Algebra 2 Honors Vocabulary Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What are real numbers?

The set consisting of all rational and irrational numbers.

What are opposites in terms of numbers?

Numbers that are the same distance away from zero but on opposite sides of it.

What is the absolute value of a number?

The distance between the graph of a number and zero.

What is an algebraic expression?

A numerical expression; a variable; or a sum, difference, product, or quotient that contains one or more variables. Signup and view all the answers

What does the commutative property state?

Order doesn't matter with addition or multiplication. Signup and view all the answers

What does the associative property state?

Grouping doesn't matter with addition and multiplication. Signup and view all the answers

What is the distributive property?

Multiplication is distributive over addition. Signup and view all the answers

What is a conjunction?

A sentence formed by joining two sentences with the word ‘and’. Signup and view all the answers

What is a disjunction?

A sentence formed by joining two sentences with the word ‘or’. Signup and view all the answers

What is a coordinate?

The ordered pair associated with each point in the xy-coordinate plane. Signup and view all the answers

What is the origin in a coordinate plane?

The point (0,0). Signup and view all the answers

What is a quadrant in a coordinate system?

One of the four regions formed by the intersecting axes in a regular coordinate system. Signup and view all the answers

What is the slope of a line?

The measure of the steepness of the line. Signup and view all the answers

What is standard form?

Ax + By = C. Signup and view all the answers

What is point-slope form?

y - Y = M(x - X). Signup and view all the answers

What is a coefficient?

The numerical factor of a term. Signup and view all the answers

What is slope-intercept form?

y = mx + b. Signup and view all the answers

What is a monomial?

A number, a variable, or the product of a constant and one or more variables. Signup and view all the answers

What is the degree of a polynomial?

The greatest of the degrees of its terms after the polynomial has been simplified. Signup and view all the answers

What is a function?

A relation in which different ordered pairs have different first coordinates. Signup and view all the answers

What is a relation?

Any set of ordered pairs. Signup and view all the answers

What is a prime number?

An integer greater than one whose only positive integral factors are itself and one. Signup and view all the answers

What is prime factorization?

Expressing a positive integer as a product of primes. Signup and view all the answers

What is a rational expression?

An algebraic expression that can be expressed as a quotient of polynomials. Signup and view all the answers

What is an extraneous root?

A root of a transformed equation that is not a root of the original equation. Signup and view all the answers

What are like radicals?

Two radicals with the same index and radicand. Signup and view all the answers

What is a rational number?

A number that can be written as a fraction. Signup and view all the answers

What is an irrational number?

A number that is infinite and non-repeating. Signup and view all the answers

What is a pure imaginary number?

Any number in the form bi. Signup and view all the answers

What is a complex number?

A number in the form a + bi. Signup and view all the answers

What is the quadratic formula?

ax² + bx + c = 0. Signup and view all the answers

What is the discriminant?

b² - 4ac. Signup and view all the answers

What is a parabola?

The graph of the equation in the form y - k = a(x - h)². Signup and view all the answers

What is a vertex?

The point (h, k). Signup and view all the answers

What is a dividend?

A quantity to be divided. Signup and view all the answers

What is a divisor?

The quantity to which another quantity is divided. Signup and view all the answers

What is the division algorithm?

Dividend = Quotient x Divisor + Remainder. Signup and view all the answers

Study Notes

Real Numbers

Include both rational (fractions, integers) and irrational numbers (non-repeating decimals).

Opposites

Defined as numbers equidistant from zero but located on opposite sides of the number line.

Absolute Value

Represents the distance from zero on the number line, always positive.

Algebraic Expression

Combinations of numbers, variables, and operational symbols (sum, difference, product, quotient).

Commutative Property

In both addition and multiplication, order of operations does not affect the result.

Associative Property

For addition and multiplication, how numbers are grouped does not change the outcome.

Distributive Property

Multiplication can be distributed across addition, facilitating simplification of expressions.

Conjunction

A logical statement formed by combining two statements with "and".

Disjunction

A logical statement formed by combining two statements with "or".

Coordinate

An ordered pair (x, y) representing a specific point in the xy-coordinate plane.

Origin

The point of intersection for the x and y axes, denoted as (0,0).

Quadrant

The coordinate plane is divided into four regions by the intersecting axes.

Slope of a Line

Measures how steep a line is, calculated as the ratio of vertical change to horizontal change.

Standard Form

Represents a linear equation in the form Ax + By = C.

Point-Slope Form

Format for linear equations expressed as y - Y = M(x - X), capturing slope and a point on the line.

Coefficient

The numerical factor that multiplies a variable in an algebraic term.

Slope-Intercept Form

Linear equations expressed as y = mx + b, where m is the slope and b is the y-intercept.

Monomial

A single term that can be a constant, variable, or a product of constants and variables.

Degree of a Polynomial

Identifies the highest degree among the terms in a polynomial after simplification.

Function

A relation where each input has a unique output, ensuring no repeated first coordinates.

Relation

A set of ordered pairs that can represent various mathematical relationships.

Prime Number

An integer greater than one with no divisors other than one and itself.

Prime Factorization

The process of breaking down a positive integer into a product of prime numbers.

Rational Expression

An algebraic expression that can be simplified into a quotient of two polynomials.

Extraneous Root

A solution to a modified equation that does not satisfy the original equation.

Like Radicals

Radicals that share the same index and radicand, permitting direct addition or subtraction.

Rational Number

Any number that can be expressed as a fraction or ratio of two integers.

Irrational Number

A number that cannot be expressed as a simple fraction, characterized by infinitely non-repeating decimals.

Pure Imaginary Number

A complex number exclusively of the form bi, where b is a real number.

Complex Number

A number expressed in the form a + bi, combining a real part (a) and an imaginary part (bi).

Quadratic Formula

The solution for quadratic equations in the standard form ax² + bx + c = 0.

Discriminant

Calculated as b² - 4ac, helps determine the nature and number of roots of a quadratic equation.

Parabola

The graph representation of a quadratic equation characterized by the form y - k = a(x - h)².

Vertex

The highest or lowest point of a parabola, identified as the point (h, k).

Dividend

The quantity that is being divided in a division operation.

Divisor

The quantity by which another quantity is divided during the division process.

Division Algorithm

Describes the relationship: Dividend = Quotient × Divisor + Remainder.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of key vocabulary in Algebra 2 Honors. This quiz includes definitions of important terms such as real numbers, opposites, absolute value, and algebraic expressions. Perfect for students looking to reinforce their algebra vocabulary skills.