This page delves into more complex mathematical concepts, focusing on powers, distributive properties, and functions. It provides a thorough explanation of linear and affine functions, along with their graphical representations.

Definition: A linear function f$x$ = ax always passes through the origin, while an affine function f$x$ = ax + b intersects the y-axis at point (0,b).

Example: For the affine function f$x$ = 3x + 1, f(0) = 1, meaning it intersects the y-axis at point (0,1).

Highlight: The distributive property states that a$b+c$ = ab + ac, which is fundamental in algebraic operations.

Vocabulary:

• Distributive Property: A mathematical property that relates multiplication and addition
• Affine Function: A function of the form f$x$ = ax + b, where a and b are constants

The page covers:

• Power rules and properties
• Distributive properties
• Linear and affine functions
• Trigonometry basics
• Probability concepts
• Geometric transformations

This page presents a comprehensive collection of geometric formulas and fundamental mathematical operations. The content focuses on volume and area calculations for various geometric shapes, along with basic fraction operations.

Definition: Perimeter $p$ is defined as the sum of all sides of a geometric figure.

Example: For a rectangle, perimeter is calculated as p = $L + l$ × 2, where L is length and l is width.

Highlight: Volume calculations are particularly important for 3D shapes like cylinders $V = πr²h$ and spheres $V = 4πr³/3$.

Vocabulary:

• Parallelepiped: A three-dimensional figure with six faces, each being a parallelogram
• Prism: A solid geometric figure with two parallel faces (bases) and flat sides

The page includes detailed formulas for:

• Basic shapes (squares, rectangles)
• Three-dimensional figures (cubes, cylinders, prisms)
• Circular objects (circles, spheres)
• Fraction operations (addition, subtraction, multiplication, division)