Questions and Answers
What does it mean to evaluate?
To figure out or compute.
What does it mean to simplify an expression?
To use the rules of arithmetic and algebra to rewrite an expression as simply as possible.
What does it mean to solve in mathematics?
Find all solutions to an equation, inequality, or a system of equations and/or inequalities.
What is a variable?
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What is an expression in mathematics?
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What is the Identity Property of Addition?
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What is the Inverse Property of Addition?
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What is the Commutative Property of Addition?
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What is the Associative Property of Addition?
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What is the Identity Property of Multiplication?
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What is the Inverse Property of Multiplication?
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What is the Commutative Property of Multiplication?
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What is the Associative Property of Multiplication?
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What is the Distributive Property?
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What is the Multiplicative Property of Zero?
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What is the Substitution Property?
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What is the Reflexive Property of Equality?
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What is the Symmetric Property of Equality?
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What is the Transitive Property of Equality?
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What is an inequality?
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What is the Transitive Property for Inequality?
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What is the Addition/Subtraction Property of Inequality?
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What is an equation?
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What is a trinomial?
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What is a term in an expression?
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What is a factor?
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What is the Greatest Common Factor?
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What is the Difference of Squares?
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What is a numerical coefficient?
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What is a leading coefficient?
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What does FOIL stand for in mathematics?
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What is a binomial?
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Study Notes
Key Concepts
- Evaluate: Computing the value of an expression, e.g., evaluating (12 + 5) results in (17).
- Simplify: The process of rewriting an expression in its simplest form using arithmetic and algebraic rules.
- Solve: Finding all possible solutions to equations, inequalities, or systems of equations/inequalities.
- Variable: A symbol or letter representing a quantity that can change or take different values.
- Expression: A mathematical combination of numbers and/or variables using operations, excluding equalities or inequalities.
Properties of Addition
- Identity Property of Addition: States that adding zero to any number returns the same number (e.g., (a + 0 = a)).
- Inverse Property of Addition: Adding a number and its opposite equals zero (e.g., (a + (-a) = 0)).
- Commutative Property of Addition: The order of addition does not affect the sum (e.g., (a + b = b + a)).
- Associative Property of Addition: Grouping of numbers in addition can be changed without affecting the sum (e.g., ((a + b) + c = a + (b + c))).
Properties of Multiplication
- Identity Property of Multiplication: Multiplying any number by one yields that number.
- Inverse Property of Multiplication: Multiplying a number by its reciprocal equals one.
- Commutative Property of Multiplication: The order of multiplication does not change the product (e.g., (ab = ba)).
- Associative Property of Multiplication: Changing the grouping in multiplication does not affect the product (e.g., ((ab)c = a(bc))).
- Distributive Property: Distributes multiplication across addition (e.g., (a(b+c) = ab + ac)).
- Multiplicative Property of Zero: Any number multiplied by zero results in zero.
Properties of Equality
- Substitution Property: Allows substitution of equal values in equations or inequalities (if (a = b), then (b) can replace (a)).
- Reflexive Property of Equality: Any real number is equal to itself (e.g., (a = a)).
- Symmetric Property of Equality: If one quantity equals another, the second equals the first (e.g., if (a = b), then (b = a)).
- Transitive Property of Equality: If one quantity equals a second, and the second equals a third, then the first equals the third (e.g., if (a = b) and (b = c), then (a = c)).
Inequalities
- Inequality: A mathematical statement comparing two quantities.
- Transitive Property for Inequality: Similar to equality but applies to inequalities (e.g., if (a < b) and (b < c), then (a < c)).
- Addition/Subtraction Property of Inequality: Adding or subtracting the same number does not alter the inequality.
Equations and Polynomials
- Equation: A statement asserting that two mathematical expressions are equal.
- Trinomial: A polynomial consisting of three non-like terms.
- Term: Parts of an expression separated by addition or subtraction.
- Factor: An integer or algebraic expression that divides another integer or expression evenly.
- Greatest Common Factor (GCF): The largest factor shared by a set of numbers or algebraic expressions.
- Difference of Squares: Expression representing the difference between two squared terms.
- (Numerical) Coefficient: A numerical factor multiplying a variable in an expression.
- Leading Coefficient: The coefficient of the leading term in an algebraic expression.
Other Notable Terms
- FOIL: A method for distributing two binomials, standing for First, Outer, Inner, and Last terms.
- Binomial: A polynomial consisting of two terms.
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Test your knowledge of key terms from Algebra 2, Unit 1, focusing on expressions, equations, and inequalities. These flashcards cover essential vocabulary such as evaluate, simplify, and solve, providing definitions and examples to enhance your understanding.