Algebra Definitions Flashcards
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Questions and Answers

What is the absolute value?

  • A phrase that can use numbers, variables, and operation symbols
  • The distance a number is from zero on a number line (correct)
  • A polynomial of two terms
  • The opposite of a number

    • 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?

    <p>A number sequence formed by adding a fixed number to each previous term</p> Signup and view all the answers

    What is the axis of symmetry?

    <p>A line that divides a parabola into two matching halves</p> Signup and view all the answers

    What is a base in mathematics?

    <p>A number that is multiplied repeatedly</p> Signup and view all the answers

    What is a binomial?

    <p>A polynomial of two terms</p> Signup and view all the answers

    What is a coefficient?

    <p>The numerical factor when a term has a variable</p> Signup and view all the answers

    What is a common difference?

    <p>The fixed number added to each term of an arithmetic sequence</p> Signup and view all the answers

    What is a common ratio?

    <p>The fixed number used to find terms in a geometric sequence</p> Signup and view all the answers

    What is the complement of an event?

    <p>Possible outcomes that are not in the event</p> Signup and view all the answers

    What are compound inequalities?

    <p>Two inequalities that are joined by 'and' or 'or'</p> Signup and view all the answers

    What is a conclusion in logic?

    <p>The part following 'then' in a conclusion</p> Signup and view all the answers

    What is a conditional statement?

    <p>An 'if-then' statement</p> Signup and view all the answers

    What is a conjecture?

    <p>Conclusion reached by inductive reasoning</p> Signup and view all the answers

    What are conjugates?

    <p>The expressions a+√b and a-√b where a and b are rational numbers</p> Signup and view all the answers

    What are consecutive integers?

    <p>Integers in counting order</p> Signup and view all the answers

    What is a constant?

    <p>A quantity that does not vary</p> Signup and view all the answers

    What is continuous data?

    <p>Numerical data values that can be measured</p> Signup and view all the answers

    What is a coordinate plane?

    <p>A two-dimensional region determined by a pair of axes</p> Signup and view all the answers

    What are coordinates?

    <p>Ordered pairs that identify points on a coordinate plane</p> Signup and view all the answers

    What is cosine?

    <p>The ratio of the adjacent side to the hypotenuse of a right-angled triangle</p> Signup and view all the answers

    What is a counterexample?

    <p>Refutation by example</p> Signup and view all the answers

    What are cross products?

    <p>The product of the numerator of one fraction with the denominator of the other fraction</p> Signup and view all the answers

    What is a decay factor?

    <p>The constant factor that each value in an exponential decay pattern is multiplied by</p> Signup and view all the answers

    What is the degree of a monomial?

    <p>The sum of the exponents of all its variables</p> Signup and view all the answers

    What is dilation in math?

    <p>The act of expanding an aperture</p> Signup and view all the answers

    What is direct variation?

    <p>y = kx</p> Signup and view all the answers

    What is a discriminant in mathematics?

    <p>b² - 4ac</p> Signup and view all the answers

    What are edges in geometry?

    <p>The intersection of faces of a 3-D figure</p> Signup and view all the answers

    What is an element in a composite entity?

    <p>An artifact that is one of the individual parts of which a composite entity is made up</p> Signup and view all the answers

    What does elimination mean in various contexts?

    <p>The process of removing or excluding something</p> Signup and view all the answers

    What does equal mean in a group context?

    <p>A person who is of equal standing with another in a group</p> Signup and view all the answers

    What is an equation?

    <p>A mathematical statement that two expressions are equal</p> Signup and view all the answers

    What does evaluate mean in mathematics?

    <p>Place a value on</p> Signup and view all the answers

    What is an exponent?

    <p>A mathematical notation indicating the number of times a quantity is multiplied by itself</p> Signup and view all the answers

    What is an expression in mathematics?

    <p>A combination of numbers, variables, and operation symbols</p> Signup and view all the answers

    What are factors?

    <p>Numbers that are multiplied together to get a product</p> Signup and view all the answers

    What is the foil method?

    <p>To multiply 2 binomials and find the sum of the products</p> Signup and view all the answers

    What is a formula in mathematics?

    <p>A symbolic representation using variables and constants</p> Signup and view all the answers

    What is a function?

    <p>The actions and activities assigned to or required of a person or group</p> Signup and view all the answers

    What is a graph?

    <p>A drawing illustrating the relations between certain quantities plotted with reference to a set of axes</p> Signup and view all the answers

    What is a half-plane?

    <p>The region of the graph of an inequality on one side of a boundary</p> Signup and view all the answers

    What does inconsistent mean?

    <p>Not in agreement</p> Signup and view all the answers

    What does independent mean in algebra?

    <p>A variable or equation that does not depend on another</p> Signup and view all the answers

    Study Notes

    Algebra Definitions

    • Absolute Value: Represents the distance of a number from zero on a number line, always non-negative.

    • Additive Inverse: The value that, when added to a number, yields zero; effectively, the opposite of the number.

    • Algebraic Expression: A combination of numbers, variables, and operation symbols representing a mathematical quantity.

    • Arithmetic Sequence: A sequence of numbers where each term is generated by adding a constant (fixed number) to the previous term.

    • Axis of Symmetry: A vertical line that divides a parabola into two mirror-image halves, essential in analyzing quadratic functions.

    • Base: The number that is multiplied by itself in exponential expressions, determining the foundational value of powers.

    • Binomial: A polynomial consisting of exactly two terms joined by a plus or minus sign; significant in algebraic operations.

    • Coefficient: The numerical factor in a term, particularly affecting the variable; crucial for determining the magnitude of terms in expressions.

    • Common Difference: The consistent value added between consecutive terms of an arithmetic sequence, defining the sequence's linear nature.

    • Common Ratio: The fixed multiplicative factor between consecutive terms in a geometric sequence, pivotal for identifying exponential growth or decay.

    • Complement of an Event: The set of all possible outcomes that do not occur within a specific event, illustrating the concept of probability.

    • Compound Inequalities: Formed by connecting two inequalities with "and" or "or," allowing for simultaneous conditions in algebraic expressions.

    • Conclusion: The result or outcome drawn from logical reasoning; appears after the "then" in conditional statements.

    • Conditional: A logical statement formatted as "if-then," integral to forming implications and drawing conclusions in mathematics.

    • Conjecture: A hypothesis formed through inductive reasoning that may not yet be proven, often serving as a starting point for further investigation.

    • Conjugates: Involving two expressions of the form a+√b and a-√b, used in various algebraic manipulations, especially in simplifying fractions.

    • Consecutive Integers: A series of whole numbers that follow each other without interruption, relevant in number theory and algebra.

    • Constant: A fixed value in mathematics that does not change regardless of the variable inputs in functions or equations.

    • Continuous Data: Numerical data that can take any real value within a given range, typically measured rather than counted.

    • Coordinate Plane: A two-dimensional plane defined by a pair of perpendicular axes (x and y), used for graphing functions and points.

    • Coordinates: An ordered pair (x, y) that specifies a location on the coordinate plane and is essential for graphing points.

    • 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.

    • Counterexample: An instance that disproves a conjecture or statement, crucial for verifying the validity of mathematical claims.

    • Cross Products: The result generated from multiplying the numerator of one fraction by the denominator of another, used in solving proportions.

    • Decay Factor: The constant ratio applied to diminish values in exponential decay scenarios, determining how quickly a quantity decreases over time.

    • Degree of a Monomial: Calculated as the sum of exponents of all variables within the term, reflecting its overall complexity.

    • Dilation: A transformation that alters the size of a shape without changing its proportions, affecting graphical representations.

    • Direct Variation: Expressed as y = kx, indicating a linear relationship where y changes directly with x based on the constant k.

    • Discriminant: Found using the formula b² - 4ac in quadratic equations, it determines the nature and number of roots.

    • Edges: The lines formed at the intersection of two faces on a three-dimensional figure, important for understanding geometric structures.

    • Element: Individual components that make up a larger whole, particularly relevant in set theory and mathematical structures.

    • Equation: A mathematical statement that asserts the equality of two expressions, foundational in solving algebraic problems.

    • Evaluate: The process of calculating the value of an expression or function for given inputs.

    • Exponent: A notation that indicates how many times a base is multiplied by itself, essential in working with powers and roots.

    • Expression: A combination of numbers, variables, and operators that represent a value, distinguished from equations.

    • Factors: Numbers that can be multiplied together to yield a product, crucial for factorization in algebra.

    • Foil Method: A technique for multiplying two binomials by combining the products of their outer and inner terms.

    • Formula: A mathematical relationship or rule expressed in symbols, guiding calculations and solutions.

    • Function: A relation that assigns exactly one output for each input, foundational in mathematics for modeling relationships.

    • Graph: A visual representation illustrating relationships between quantities, revealing trends and patterns.

    • Half-Plane: Refers to one side of a boundary line in an inequality graph, indicating possible solutions or regions.

    • Inconsistent: A term describing a set of equations or inequalities that cannot simultaneously hold true, highlighting contradictions in systems of equations.

    • 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.

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