CPM Algebra Chapter 3 Flashcards

Questions and Answers

What is an algebra tile?

A law of exponents

A tool that helps visualize area (correct)

A method of solving equations

A type of polynomial

What is a binomial?

An expression that is the sum or difference of exactly two terms, each of which is a monomial.

What does the Distributive Property state?

For any numbers or expressions a, b, and c, a(b + c) = ab + ac.

What are 'legal' moves in the context of algebra tiles?

Moves that keep the relationship between the two sides of the equation mat intact. Signup and view all the answers

What is an exponent?

A number that indicates how many times to use the base as a multiplier. Signup and view all the answers

What are integers?

{...−3, −2, −1, 0, 1, 2, 3,...} Signup and view all the answers

What is a polynomial?

An expression that is the sum or difference of two or more monomials. Signup and view all the answers

What does it mean to solve an equation?

To find all the solutions to an equation or an inequality. Signup and view all the answers

What is a term in an expression?

A single number, variable, or the product of numbers and variables. Signup and view all the answers

What is the area in this course?

The number of square units needed to fill up a region on a flat surface. Signup and view all the answers

What does it mean for a set of numbers to be closed under an operation?

The result of applying the operation to any two numbers in the set produces a number in the set. Signup and view all the answers

What is an expression?

A combination of individual terms separated by plus or minus signs. Signup and view all the answers

What is a product?

The result of multiplying. Signup and view all the answers

What is the standard form for a linear equation?

ax + by = c, where a, b, and c are real numbers and a and b are not both zero. Signup and view all the answers

Study Notes

Algebra Tiles

Algebra tiles are manipulatives representing constant or variable quantities through area.
Tiles include large squares (x², y²), rectangles (x-by-1, y-by-1, x-by-y), and unit tiles (1-by-1).
Positive quantities are represented by shaded tiles, while unshaded tiles indicate negative quantities.

Binomial

Defined as an expression consisting of the sum or difference of exactly two terms.
Example: −2x + 3y² qualifies as a binomial.

Distributive Property

Allows expression products to be expressed as sums of terms.
Formula: a(b + c) = ab + ac. Example: 2(x + 4) becomes 2x + 8 using this property.
Can be demonstrated using algebra tiles or a generic rectangle.

Legal Moves

"Legal" moves maintain the equality of expressions on both sides of an equation mat.
Examples include removing identical tiles from both sides to preserve equality.

Exponent

In expressions of the form b^a, 'a' is called the exponent specifying how many times the base (b) is multiplied by itself.
Exponential rules: x^0 = 1 for any non-zero x; negative exponents indicate reciprocals, e.g., x^(-n) = 1/x^n.

Integers

Defined as the set {...−3, −2, −1, 0, 1, 2, 3,...}, encompassing positive and negative whole numbers and zero.

Polynomial

An expression formed by the sum or difference of two or more monomials.
Example: x⁸ - 4x⁶y + 6x⁴y² is classified as a polynomial.

Solve

Refers to finding all solutions to equations or inequalities.
Example: Solving x² = 9 results in solutions x = 3 and x = −3.
An equation can be manipulated to express a variable in terms of others, e.g., from 2y − 8x = 16 to y = 4x + 8.

Term

A term may be a single number, variable, or products of numbers and variables.
Terms in the expression 1.2x - 45 + 3xy² are 1.2x, -45, and 3xy².

Area

In math, area measures the number of square units needed to fill a flat region.
The concept of area extends to more complex surfaces in advanced study.

Closed Sets

A numerical set is closed under an operation if applying the operation to any two numbers within the set results in a number still within the set.
Example: Whole numbers are closed under addition but not under division.

Expression

An expression consists of individual terms combined by plus or minus signs, lacking an "equals" component.
Numerical expressions involve only numbers, while algebraic expressions incorporate variables (e.g., y - 3/4 + x).

Product

The outcome of multiplying two or more values.
Example: The product of 4 and 5 equals 20; multiplying 3a and 8b² yields 24ab².

Standard Form

The standard form for a linear equation is expressed as ax + by = c, where a, b, and c are real numbers, and not both a and b can be zero.
Example: 2.5x − 3y = 12 is in standard form.

Description

This quiz features flashcards based on Chapter 3 of CPM Algebra. It focuses on algebra tiles, their definitions, and applications within algebraic concepts. Ideal for reinforcing understanding of algebraic manipulative tools and their representations.