Questions and Answers
What does PEMDAS stand for?
What is the Reflexive Property of Equality?
a=a
What does the Symmetric Property of Equality state?
If a=b, then b=a
What does the Transitive Property of Equality state?
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What is the Addition and Subtraction Properties of Equality?
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What does the Multiplication and Division Properties of Equality state?
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What is a Relation?
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What is a Function?
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What is the Domain of a relation?
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What is the Range of a relation?
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What is Standard form in algebra?
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What is a Linear equation?
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What is a 0 slope line?
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What does a No slope line represent?
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What is the Slope-intercept form of a line?
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What is the Determinant of a 2 by 2 matrix?
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What are the Dimensions of a matrix?
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What is the Determinant of a 3 by 3 matrix?
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How is the Area of a triangle calculated?
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How do you solve a matrix equation?
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What is the Degree of a monomial?
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What is the Product of Powers rule?
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What is the Product of a Power rule?
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What is the Power of a Product rule?
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What is the Quotient of Powers rule?
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What is the Power of Quotients rule?
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What is the Negative Powers rule?
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What is the Difference of 2 Squares?
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What is the Difference of 2 Cubes?
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What is the Sum of 2 Cubes?
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What is the Multiplication Property of Radicals?
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What is the Division Property of Radicals?
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What are Rational Exponents?
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What is a Quadratic Equation in Standard Form?
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What is a Quadratic Equation in Vertex Form?
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What is the Zero Product Property?
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What is the Quadratic Formula?
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Study Notes
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).
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Test your knowledge of Algebra 2 concepts with these flashcards. Cover topics like the Order of Operations and various Properties of Equality. Perfect for reinforcing key algebraic principles and improving your mathematical skills.