Number Systems

Real Numbers: A combination of rational and irrational numbers.
Rational Numbers: Can be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Properties:
  - Closure: The result of adding, subtracting, multiplying, or dividing two rational numbers is always a rational number.
  - Commutativity: The order of rational numbers does not change the result of addition and multiplication.
  - Associativity: The order in which rational numbers are added or multiplied does not change the result.
  - Distributivity: a(b + c) = ab + ac
Irrational Numbers: Cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Examples: π, e, √2
Recurring Decimals: Decimals that have a repeating pattern of digits.
- Example: 0.12341234...
Non-Recurring Decimals: Decimals that do not have a repeating pattern of digits.
- Example: π

Polynomial: An expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
- Example: 2x^2 + 3x - 4
Degree of a Polynomial: The highest power of the variable in the polynomial.
- Example: The degree of 2x^2 + 3x - 4 is 2.
Terms of a Polynomial: The individual parts of the polynomial separated by + or - signs.
- Example: The terms of 2x^2 + 3x - 4 are 2x^2, 3x, and -4.
Types of Polynomials:
- Monomial: A polynomial with only one term.
  - Example: 2x^2
- Binomial: A polynomial with two terms.
  - Example: x^2 + 3x
- Trinomial: A polynomial with three terms.
  - Example: x^2 + 3x - 4
Addition and Subtraction of Polynomials:
- To add or subtract polynomials, combine like terms.
- Example: (2x^2 + 3x) + (x^2 - 2x) = 3x^2 + x

Cartesian Plane: A two-dimensional plane with a horizontal x-axis and a vertical y-axis.
Coordinates: A pair of numbers (x, y) that represent a point on the Cartesian plane.
Plotting Points: To mark a point on the Cartesian plane using its coordinates.
Distance Formula: The distance between two points (x1, y1) and (x2, y2) is given by √((x2 - x1)^2 + (y2 - y1)^2).
Section Formula: The coordinates of a point that divides a line segment in the ratio m:n are given by ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)).
Midpoint Formula: The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by ((x1 + x2) / 2, (y1 + y2) / 2).

Real numbers combine rational and irrational numbers.
Rational numbers can be expressed as p/q, where p and q are integers and q ≠ 0, and have properties of closure, commutativity, associativity, and distributivity.
Irrational numbers cannot be expressed as p/q, and examples include π, e, and √2.
Recurring decimals have a repeating pattern of digits, such as 0.12341234..., while non-recurring decimals do not, like π.

A polynomial is an expression consisting of variables and coefficients combined using addition, subtraction, and multiplication.
The degree of a polynomial is the highest power of the variable, such as 2 in 2x^2 + 3x - 4.
Terms of a polynomial are individual parts separated by + or - signs, like 2x^2, 3x, and -4 in 2x^2 + 3x - 4.
Types of polynomials include monomials (one term), binomials (two terms), and trinomials (three terms).
To add or subtract polynomials, combine like terms, such as (2x^2 + 3x) + (x^2 - 2x) = 3x^2 + x.

The Cartesian plane is a two-dimensional plane with a horizontal x-axis and a vertical y-axis.
Coordinates are a pair of numbers (x, y) representing a point on the Cartesian plane.
Plotting points involves marking a point on the plane using its coordinates.
The distance formula calculates the distance between two points (x1, y1) and (x2, y2) as √((x2 - x1)^2 + (y2 - y1)^2).
The section formula gives the coordinates of a point dividing a line segment in the ratio m:n as ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)).
The midpoint formula calculates the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) as ((x1 + x2) / 2, (y1 + y2) / 2).