Numbers and Operations Basics

Number Systems:
- Natural Numbers: 1, 2, 3, ...
- Whole Numbers: 0, 1, 2, 3, ...
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational Numbers: fractions, e.g., 1/2, 3/4
- Irrational Numbers: non-repeating decimals, e.g., π, e
- Real Numbers: all rational and irrational numbers
- Complex Numbers: a + bi, where a and b are real numbers and i is the imaginary unit
Operations:
- Addition: combining two or more numbers to get a total or sum
- Subtraction: finding the difference between two numbers
- Multiplication: repeated addition, e.g., 3 × 4 = 3 + 3 + 3 + 3
- Division: sharing or grouping, e.g., 12 ÷ 3 = 4
- Order of Operations (PEMDAS/BODMAS): parentheses, exponents, multiplication and division, addition and subtraction

Variables and Expressions:
- Variables: letters or symbols representing unknown values
- Expressions: combinations of variables, numbers, and operations
- Simplifying Expressions: combining like terms
Equations and Inequalities:
- Equations: statements with equal values, e.g., 2x + 3 = 5
- Inequalities: statements with unequal values, e.g., 2x - 4 > 0
- Solving Equations and Inequalities: finding the value(s) that make the statement true

Points, Lines, and Planes:
- Points: locations in space, represented by coordinates (x, y)
- Lines: sets of points extending infinitely in two directions
- Planes: flat surfaces extending infinitely in all directions
Angles and Measurement:
- Angles: formed by two rays sharing a common endpoint
- Types of Angles: acute, obtuse, right, straight, reflex
- Measuring Angles: degrees, radians
- Perimeter and Area: calculating the distance around and within shapes

Types of Data:
- Qualitative: categorical, descriptive data
- Quantitative: numerical data
- Discrete: individual, countable data
- Continuous: measurable, uncountable data
Graphs and Charts:
- Types of Graphs: bar, histogram, line, scatter, circle
- Interpreting Graphs: understanding the data and relationships represented

Number Systems include Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers, and Complex Numbers.
Natural Numbers start from 1 and are infinite, while Whole Numbers include 0 and are also infinite.
Integers include all positive and negative whole numbers, and Rational Numbers are fractions, such as 1/2 or 3/4.
Irrational Numbers are non-repeating decimals, like π or e, and Real Numbers comprise all Rational and Irrational Numbers.
Complex Numbers have a real part and an imaginary part, written as a + bi, where a and b are Real Numbers and i is the imaginary unit.
Operations include Addition, Subtraction, Multiplication, and Division, with specific definitions and examples.
The Order of Operations follows the PEMDAS/BODMAS rule, prioritizing calculations within parentheses, then exponents, followed by multiplication and division, and finally addition and subtraction.

Variables are letters or symbols representing unknown values, and Expressions combine variables, numbers, and operations.
Simplifying Expressions involves combining like terms to reduce complexity.
Equations are statements with equal values, and Inequalities are statements with unequal values, with examples and explanations.
Solving Equations and Inequalities involves finding the value(s) that make the statement true.

Points are locations in space, represented by coordinates (x, y), and Lines are sets of points extending infinitely in two directions.
Planes are flat surfaces extending infinitely in all directions, with examples and descriptions.
Angles are formed by two rays sharing a common endpoint, with different types, including acute, obtuse, right, straight, and reflex angles.
Measuring Angles involves using degrees or radians, with explanations of each method.
Perimeter and Area calculations involve finding the distance around and within shapes, with formulas and examples.

Types of Data include Qualitative, Quantitative, Discrete, and Continuous data, with definitions and explanations.
Qualitative data is categorical or descriptive, while Quantitative data is numerical, and Discrete data is individual and countable, whereas Continuous data is measurable and uncountable.
Graphs and Charts include Bar, Histogram, Line, Scatter, and Circle graphs, with explanations of each type.
Interpreting Graphs involves understanding the data and relationships represented, with examples and applications.