Math Basics: Numbers and Operations

Study Notes

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, e.g. 3/4, 22/7
- Irrational Numbers: non-repeating decimals, e.g. π, e
- Real Numbers: all rational and irrational numbers
Number Operations:
- Addition: a + b = c
- Subtraction: a - b = c
- Multiplication: a × b = c
- Division: a ÷ b = c
- Exponentiation: a^b = c

Variables and Expressions:
- Variables: letters or symbols representing unknown values
- Expressions: combinations of variables, numbers, and operations
- Equations: expressions equal to each other
Linear Equations:
- Slope-Intercept Form: y = mx + b
- Standard Form: Ax + By = C
- Graphing: plotting points on a coordinate plane
Quadratic Equations:
- Standard Form: ax^2 + bx + c = 0
- Factoring: finding roots by factoring
- Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a

Points, Lines, and Planes:
- Points: locations in space
- Lines: sets of points extending infinitely
- Planes: flat surfaces
Angles and Measurements:
- Types of Angles: acute, right, obtuse, straight
- Degree Measure: 360° in a circle
- Trigonometry: relationships between angles and side lengths
Shapes and Solids:
- 2D Shapes: triangles, quadrilaterals, polygons, circles
- 3D Solids: pyramids, prisms, spheres, cylinders

Limits:
- Concept of limits: approaching a value
- Rules of limits: sum, product, chain rule
Derivatives:
- Definition: rate of change
- Rules of differentiation: power rule, product rule, quotient rule
Integrals:
- Definition: accumulation of rates
- Rules of integration: substitution, integration by parts

Natural Numbers are positive integers starting from 1, e.g. 1, 2, 3,...
Whole Numbers include 0 and all positive integers, e.g. 0, 1, 2, 3,...
Integers include all whole numbers and their negative counterparts, e.g. ..., -3, -2, -1, 0, 1, 2, 3,...
Rational Numbers are fractions, e.g. 3/4, 22/7, and can be expressed as decimals
Irrational Numbers are non-repeating decimals, e.g. π, e
Real Numbers encompass all rational and irrational numbers
Addition is the operation of combining two or more numbers to get a total or a sum, e.g. a + b = c
Subtraction is the operation of finding the difference between two numbers, e.g. a - b = c
Multiplication is the operation of repeated addition, e.g. a × b = c
Division is the operation of splitting a number into equal parts or groups, e.g. a ÷ b = c
Exponentiation is the operation of raising a number to a power, e.g. a^b = c

Variables are letters or symbols representing unknown values
Expressions are combinations of variables, numbers, and operations
Equations are expressions equal to each other
Slope-Intercept Form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept
Standard Form of a linear equation is Ax + By = C, where A, B, and C are constants
Graphing linear equations involves plotting points on a coordinate plane
Quadratic Equations are of the form ax^2 + bx + c = 0, where a, b, and c are constants
Factoring quadratic equations involves finding roots by factoring
The Quadratic Formula is x = (-b ± √(b^2 - 4ac)) / 2a, used to find the roots of a quadratic equation

The concept of limits involves approaching a value
Rules of limits include the sum, product, and chain rule
Derivatives measure the rate of change of a function
Rules of differentiation include the power rule, product rule, and quotient rule
Integrals measure the accumulation of rates of change
Rules of integration include substitution and integration by parts