33 terms

ECHS-MrsZTEACHER

Integrated Math Unit 1 - Expressions, Equations, and Inequalities

Algebraic Expression

A mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide)

Algebraic Equation

A mathematical statement that two expressions are equivalent.

Inequality

A statement that compares two expressions by using one of the following symbols: < > ≤ ≥ ≠

Degree of a monomial

Determined by finding the sum of the exponents of its variable factors. 3x⁴y³ is a seventh degree monomial

Degree of a polynomial

The degree of its monomial with the greatest degree. 3x⁴y³ + 2x⁸ - 7x³y⁶ is a polynomial of the ninth degree.

Standard Form

A one-variable polynomial in which all like terms have been combined and its terms are in descending order by degree.

Constant

A monomial with a degree of zero. Example 6x⁰. A non-changing numerical value. In the linear equation y = 5x + 2 the 2 is called the ____________.

Linear

A relation that is directly proportional such the one variable either grows or decreases proportionally with the other; having a constant rate of change; a first degree equation whose graph is a line

Non-linear

A relation that is not linear. The equation is not a first degree equation. The relation's graph is not a line.

Exponent

The number that indicates how many times the base in a power is used as a factor.

Factor

A number or quantity that when multiplied with another produces a given number or expression. Given 7x³y⁶ it has many ___________ including 7, x, and y.

Coefficient

A constant by which a variable is multiplied. Given 7x³y⁶ then 7 is the ____________.

Constant

A polynomial with a degree of 0. Ex. 4

Linear

A polynomial with a degree of 1. Ex. 2x + 3

Quadratic

A polynomial with a degree of 2. Ex. 4x² + 3

Cubic

A polynomial with a degree of 3. Ex. 2x³ + 5

Quartic

A polynomial with a degree of 4. Ex. 2x⁴ + 3

Quintic

A polynomial with a degree of 5. Ex. 2x⁵ + 3x

Term

either a single number or a variable, or numbers and variables multiplied together

Monomial

An algebraic expression which has one term. Ex. 3x

Binomial

An algebraic expression which has two terms. Ex. 3x + 2

Trinomial

An algebraic expression which has three terms. Ex 3x² + 2x + 1

Polynomial

An algebraic expression which is a monomial or a sum of monomials. It is sometimes referred to as a multinomial.

Leading coefficient

The coefficient of the term with the highest degree. In 5x⁴ + 3x²

the five would be the ____________________ ___________.

the five would be the ____________________ ___________.

Literal Equation

An equation where variables represent known and unknown values. It allows us to represent things like distance, time, interest, and slope as variables in an equation. In simplest terms a fancy name for a formula.

Order of Operations

A rule used to clarify which procedures should be performed first in a given mathematical expression in order to simplify PEMDAS

Comparison

To examine two quantities mathematically in order to find the value of their RATIO or to determine which of them is greater, smaller or if they are equal.

Standard N.Q.1

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

Standard N.Q.2

Define appropriate quantities for the purpose of descriptive modeling.

Standard N.Q.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Standard A.SSE.1

Interpret expressions that represent a quantity in terms of its context. a) Interpret parts of an expression, such as terms, factors, and coefficients.

Standard A.REI.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Standard A.CED.4

Rearrange formulas to highlight a quantity of interest, using the same reason as in solving equations. For example, rearrange Ohm's law v = IR to highlight resistance R.