Math: Numbers and Operations

Real Numbers: Include all rational and irrational numbers, can be represented on the number line
Properties of Real Numbers:
- Commutative Property: a + b = b + a, ab = ba
- Associative Property: (a + b) + c = a + (b + c), (ab)c = a(bc)
- Distributive Property: a(b + c) = ab + ac
Order of Operations: Follow the order of parentheses, exponents, multiplication and division, and addition and subtraction

Expressions: A collection of variables, constants, and algebraic operations
Equations: Two expressions equal to each other
Simplifying Expressions:
- Combine like terms
- Use the distributive property
- Use the properties of real numbers
Solving Linear Equations:
- Add, subtract, multiply, or divide both sides by the same value
- Use inverse operations to isolate the variable

Domain and Range: Domain is the set of input values, range is the set of output values
Function Notation: f(x) = output value, where x is the input value
Types of Functions:
- Linear Functions: f(x) = mx + b, where m is the slope and b is the y-intercept
- Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants
Graphing Functions:
- Use the x-axis for the domain and the y-axis for the range
- Identify the x-intercept(s) and y-intercept

Angles and Triangles:
- Degrees, minutes, and seconds
- Right triangles, acute angles, and obtuse angles
Trigonometric Ratios:
- Sine (sin), cosine (cos), and tangent (tan)
- sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, tan(A) = opposite side / adjacent side
Identities and Formulas:
- Pythagorean Identity: sin^2(A) + cos^2(A) = 1
- Sum and Difference Formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.

Coordinate Plane:
- Quadrants, x-axis, y-axis, and origin
- Plotting points and graphing equations
Circle Equations:
- Standard form: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius
- General form: x^2 + y^2 + Dx + Ey + F = 0
Conic Sections:
- Parabolas, ellipses, and hyperbolas
- Equations and graphs of each

Real numbers include all rational and irrational numbers and can be represented on the number line.
The Commutative Property of Real Numbers states that the order of numbers does not change the result: a + b = b + a, ab = ba.
The Associative Property of Real Numbers states that the order in which numbers are grouped does not change the result: (a + b) + c = a + (b + c), (ab)c = a(bc).
The Distributive Property of Real Numbers states that multiplication can be distributed over addition: a(b + c) = ab + ac.
The Order of Operations follows the order of parentheses, exponents, multiplication and division, and addition and subtraction.

An algebraic expression is a collection of variables, constants, and algebraic operations.
An equation is two expressions equal to each other.
To simplify expressions, combine like terms, use the distributive property, and use the properties of real numbers.
To solve linear equations, add, subtract, multiply, or divide both sides by the same value, and use inverse operations to isolate the variable.

The domain of a function is the set of input values, and the range is the set of output values.
Function notation is f(x) = output value, where x is the input value.
Linear functions have the form f(x) = mx + b, where m is the slope and b is the y-intercept.
Quadratic functions have the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
To graph functions, use the x-axis for the domain and the y-axis for the range, and identify the x-intercept(s) and y-intercept.

Angles can be measured in degrees, minutes, and seconds.
Right triangles have acute angles and obtuse angles.
The sine, cosine, and tangent ratios are defined as sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, and tan(A) = opposite side / adjacent side.
The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1.
The Sum and Difference Formulas include sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.

The coordinate plane has four quadrants, an x-axis, a y-axis, and an origin.
Points can be plotted and equations can be graphed on the coordinate plane.
Circle equations can be written in standard form: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
Circle equations can also be written in general form: x^2 + y^2 + Dx + Ey + F = 0.
Conic sections include parabolas, ellipses, and hyperbolas, each with its own equation and graph.