Algebraic Expressions Study Cards

Enhance Your Learning with Algebraic Expressions Flash Cards for quick learning



Variable

A symbol, usually a letter, that represents an unknown quantity or a value that can change.

Constant

A value that does not change and has a fixed numerical value.

Coefficient

The numerical factor of a term that contains a variable.

Term

A single number, variable, or the product of numbers and variables.

Like Terms

Terms that have the same variables raised to the same powers.

Combining Like Terms

The process of simplifying an expression by adding or subtracting like terms.

Distributive Property

The property that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Simplifying Expressions

The process of reducing an expression to its simplest form by combining like terms and using the distributive property.

Evaluating Expressions

The process of finding the value of an expression by substituting a given value for each variable and simplifying.

Solving Equations

The process of finding the value(s) of the variable(s) that make an equation true.

Linear Equation

An equation that can be written in the form ax + b = 0, where a and b are constants and a is not equal to 0.

Quadratic Equation

An equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0.

Factoring Expressions

The process of writing an expression as a product of its factors.

Greatest Common Factor (GCF)

The largest factor that two or more numbers or expressions have in common.

Expanding Expressions

The process of multiplying out the terms in an expression to simplify it.

Word Problems

Mathematical problems that are presented as written descriptions or scenarios and require the use of algebraic expressions and equations to solve.

Graphing Linear Equations

The process of representing linear equations on a coordinate plane using points and lines.

X-Intercept

The x-coordinate of the point where a graph intersects the x-axis.

Y-Intercept

The y-coordinate of the point where a graph intersects the y-axis.

Slope

The ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.

Slope-Intercept Form

The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

The equation of a line in the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Standard Form

The equation of a line in the form Ax + By = C, where A, B, and C are constants and A and B are not both zero.

Parallel Lines

Lines in the same plane that never intersect and have the same slope.

Perpendicular Lines

Lines that intersect at a right angle and have slopes that are negative reciprocals of each other.

System of Equations

A set of two or more equations with the same variables.

Solution

A value or set of values that make an equation or system of equations true.

Inequality

A mathematical sentence that compares two expressions using the symbols <, >, ≤, or ≥.

Compound Inequality

Two or more inequalities joined together by the word 'and' or 'or'.

Absolute Value

The distance between a number and zero on a number line. It is always positive or zero.

Absolute Value Inequality

An inequality that contains an absolute value expression.

Exponent

A number that represents the number of times a base is multiplied by itself.

Base

The number that is multiplied repeatedly in an exponential expression.

Power

The result of raising a base to an exponent.

Product of Powers

When multiplying two powers with the same base, add the exponents.

Quotient of Powers

When dividing two powers with the same base, subtract the exponents.

Power of a Power

When raising a power to another power, multiply the exponents.

Zero Exponent

Any nonzero number raised to the power of zero is equal to 1.

Negative Exponent

A negative exponent indicates the reciprocal of the base raised to the positive exponent.

Scientific Notation

A way of expressing numbers that are very large or very small using powers of 10.

Radical

The symbol √ used to indicate a square root or other root of a number.

Radicand

The number or expression inside a radical symbol.

Index

The number that indicates the root to be taken.

Rational Exponent

An exponent that is a fraction or a decimal.

Rationalizing the Denominator

The process of eliminating radicals from the denominator of a fraction.

Complex Number

A number that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Real Number

Any number that can be found on the number line, including rational and irrational numbers.

Irrational Number

A number that cannot be expressed as a fraction or a decimal that terminates or repeats.

Domain

The set of all possible input values (x-values) of a function.

Range

The set of all possible output values (y-values) of a function.

Function

A relation in which each input value (x-value) is paired with exactly one output value (y-value).

Vertical Line Test

A test used to determine if a graph represents a function. If any vertical line intersects the graph in more than one point, the graph does not represent a function.

Horizontal Line Test

A test used to determine if a function is one-to-one. If any horizontal line intersects the graph in more than one point, the function is not one-to-one.

Inverse Function

A function that undoes the action of another function. The inverse function of f is denoted as f^(-1).

Composite Function

A function that is formed by combining two functions, where the output of one function becomes the input of the other function.

Piecewise Function

A function that is defined by different rules or formulas for different parts of its domain.

Arithmetic Sequence

A sequence in which the difference between any two consecutive terms is constant.

Geometric Sequence

A sequence in which each term after the first is found by multiplying the previous term by a constant called the common ratio.

Arithmetic Series

The sum of the terms in an arithmetic sequence.

Geometric Series

The sum of the terms in a geometric sequence.

Binomial

An algebraic expression with two unlike terms.

Trinomial

An algebraic expression with three unlike terms.

Polynomial

An algebraic expression with one or more terms.

Degree of a Polynomial

The highest exponent of the variable in a polynomial.

Monomial

A polynomial with only one term.

Binomial Theorem

A formula for expanding a binomial raised to a positive integer power.