Math U See Algebra 1 Terms by Lesson

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Questions and Answers

What is Algebra?

An ancient form of counting.

A system only for whole numbers.

A type of geometry.

A system that uses letters to represent unknown numbers and variables. (correct)

What does the Associative Property state?

The way in which numbers are grouped does not change their sum or product.

What is the definition of Base in mathematics?

The number on which a place value system is built; our decimal system is base 10.

What does the Commutative Property state?

The order in which numbers are added or multiplied does not change the sum or product. Signup and view all the answers

What is an Exponent?

Tells how many times a number is multiplied by itself. Signup and view all the answers

What are Factors?

Numbers that are multiplied together to get a product. Signup and view all the answers

What does Factoring mean?

Finding the factors of a given number. Signup and view all the answers

What is the Greatest Common Factor (GCF)?

The largest number that will divide evenly into two or more numbers. Signup and view all the answers

What is a Reciprocal?

The fraction that when multiplied by another fraction equals one. Signup and view all the answers

What is Absolute Value?

How far a number is from zero (always positive). Signup and view all the answers

Define Composite Numbers.

A whole number greater than 1 that has more than two factors. Signup and view all the answers

What is the Least Common Multiple (LCM)?

The smallest multiple that two or more numbers have in common. Signup and view all the answers

What are Square Roots?

The factors of a square; for example, 3 is the square root of 9. Signup and view all the answers

What is a Binomial?

An algebraic expression with two terms. Signup and view all the answers

What are Counting Numbers?

The numbers used to count; the members of the set {1,2,3,4,5,...}. Signup and view all the answers

Define Integers.

The positive and negative counting numbers, plus zero. Signup and view all the answers

What are Irrational Numbers?

Numbers that cannot be expressed as a ratio of two integers. Signup and view all the answers

What are Natural Numbers?

Another name for counting numbers. Signup and view all the answers

What is Perimeter?

The distance around the outside of a two-dimensional figure. Signup and view all the answers

What is a Polynomial?

An algebraic expression with more than one term. Signup and view all the answers

Define Rational Numbers.

All positive and negative integers, fractions, and decimal numbers. Signup and view all the answers

What are Real Numbers?

All rational and irrational numbers; all numbers. Signup and view all the answers

What is a Trinomial?

A polynomial with three terms. Signup and view all the answers

What are Whole Numbers?

Counting numbers and zero. Signup and view all the answers

What does the Distributive Property state?

A common factor is 'distributed' among the terms of an equation. Signup and view all the answers

What is Analytic Geometry?

Algebra shown geometrically on a graph. Signup and view all the answers

Define Cartesian Coordinate System.

The X-Y graphing system named for Rene' Descartes. Signup and view all the answers

What is a Line in mathematics?

An infinite number of connected points. Signup and view all the answers

What is Magnitude in a mathematical context?

Size or force. Signup and view all the answers

What is the Origin in a Cartesian plane?

The point where the X- and Y- axes intersect on a graph. Signup and view all the answers

What does the Pythagorean Theorem describe?

The relationship between the legs and hypotenuse of a right triangle. Signup and view all the answers

What is a Quadrant in the coordinate plane?

One of four sections into which the coordinate plane is divided. Signup and view all the answers

What is a Resultant Vector?

The vector sum of two or more vectors. Signup and view all the answers

What is a Vector?

A unit of measure that includes direction and magnitude. Signup and view all the answers

What is the X-axis?

The horizontal axis on a coordinate plane. Signup and view all the answers

What is the Y-axis?

The vertical axis on a coordinate plane. Signup and view all the answers

What is the X-intercept?

The point where a line crosses the X-axis. Signup and view all the answers

What is the Y-intercept?

The point where a line crosses the Y-axis. Signup and view all the answers

What is Slope?

Rise over run; represented by m. Signup and view all the answers

Study Notes

Algebra Concepts

Algebra represents unknown numbers and variables using letters, operating under base x.
Associative Property dictates that changing the grouping of numbers does not alter their sum or product.
Base refers to the foundational number system, with our decimal system being base 10.
Commutative Property states that the order of addition or multiplication does not affect the result.
Exponents indicate how many times a number is multiplied by itself.
Factors are numbers multiplied together to yield a product.
Factoring involves identifying the factors of a specific number.
Greatest Common Factor (GCF) is the largest number that evenly divides two or more numbers.
Reciprocals are fractions that multiply to yield one, e.g., the reciprocal of N/D is D/N.

Number Types and Properties

Absolute Value describes the distance of a number from zero, expressed as a positive value.
Composite Numbers are whole numbers greater than 1 that possess more than two factors.
Least Common Multiple (LCM) identifies the smallest common multiple of two or more numbers.
Square Roots are numbers that, when multiplied by themselves, yield a square (e.g., 3 is the square root of 9).
Binomials are algebraic expressions containing exactly two terms.
Counting Numbers, also known as natural numbers, start from 1 and progress sequentially (1, 2, 3…).
Integers encompass both positive and negative counting numbers, as well as zero.
Irrational Numbers cannot be expressed as a ratio of integers and have non-ending, non-repeating decimal expansions.
Natural Numbers are equivalent to counting numbers.
Perimeter calculates the total distance around a two-dimensional figure.
Polynomials consist of algebraic expressions with more than one term.
Rational Numbers include all integers, fractions, and decimal values, both positive and negative.
Real Numbers consist of all rational and irrational numbers.

Advanced Algebra Topics

Trinomials are polynomials that contain three terms.
Whole Numbers encompass counting numbers and zero.
Distributive Property allows a common factor to be distributed across terms in an equation, such as a(b + c) = ab + ac.

Geometry and Coordinate Systems

Analytic Geometry integrates algebraic concepts onto geometric graphs.
The Cartesian Coordinate System, named after René Descartes, utilizes X and Y axes for graphing.
A Line is defined as an infinite collection of connected points.
Magnitude refers to the size or strength of a measurement.
The Origin is the intersection point of the X and Y axes, serving as the starting point of a ray.
The Pythagorean Theorem relates the lengths of the legs and hypotenuse in a right triangle.
Quadrants divide the coordinate plane into four sections for graphing.
Resultant Vectors represent the vector sum of multiple vectors.
Vectors are measurements characterized by both direction and magnitude.
The X-axis is the horizontal line in a coordinate plane.
The Y-axis is the vertical line in a coordinate plane.

Intercepts and Slope

The X-intercept is the point where a line intersects the X-axis.
The Y-intercept is the point where a line intersects the Y-axis.
Slope is calculated as the rise over run and is typically represented by the letter m.

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Test your knowledge of key terms from Algebra 1 with these flashcards. Each term is defined clearly and is associated with specific lessons. Perfect for students looking to reinforce their understanding of algebra concepts.