Questions and Answers
What is the absolute value?
What is the additive inverse?
The opposite of a number
What is an algebraic expression?
A phrase that can use numbers, variables, and operation symbols
What is an arithmetic sequence?
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What is the axis of symmetry?
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What is a base in mathematics?
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What is a binomial?
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What is a coefficient?
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What is a common difference?
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What is a common ratio?
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What is the complement of an event?
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What are compound inequalities?
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What is a conclusion in logic?
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What is a conditional statement?
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What is a conjecture?
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What are conjugates?
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What are consecutive integers?
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What is a constant?
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What is continuous data?
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What is a coordinate plane?
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What are coordinates?
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What is cosine?
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What is a counterexample?
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What are cross products?
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What is a decay factor?
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What is the degree of a monomial?
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What is dilation in math?
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What is direct variation?
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What is a discriminant in mathematics?
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What are edges in geometry?
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What is an element in a composite entity?
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What does elimination mean in various contexts?
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What does equal mean in a group context?
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What is an equation?
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What does evaluate mean in mathematics?
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What is an exponent?
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What is an expression in mathematics?
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What are factors?
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What is the foil method?
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What is a formula in mathematics?
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What is a function?
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What is a graph?
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What is a half-plane?
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What does inconsistent mean?
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What does independent mean in algebra?
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Study Notes
Algebra Definitions
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Absolute Value: Represents the distance of a number from zero on a number line, always non-negative.
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Additive Inverse: The value that, when added to a number, yields zero; effectively, the opposite of the number.
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Algebraic Expression: A combination of numbers, variables, and operation symbols representing a mathematical quantity.
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Arithmetic Sequence: A sequence of numbers where each term is generated by adding a constant (fixed number) to the previous term.
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Axis of Symmetry: A vertical line that divides a parabola into two mirror-image halves, essential in analyzing quadratic functions.
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Base: The number that is multiplied by itself in exponential expressions, determining the foundational value of powers.
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Binomial: A polynomial consisting of exactly two terms joined by a plus or minus sign; significant in algebraic operations.
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Coefficient: The numerical factor in a term, particularly affecting the variable; crucial for determining the magnitude of terms in expressions.
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Common Difference: The consistent value added between consecutive terms of an arithmetic sequence, defining the sequence's linear nature.
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Common Ratio: The fixed multiplicative factor between consecutive terms in a geometric sequence, pivotal for identifying exponential growth or decay.
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Complement of an Event: The set of all possible outcomes that do not occur within a specific event, illustrating the concept of probability.
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Compound Inequalities: Formed by connecting two inequalities with "and" or "or," allowing for simultaneous conditions in algebraic expressions.
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Conclusion: The result or outcome drawn from logical reasoning; appears after the "then" in conditional statements.
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Conditional: A logical statement formatted as "if-then," integral to forming implications and drawing conclusions in mathematics.
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Conjecture: A hypothesis formed through inductive reasoning that may not yet be proven, often serving as a starting point for further investigation.
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Conjugates: Involving two expressions of the form a+√b and a-√b, used in various algebraic manipulations, especially in simplifying fractions.
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Consecutive Integers: A series of whole numbers that follow each other without interruption, relevant in number theory and algebra.
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Constant: A fixed value in mathematics that does not change regardless of the variable inputs in functions or equations.
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Continuous Data: Numerical data that can take any real value within a given range, typically measured rather than counted.
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Coordinate Plane: A two-dimensional plane defined by a pair of perpendicular axes (x and y), used for graphing functions and points.
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Coordinates: An ordered pair (x, y) that specifies a location on the coordinate plane and is essential for graphing points.
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Cosine: A trigonometric function defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle, foundational in trigonometry.
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Counterexample: An instance that disproves a conjecture or statement, crucial for verifying the validity of mathematical claims.
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Cross Products: The result generated from multiplying the numerator of one fraction by the denominator of another, used in solving proportions.
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Decay Factor: The constant ratio applied to diminish values in exponential decay scenarios, determining how quickly a quantity decreases over time.
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Degree of a Monomial: Calculated as the sum of exponents of all variables within the term, reflecting its overall complexity.
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Dilation: A transformation that alters the size of a shape without changing its proportions, affecting graphical representations.
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Direct Variation: Expressed as y = kx, indicating a linear relationship where y changes directly with x based on the constant k.
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Discriminant: Found using the formula b² - 4ac in quadratic equations, it determines the nature and number of roots.
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Edges: The lines formed at the intersection of two faces on a three-dimensional figure, important for understanding geometric structures.
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Element: Individual components that make up a larger whole, particularly relevant in set theory and mathematical structures.
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Equation: A mathematical statement that asserts the equality of two expressions, foundational in solving algebraic problems.
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Evaluate: The process of calculating the value of an expression or function for given inputs.
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Exponent: A notation that indicates how many times a base is multiplied by itself, essential in working with powers and roots.
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Expression: A combination of numbers, variables, and operators that represent a value, distinguished from equations.
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Factors: Numbers that can be multiplied together to yield a product, crucial for factorization in algebra.
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Foil Method: A technique for multiplying two binomials by combining the products of their outer and inner terms.
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Formula: A mathematical relationship or rule expressed in symbols, guiding calculations and solutions.
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Function: A relation that assigns exactly one output for each input, foundational in mathematics for modeling relationships.
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Graph: A visual representation illustrating relationships between quantities, revealing trends and patterns.
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Half-Plane: Refers to one side of a boundary line in an inequality graph, indicating possible solutions or regions.
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Inconsistent: A term describing a set of equations or inequalities that cannot simultaneously hold true, highlighting contradictions in systems of equations.
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Independent: Refers to variables or quantities that are not influenced or determined by others, crucial in understanding systems and functions.
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Test your knowledge of fundamental algebra definitions with these flashcards. Each card presents a key term along with its definition, helping you to reinforce your understanding of algebra concepts. Perfect for students preparing for exams or anyone looking to refresh their algebra skills.
