Mathematics can sometimes feel overwhelming, but having an organized summary of the most important formulas can be the key to mastering the subject. This practical guide compiles the essential formulas, helping students review and prepare for exams like the ENEM, university entrance exams, and other competitive tests.
1. Algebra Formulas
- First-degree equation:
\( ax + b = 0 \)
Solution: \( x = -b / a \) - Second-degree equation:
\( ax^2 + bx + c = 0 \)
Bhaskara formula:
\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) - Notable Products:
- Square of the sum: \( (a + b)^2 = a^2 + 2ab + b^2 \)
- Square of the difference: \( (a - b)^2 = a^2 - 2ab + b^2 \)
- Product of the sum by the difference: \( (a + b)(a - b) = a^2 - b^2 \)
2. Geometry Formulas
- Perimeter of a rectangle:
\( P = 2(b + h) \) (base + height). - Area of a triangle:
\( A = \frac{b \cdot h}{2} \) - Area of a circle:
\( A = \pi \cdot r^2 \) - Circumference:
\( C = 2\pi \cdot r \) - Volume of a cube:
\( V = a^3 \) (side cubed). - Volume of a cylinder:
\( V = \pi \cdot r^2 \cdot h \)
3. Function Formulas
- First-degree function:
\( f(x) = ax + b \), where \( a \neq 0 \) - Second-degree function:
\( f(x) = ax^2 + bx + c \), where \( a \neq 0 \)
Vertex of the parabola:
- \( x_v = -b / (2a) \)
- \( y_v = -\Delta / (4a) \)
4. Trigonometry Formulas
- Sine, Cosine, and Tangent in a right triangle:
- \( \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \)
- \( \cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}} \)
- \( \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \) - Fundamental relation:
\( \sin^2(\theta) + \cos^2(\theta) = 1 \)
5. Probability and Statistics Formulas
- Probability:
\( P(A) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \) - Arithmetic mean:
\( \bar{x} = \frac{\sum x_i}{n} \) - Standard deviation:
\( \sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} \)
Final Tips
- Practice with exercises: Solve practical problems to reinforce the formulas.
- Create flashcards: Make cards with formulas for quick revision.
- Use visual associations: Draw geometric shapes or diagrams to understand applications.
With these essential formulas in hand, your studies will be much more organized and efficient. Save this summary and come back whenever you need a quick review before an exam!
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