Algebric Expressions And Equations Study Cards

Enhance Your Learning with Algebraic Expressions and Equations Flash Cards for quick learning



Variable

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

Coefficient

A number multiplied by a variable in an algebraic expression.

Like Terms

Terms in an algebraic expression that have the same variables raised to the same powers.

Simplifying Expressions

Combining like terms and performing operations to make an expression simpler.

Evaluating Expressions

Replacing variables with given values and calculating the result of an expression.

Solving Equations

Finding the value(s) of the variable that make an equation true.

Linear Equation

An equation that represents a straight line when graphed.

Quadratic Equation

An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Systems of Equations

A set of equations with the same variables that are solved simultaneously.

Inequality

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

Word Problem

A mathematical problem presented in the form of a real-life situation.

Polynomial

An algebraic expression with one or more terms, each consisting of a variable raised to a non-negative integer exponent.

Factoring

Rewriting an expression as a product of its factors.

Rational Expression

An algebraic expression that represents a ratio of two polynomials.

Exponent

A number that represents the repeated multiplication of a base.

Radical

The symbol √ used to represent the square root or other roots of a number.

Absolute Value

The distance of a number from zero on a number line, always positive.

Domain

The set of all possible input values of a function or relation.

Range

The set of all possible output values of a function or relation.

Function

A relation in which each input value is associated with exactly one output value.

Inverse Function

A function that undoes the effect of another function.

Vertical Line Test

A test used to determine if a relation is a function by checking if any vertical line intersects the graph more than once.

Horizontal Line Test

A test used to determine if a function is one-to-one by checking if any horizontal line intersects the graph more than once.

Arithmetic Sequence

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric Sequence

A sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Arithmetic Mean

The average of a set of numbers, calculated by dividing the sum of the numbers by the count of numbers.

Geometric Mean

The positive square root of the product of two numbers.

Function Notation

A way to represent a function using symbols and parentheses.

Composite Function

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

Piecewise Function

A function that is defined by different expressions or rules for different intervals or subdomains of its domain.

Quadratic Formula

A formula used to find the solutions of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / (2a)

Discriminant

The expression b^2 - 4ac in the quadratic formula, used to determine the nature of the solutions of a quadratic equation.

Completing the Square

A method used to solve quadratic equations by adding a constant term to make a perfect square trinomial.

Vertex

The highest or lowest point on the graph of a quadratic function, also known as the maximum or minimum point.

Axis of Symmetry

A vertical line that divides the graph of a quadratic function into two symmetric parts.

Standard Form

The form of a quadratic equation written as ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Linear System

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

Solution

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

Consistent System

A system of equations that has at least one solution.

Inconsistent System

A system of equations that has no solution.

Dependent System

A system of equations that has infinitely many solutions.

Independent System

A system of equations that has exactly one solution.

Compound Inequality

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

Interval Notation

A way to represent an interval using brackets and parentheses.

Absolute Value Inequality

An inequality that involves the absolute value of a variable.

Extraneous Solution

A solution that does not satisfy the original equation or inequality.

Direct Variation

A relationship between two variables in which their ratio is constant.

Inverse Variation

A relationship between two variables in which their product is constant.

Joint Variation

A relationship between three or more variables in which their product is constant.

Arithmetic Word Problem

A word problem that involves arithmetic operations such as addition, subtraction, multiplication, or division.

Geometric Word Problem

A word problem that involves geometric concepts such as area, perimeter, volume, or ratios.

Polynomial Word Problem

A word problem that involves polynomial expressions or equations.

Rational Word Problem

A word problem that involves rational expressions or equations.

Exponential Word Problem

A word problem that involves exponential growth or decay.

Radical Word Problem

A word problem that involves radical expressions or equations.

Quadratic Word Problem

A word problem that involves quadratic equations or functions.

Function Word Problem

A word problem that involves functions and their properties.