Algebra Fundamentals

Variables and Expressions:
- Variables: letters or symbols that represent unknown values
- Expressions: combinations of variables, constants, and mathematical operations
Equations and Inequalities:
- Equations: statements that two expressions are equal
- Inequalities: statements that one expression is greater than, less than, or equal to another
Functions:
- Domain: set of input values for a function
- Range: set of output values for a function
- Linear functions: functions of the form f(x) = ax + b, where a and b are constants
Graphing:
- Graphs: visual representations of functions
- x-axis: horizontal axis, represents input values
- y-axis: vertical axis, represents output values

Limits:
- Definition: a value that a function approaches as the input gets arbitrarily close
- Notation: lim x→a f(x) = L
Derivatives:
- Definition: rate of change of a function with respect to the input
- Notation: f'(x) or (d/dx)f(x)
- Rules: power rule, product rule, quotient rule, and chain rule
Integrals:
- Definition: accumulation of the rates of change of a function over a given interval
- Notation: ∫f(x)dx or ∫[a,b] f(x)dx
- Types: definite and indefinite integrals

Points, Lines, and Planes:
- Points: locations in space, represented by coordinates (x, y, z)
- Lines: sets of points extending infinitely in two directions
- Planes: flat surfaces extending infinitely in all directions
Angles and Measurements:
- Angles: formed by two rays sharing a common endpoint
- Degrees: units of measurement for angles
- Types: acute, obtuse, right, and straight angles
Properties of Shapes:
- Congruent: shapes with the same size and shape
- Similar: shapes with the same shape but not necessarily the same size
- Perimeter: distance around a shape
- Area: amount of space inside a shape

Triangles:
- Angles: measured in degrees or radians
- Sides: opposite, adjacent, and hypotenuse
- Pythagorean theorem: a^2 + b^2 = c^2, where c is the hypotenuse
Trigonometric Functions:
- Sine (sin): opposite side over hypotenuse
- Cosine (cos): adjacent side over hypotenuse
- Tangent (tan): opposite side over adjacent side
Identities and Formulas:
- Pythagorean identity: sin^2(x) + cos^2(x) = 1
- Sum and difference formulas for sine, cosine, and tangent

Variables are letters or symbols that represent unknown values.
Expressions are combinations of variables, constants, and mathematical operations.
Equations are statements that two expressions are equal.
Inequalities are statements that one expression is greater than, less than, or equal to another.
Domain of a function is the set of input values.
Range of a function is the set of output values.
Linear functions are functions of the form f(x) = ax + b, where a and b are constants.
Graphs are visual representations of functions.
x-axis represents input values.
y-axis represents output values.

Limit is a value that a function approaches as the input gets arbitrarily close.
Notation for limit is lim x→a f(x) = L.
Derivative is the rate of change of a function with respect to the input.
Notation for derivative is f'(x) or (d/dx)f(x).
Rules for derivatives include power rule, product rule, quotient rule, and chain rule.
Integral is the accumulation of the rates of change of a function over a given interval.
Notation for integral is ∫f(x)dx or ∫[a,b] f(x)dx.
There are two types of integrals: definite and indefinite integrals.

Perform operations with different number systems: integers, decimals, fractions, and whole numbers
Apply PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) to follow the order of operations