Questions and Answers
What is Algebra?
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?
Signup and view all the answers
What is an Exponent?
Signup and view all the answers
What are Factors?
Signup and view all the answers
What does Factoring mean?
Signup and view all the answers
What is the Greatest Common Factor (GCF)?
Signup and view all the answers
What is a Reciprocal?
Signup and view all the answers
What is Absolute Value?
Signup and view all the answers
Define Composite Numbers.
Signup and view all the answers
What is the Least Common Multiple (LCM)?
Signup and view all the answers
What are Square Roots?
Signup and view all the answers
What is a Binomial?
Signup and view all the answers
What are Counting Numbers?
Signup and view all the answers
Define Integers.
Signup and view all the answers
What are Irrational Numbers?
Signup and view all the answers
What are Natural Numbers?
Signup and view all the answers
What is Perimeter?
Signup and view all the answers
What is a Polynomial?
Signup and view all the answers
Define Rational Numbers.
Signup and view all the answers
What are Real Numbers?
Signup and view all the answers
What is a Trinomial?
Signup and view all the answers
What are Whole Numbers?
Signup and view all the answers
What does the Distributive Property state?
Signup and view all the answers
What is Analytic Geometry?
Signup and view all the answers
Define Cartesian Coordinate System.
Signup and view all the answers
What is a Line in mathematics?
Signup and view all the answers
What is Magnitude in a mathematical context?
Signup and view all the answers
What is the Origin in a Cartesian plane?
Signup and view all the answers
What does the Pythagorean Theorem describe?
Signup and view all the answers
What is a Quadrant in the coordinate plane?
Signup and view all the answers
What is a Resultant Vector?
Signup and view all the answers
What is a Vector?
Signup and view all the answers
What is the X-axis?
Signup and view all the answers
What is the Y-axis?
Signup and view all the answers
What is the X-intercept?
Signup and view all the answers
What is the Y-intercept?
Signup and view all the answers
What is Slope?
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
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.