Basic Math Concepts

Types of Numbers:
- Natural Numbers (1, 2, 3, ...)
- Whole Numbers (0, 1, 2, 3, ...)
- Integers (...,-3, -2, -1, 0, 1, 2, 3, ...)
- Rational Numbers (fractions, decimals)
- Irrational Numbers (non-repeating, non-terminating decimals)
Number Operations:
- Addition (+)
- Subtraction (-)
- Multiplication (×)
- Division (÷)
- Exponents (powers)
- Roots (square, cube, etc.)

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:
- Linear Equations (e.g. 2x + 3 = 5)
- Quadratic Equations (e.g. x^2 + 4x + 4 = 0)
- Inequalities (e.g. 2x - 3 > 5)

Points, Lines, and Planes:
- Points (locations in space)
- Lines (sets of points extending infinitely)
- Planes (flat surfaces)
Angles and Measurements:
- Angle types (acute, obtuse, right, straight)
- Degree measurements (0° - 360°)
- Calculating perimeter and area of shapes

Data Analysis:
- Types of data (qualitative, quantitative)
- Data visualization (charts, graphs, tables)
- Measures of central tendency (mean, median, mode)
Probability:
- Basic concepts (events, sample spaces, probability rules)
- Calculating probability (theoretical, experimental)
- Conditional probability and independence

Limits:
- Concept of limits
- Evaluating limits (direct substitution, factoring)
Derivatives:
- Definition of derivatives
- Rules of differentiation (power rule, product rule, etc.)
- Applications of derivatives (optimization, motion)
Integrals:
- Definition of integrals
- Basic integration rules (substitution, integration by parts)
- Applications of integrals (area, volume, work)

There are five types of numbers: Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Irrational Numbers.
Natural Numbers are positive integers starting from 1.
Whole Numbers are non-negative integers including 0.
Integers include all whole numbers and their negative counterparts.
Rational Numbers are expressed as fractions or decimals.
Irrational Numbers are non-repeating, non-terminating decimals.
There are six basic number operations: Addition, Subtraction, Multiplication, Division, Exponents, and Roots.
Addition and subtraction are inverse operations, as are multiplication and division.
Exponents represent repeated multiplication, and roots represent the opposite operation.

Variables are letters or symbols representing unknown values.
Expressions are combinations of variables, numbers, and operations.
Simplifying expressions involves combining like terms.
Equations are statements that express the equality of two expressions.
Inequalities are statements that compare two expressions using greater than, less than, or equal to.

Data can be qualitative or quantitative.
Data visualization involves using charts, graphs, and tables to display data.
Measures of central tendency include the mean, median, and mode.
Probability is a measure of the likelihood of an event occurring.
Probability rules include the complement rule and the multiplication rule.
Conditional probability and independence are used to calculate the probability of multiple events.

Limits are used to study how functions behave as the input approaches a certain value.
The concept of limits is essential for understanding calculus.
Evaluating limits involves using direct substitution, factoring, or other methods.
Derivatives measure the rate of change of a function.
The definition of derivatives involves the limit of the difference quotient.
Rules of differentiation include the power rule, product rule, and quotient rule.
Applications of derivatives include optimization and motion problems.
Integrals are used to calculate the area under curves or the accumulation of a quantity.
The definition of integrals involves the limit of the sum of the areas of rectangles.
Basic integration rules include substitution, integration by parts, and integration by partial fractions.
Applications of integrals include finding area, volume, and work.