Algebra 2 Part 1 Flashcards

Order of Operations

• The order of operations is abbreviated as PEMDAS, representing Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Properties of Equality

• Reflexive Property: a = a
• Symmetric Property: If a = b, then b = a
• Transitive Property: If a = b and b = c, then a = c
• Addition/Subtraction Properties: If a = b, then a + c = b + c and a - c = b - c
• Multiplication/Division Properties: If a = b, then a * c = b * c and a / c = b / c

Relations and Functions

• A relation is defined as a set of ordered pairs.
• A function is a specific type of relation where each x-coordinate corresponds to exactly one y-coordinate.
• The domain of a relation is the set of all x-coordinates, while the range is the set of all y-coordinates.

Linear Equations

• Standard form of a linear equation: ax + by = c
• A linear equation graphically represents a straight line.
• A line with 0 slope is horizontal, while a vertical line has no slope.
• Slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope.

Matrices

• The determinant of a 2x2 matrix is calculated as ad - bc.
• Dimensions of a matrix are defined by the number of rows and columns.
• The determinant of a 3x3 matrix is calculated using the formula: aei + bfg + cdh - gec - hfa - idb.

Area and Solving Matrices

• The area of a triangle defined by vertices (a, b), (c, d), (e, f) is given by 1/2 * | a b 1 | { c d 1 } { e f 1 }.
• To solve a matrix equation, find the inverse of the first matrix.

Monomials and Exponents

• The degree of a monomial is the total of the exponents of its variables.
• Product of Powers rule: a^m * a^n = a^(m+n)
• Power of a Product rule: (ab)^m = a^m * b^m
• Quotient of Powers rule: a^m / a^n = a^(m-n)
• Negative Powers rule: a^-n = 1/(a^n) and 1/(a^-n) = a^n

Special Factorizations

• Difference of 2 Squares: a^2 - b^2 = (a - b)(a + b)
• Difference of 2 Cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
• Sum of 2 Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Radicals and Rational Exponents

• The Multiplication Property of Radicals states that the nth root of ab equals the nth root of a times the nth root of b.
• The Division Property states that the nth root of a/b equals the nth root of a divided by the nth root of b.
• Rational exponents can be expressed as b^(m/n) = (nth root of b)^m.

Quadratic Equations

• Quadratic equations in standard form: y = ax^2 + bx + c where a ≠ 0.
• Vertex form of a quadratic equation is represented as y = a(x - h)^2 + k, where a ≠ 0.
• The Zero Product Property states that if ab = 0, then a = 0, b = 0, or both.
• The quadratic formula for solving quadratic equations is x = (-b ± √(b² - 4ac)) / (2a).