tip**: When working on logical puzzles, break them down step by step, focusing on the temporal or spatial relationships involved.

The document you uploaded is a selection test from the Universidad de Los Andes, focusing on mathematical, logical reasoning, and physics problems.

Explore selection test problems from Universidad de Los Andes focusing on logical reasoning, algebra, geometry, and physics. Solutions include polynomial division, triangle area calculations, and trigonometric identities. Suitable for high school students (Grades 10-12).

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