Algebra Vocabulary Flashcards

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Questions and Answers

What is a variable?

A statement of equality

A symbol used to represent a number (correct)

An equation that shows a relationship

None of the above

What is an equation?

A statement of equality

Define distributive property.

For all real numbers a, b, and c: a(b + c) = ab + ac

What is a formula?

An equation that expresses a relationship between measurements Signup and view all the answers

What is a coefficient?

A number that is multiplied by a variable Signup and view all the answers

Define opposite in terms of real numbers.

For a real number a, the real number -a Signup and view all the answers

What is the reciprocal of a nonzero real number a?

The real number 1/a Signup and view all the answers

What does it mean to factor?

To express as a product of two or more quantities Signup and view all the answers

Define power in mathematical terms.

A product in which all the factors are the same Signup and view all the answers

What is a polynomial?

A sum of monomials Signup and view all the answers

Define a binomial.

A polynomial with two terms Signup and view all the answers

What characterizes a prime polynomial?

A polynomial whose greatest monomial factor is 1 Signup and view all the answers

What are integers?

The set of whole numbers and their opposites Signup and view all the answers

What is a quadratic polynomial?

A polynomial equation of degree two Signup and view all the answers

What is an ordered pair?

A set of two elements in which the order is specified Signup and view all the answers

Define a coordinate system.

Two perpendicular number lines, or axes, used for graphing ordered pairs of numbers Signup and view all the answers

What is a solution in mathematics?

An ordered pair that satisfies an equation (or inequality) Signup and view all the answers

What does graph refer to in mathematics?

The set of all points whose coordinates satisfy an equation Signup and view all the answers

Define slope.

The steepness of a line as defined by the ratio: difference of y-coordinates/difference of x-coordinates Signup and view all the answers

What is the y-intercept in graphing?

The y-coordinate of a point where a graph intersects the y-axis Signup and view all the answers

What is slope-intercept form?

The form of a linear equation y = mx + b Signup and view all the answers

What is a system of equations?

A set of equations in the same variable Signup and view all the answers

Define a function in mathematics.

A set of ordered pairs in which no two ordered pairs have the same first element Signup and view all the answers

What is direct variation?

A function defined by an equation of the form y = kx Signup and view all the answers

Define inverse variation.

A function defined by an equation of the form y = k/x Signup and view all the answers

What is a radical?

An expression of the form square root of a square root symbol Signup and view all the answers

What is the quadratic formula?

x = -b±[√b²-4ac]/2a Signup and view all the answers

What is a parabola?

The graph of a quadratic function Signup and view all the answers

Study Notes

Algebra Vocabulary Study Notes

Variable: Represents an unknown number, commonly denoted by letters (e.g., x, y).
Equation: A statement asserting the equality of two expressions, often containing variables.
Distributive Property: Establishes that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds true.
Formula: An equation that reveals how different measurements relate to each other, often used in various fields of study.
Coefficient: A numerical factor that multiplies a variable in an expression, affecting its value.
Opposite: The negative counterpart of a real number a, represented as -a.
Reciprocal: For a nonzero real number a, its reciprocal is defined as 1/a, crucial in division operations.
Factor: The process of expressing a number or expression as a product of its components.
Power: Refers to an expression where a number, called the base, is multiplied by itself a specified number of times.
Polynomial: A mathematical expression that is the sum of one or more monomials.
Binomial: A specific type of polynomial that contains exactly two terms.
Prime Polynomial: A polynomial that cannot be factored further, having a greatest monomial factor of 1.
Integers: Include all whole numbers and their negative counterparts, forming a complete set of opposites.
Quadratic: A polynomial of degree two, characterized by its highest exponent, providing a rich field for solutions.
Ordered Pair: Two elements represented in a specific order, e.g., (x, y), essential for graphing coordinates.
Coordinate System: A framework comprising two intersecting number lines (axes) used for graphing ordered pairs.
Solution: An ordered pair that makes an equation true, representing a point of intersection in graphing.
Graph: A visual representation of all points that satisfy a particular equation, illustrating relationships between variables.
Slope: Reflects the steepness of a line, calculated as the ratio of the difference in y-coordinates to the difference in x-coordinates, also termed rise over run.
Y-Intercept: The specific point where a graph crosses the y-axis, defined by its y-coordinate when x=0.
Slope-Intercept Form: The standard form of a linear equation written as y = mx + b, where m signifies slope and b signifies the y-intercept.
System of Equations: A collection of two or more equations that share common variables, often solved simultaneously.
Function: A relation characterized by unique first elements (inputs) for each ordered pair, ensuring no repetition.
Direct Variation: A relationship defined by y = kx, where k is a nonzero constant, signifying proportionality between x and y.
Inverse Variation: Represented by y = k/x, where k is a nonzero constant, indicating an inverse relationship between x and y.
Radical: An expression involving roots, typically seen in square root forms, essential in simplifying equations.
Quadratic Formula: A solution method for quadratic equations, given by x = -b±√(b²-4ac)/(2a), applicable when a is not zero.
Parabola: The graphical representation of a quadratic function, displaying a distinct U-shape on the coordinate plane.

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Enhance your understanding of key algebra vocabulary with these flashcards. Each card defines essential terms such as variable, equation, and distributive. Perfect for students looking to solidify their math language skills.