Key Mathematical Concepts and Formulas

This comprehensive page covers essential mathematical principles across geometry, volume calculations, and functions. The content begins with geometric theorems and progresses through to complex mathematical identities.

Definition: Pythagoras' theorem states that in a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Example: A practical application shows AB² = 15² + 2, resulting in AB² = 229, with the square root of AB approximately 15.13.

Vocabulary: Antecedent and image are key terms in function notation, representing input and output values respectively.

Highlight: Volume formulas for various 3D shapes are presented systematically:

• Rectangular prism: V = L × l × h
• Prism: V = B × h
• Cylinder: V = π × r² × h
• Pyramid: V = (B × h) ÷ 3
• Cone: V = (π × r² × h) ÷ 3
• Sphere: V = (4 × π × r³) ÷ 3

Definition: Notable identities (Identités Remarquables) include:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)(a - b) = a² - b²

Example: For function evaluation, g(-3) = 4 × (-3) = -12 demonstrates how to apply a linear function to a negative number.