Questions and Answers
What is absolute value?
The distance a number is from zero (y=|x|)
What is an algebraic expression?
Contains numbers, variables, and operations (no equal sign)
What is area?
The amount of space within a 2-dimensional figure
What is a binomial?
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What is a coefficient?
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What is common difference?
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What is common ratio?
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What is a constant of variation?
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What is a constant term?
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What are coordinates?
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What is the degree of a monomial?
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What is the degree of a polynomial?
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What is difference?
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What is the distributive property?
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What is an equation?
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What are equivalent expressions?
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What does evaluate mean?
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What is an exponent?
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What is a factor?
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What does it mean to factor completely?
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What is factoring?
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What is a formula?
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What is a function?
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What is function notation?
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What is a function rule?
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What is the greatest common factor?
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What is an inequality?
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What are integers?
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What are inverse operations?
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What are irrational numbers?
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What is a leading coefficient?
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What are like terms?
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What is a literal equation?
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What is a monomial?
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What is a negative exponent?
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What are opposites?
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What is the order of operations?
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What is a perfect square?
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What are perpendicular lines?
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What is a quotient?
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What is a ratio?
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What are rational numbers?
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What are real numbers?
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What does simplify mean?
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What is a square root?
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What is substitution?
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What is sum?
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What are the terms of an expression?
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What is a trinomial?
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What is a variable?
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What are whole numbers?
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What is a zero exponent?
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What is a zero term?
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What does prime mean?
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Study Notes
Key Concepts in Algebra
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Absolute Value: Represents the distance of a number from zero on a number line, denoted mathematically as ( y = |x| ).
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Algebraic Expression: Composed of numbers, variables, and operations, but does not hold an equal sign.
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Area: Measures the amount of space enclosed within a two-dimensional shape.
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Binomial: An algebraic expression containing exactly two distinct terms.
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Coefficient: A numerical factor that multiplies a variable in an expression, often referred to as the "big" number.
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Common Difference: The fixed amount added to each term in an arithmetic sequence, establishing a uniform gap between consecutive terms.
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Common Ratio: The constant factor between consecutive terms in a geometric sequence, expressed as a ratio.
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Constant of Variation: The constant value (denoted as ( k )) that remains unchanged in direct (e.g., ( y = kx )) or inverse variation (e.g., ( xy = k )) relationships.
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Constant Term: A term in an expression that has no variable part, maintaining a specific value (e.g., in ( 2x + 3 ), the constant term is 3).
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Coordinates: An ordered pair of numbers, usually represented as ( (x, y) ), defining a specific point on a coordinate plane.
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Degree of a Monomial: Sum of the exponents in a term containing variables, indicating its overall degree.
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Degree of a Polynomial: Determined by the highest degree among its constituent terms.
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Difference: The result derived from performing subtraction between two quantities.
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Distributive Property: A fundamental property of multiplication over addition, expressed as ( a(b + c) = ab + ac ).
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Equation: A mathematical statement containing an equal sign, asserting the equality of two expressions.
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Equivalent Expressions: Two expressions that yield the same value under all substitutions, demonstrated by an equality (e.g., ( 3x + 5 = 2x - 6 )).
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Evaluate: The process of determining the value of an expression by substituting specific numbers for the variables.
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Exponent: The small number in a power that indicates how many times the base is multiplied by itself.
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Factor: An expression that, when multiplied together with others, forms a product (e.g., ( (2x - 1) ) and ( (x - 1) ) are factors).
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Factor Completely: The act of breaking down a polynomial into its prime factors.
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Factoring: The method of determining the factors of a polynomial, often rewriting it in its factored form.
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Formula: A mathematical equation that provides a method to calculate a specific value.
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Function: A relationship where each input has a single output, ensuring that no x-values repeat, although y-values can vary.
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Function Notation: A method of representing functions using symbols, commonly denoted as ( f(x) ).
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Function Rule: An expression that defines how output values are derived from input values in a function.
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Greatest Common Factor (GCF): The largest term that can evenly divide all terms in a polynomial.
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Inequality: A mathematical expression that features an inequality sign instead of an equal sign, representing non-equal relationships.
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Integers: The set of whole numbers including negative numbers, zero, and positive numbers.
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Inverse Operations: Pairs of operations that reverse each other's effects, such as addition and subtraction or multiplication and division.
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Irrational Numbers: Numbers that cannot be expressed as a simple fraction, including many roots and specific decimal forms.
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Leading Coefficient: The coefficient associated with the term of the highest degree in a polynomial, influencing its end behavior.
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Like Terms: Terms that share the same variable parts, allowing for simplification through addition or subtraction.
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Literal Equation: An equation in which letters symbolize numbers, commonly used to express mathematical relationships (e.g., ( A = lw )).
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Monomial: A polynomial that consists of only one single term.
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Negative Exponent: An exponent that indicates the reciprocal of the base raised to the opposite positive exponent.
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Opposites: Refers to the reciprocal nature of mathematical operations, including positive/negative and addition/subtraction.
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Order of Operations: A set of rules for simplifying mathematical expressions in a specific sequence, often remembered by the acronym PEMDAS.
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Perfect Square: A number whose square root is an integer, such as ( 1, 4, 9, 16 ).
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Perpendicular Lines: Lines that intersect at right angles, creating a 90-degree angle.
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Quotient: The result obtained from dividing one number by another.
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Ratio: A mathematical comparison between two quantities expressed through division, such as ( 6:4 ) or ( 6/4 ).
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Rational Numbers: Numbers that can be expressed as a fraction of two integers, including terminating and repeating decimals.
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Real Numbers: The complete set of all rational and irrational numbers, encompassing all number types.
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Simplify: The process of executing all operations in an expression to reduce it to its simplest form.
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Square Root: A number that produces a specified value when multiplied by itself.
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Substitution: A method for solving equations by replacing a variable with an expression representing its value in other equations.
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Sum: The final result obtained after performing addition on two or more numbers.
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Terms of an Expression: Individual components of an expression that are separated by either addition or subtraction.
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Trinomial: A polynomial consisting of three distinct terms.
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Variable: A symbol, often a letter, utilized to stand in for an unknown value in mathematical expressions.
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Whole Numbers: Non-negative integers that start from zero and increment upward (0, 1, 2, ...).
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Zero Exponent: A mathematical principle where any non-zero base raised to the zero power equals one.
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Zero Term: The output of a function rule when no operational adjustments have been applied.
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Prime: A natural number greater than one that has no divisors other than one and itself.
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