Algebra Vocabulary Flashcards

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Questions and Answers

What is a rational number?

Any real number

A number that can be written as a ratio (correct)

A number that cannot be written as a ratio

A type of whole number

What is an irrational number?

Any real number that cannot be expressed as a ratio of integers.

Define integers.

Whole numbers that include all the positives and negatives.

What is a whole number?

Integers with no negatives. Signup and view all the answers

What are natural numbers?

Positive integers including zero. Signup and view all the answers

What is an algebraic expression?

An expression built from integer constants, variables, and algebraic operations. Signup and view all the answers

What is a variable?

A symbol used to represent a constant or a change. Signup and view all the answers

What is a coefficient?

A numerical quantity placed before and multiplying the variable in an algebraic expression. Signup and view all the answers

What is an equation?

A statement that the values of two mathematical expressions are equal. Signup and view all the answers

Give an example of a solution to an equation with one variable.

3x - 4 = 5. Signup and view all the answers

What are like terms?

Terms that have the same variable and power. Signup and view all the answers

What is a literal equation?

The process for solving a given variable in a formula. Signup and view all the answers

What is a proportion?

Two ratios or fractions that are equal to each other. Signup and view all the answers

What is an inequality?

The relation between two expressions that are not equal. Signup and view all the answers

What does 'at least' mean?

Greater than or equal to. Signup and view all the answers

What does 'at most' mean?

Less than or equal to. Signup and view all the answers

What is a compound inequality?

Two inequality statements joined by 'or' or 'and'. Signup and view all the answers

Define relation in mathematical terms.

A collection of ordered pairs containing one object from each of two sets. Signup and view all the answers

What is a function?

A relation from a set of inputs to a set of possible outputs where each input has exactly one output. Signup and view all the answers

Define domain.

The X-axis in a graph. Signup and view all the answers

Define range.

The Y-axis in a graph. Signup and view all the answers

What is an independent variable?

The input of a function. Signup and view all the answers

What is a dependent variable?

The output of a function. Signup and view all the answers

Provide an example of a linear function.

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

What is the standard form of a linear equation?

ax + by = c. Signup and view all the answers

Define slope.

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

What is the slope formula?

(y1 - y2) / (x1 - x2). Signup and view all the answers

What is the x-intercept?

(x,0) when the line crosses the x-axis. Signup and view all the answers

What is the y-intercept?

(0,y) when the line crosses the y-axis. Signup and view all the answers

What is slope-intercept form?

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

What is point-slope form?

(y - y1) = m(x - x1). Signup and view all the answers

What is an absolute value function?

A function whose rule contains absolute-value expressions. Signup and view all the answers

Define scatter plot.

A graph with points plotted to show a possible relationship between two sets of data. Signup and view all the answers

What is a solution of a system of linear equations?

Any ordered pair that satisfies all the equations in a system. Signup and view all the answers

Provide an example of a system with one solution.

x = 7. Signup and view all the answers

What is a system with no solutions?

1 = 4. Signup and view all the answers

What is a system with many solutions?

5 = 5. Signup and view all the answers

What is an exponential function?

f(x) = ab^2. Signup and view all the answers

What is an exponent?

A number that indicates how many times the base in a power is used as a factor. Signup and view all the answers

Define monomial.

A number or a product of numbers and variables with whole number exponents. Signup and view all the answers

What is a binomial?

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

What is a trinomial?

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

Define polynomial.

A monomial or the sum of monomials. Signup and view all the answers

The rules of exponents govern the manipulation of _____ in expressions.

powers. Signup and view all the answers

What does multiplying powers entail?

x^2 + x^2 = x^4. Signup and view all the answers

What is the power of power rule?

[x^3]² = x^6. Signup and view all the answers

What is the power of product rule?

(2ab)² = 4a²b². Signup and view all the answers

What is a negative exponent?

Every variable or number raised to a negative power. Signup and view all the answers

Study Notes

Number Types

Rational Number: Can be expressed as a ratio of integers.
Irrational Number: Cannot be expressed as a ratio of integers.
Integers: Whole numbers including negatives.
Whole Numbers: Integers without negatives.
Natural Numbers: Positive integers including zero.

Algebra Fundamentals

Algebraic Expression: Combines integers, variables, and algebraic operations.
Variable: Represents a constant or changing value, typically denoted as X or Y.
Coefficient: A number multiplied by a variable in an expression.
Equation: States that two mathematical expressions are equal.

Solving Equations

Example of solution: For the equation (3x - 4 = 5), the objective is finding x.
Like Terms: Terms sharing the same variable and exponent.
Literal Equation: A formula where a specific variable is solved.

Ratios and Inequalities

Proportion: Two ratios are equal, e.g., (1/2 = 5/10).
Inequality: A relation indicating one expression is not equal to another (e.g., >, <).
Compound Inequality: Combines two inequalities using "and" or "or."

Functions and Relations

Relation: Set of ordered pairs from two different sets.
Function: A relation mapping each input to exactly one output.
Domain: Set of input values (X-axis).
Range: Set of output values (Y-axis).
Independent Variable: Input of a function.
Dependent Variable: Output of a function.

Linear Equations & Functions

Linear Equation (2 Variables): Example form (2x - 3y = 8).
Linear Function: Standard form (y = mx + b), where m is the slope.
Standard Form: Written as (ax + by = c).

Graph Characteristics

Slope: Indicates the steepness of a line.
Slope Formula: Calculated as ((y1 - y2) / (x1 - x2)).
X-intercept: Point where the line crosses the x-axis ((x, 0)).
Y-intercept: Point where the line crosses the y-axis ((0, y)).

Special Forms and Systems

Slope-Intercept Form: (y = mx + b).
Point-Slope Form: ((y - y1) = m(x - x1)).
Absolute Value Function: Involves expressions containing absolute values.
Scatter Plot: Graph shows potential relationships between two data sets.

Systems of Equations

Solution of a System: Any ordered pair that satisfies all equations in the system.
Types of Systems:
- One Solution: Exact value solution (e.g., (x = 7)).
- No Solutions: Contradictory statements (e.g., (1 = 4)).
- Many Solutions: Identities (e.g., (5 = 5)).

Exponential Functions

Exponential Function: Defined by (f(x) = ab^x).
Exponent: Indicates how many times the base is multiplied by itself.

Polynomials

Monomial: A single term consisting of numbers and variables with whole number exponents.
Binomial: A polynomial with two terms.
Trinomial: A polynomial with three terms.
Polynomial Definition: Composed of one or more terms.

Exponent Rules

Multiply Powers: Applies when multiplying like bases, e.g., (x^2 \cdot x^2 = x^4).
Power of Power: ((x^3)^2 = x^6).
Power of Product: ((2ab)^2 = 4a^2b^2).
Negative Exponent: Represents reciprocal, e.g., (2^{-1} = \frac{1}{2}).

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Test your understanding of key algebra vocabulary terms with these flashcards. Each card features an important definition that is fundamental to mastering algebra concepts. Perfect for students looking to enhance their math skills!