Podcast
Questions and Answers
What is a rational number?
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?
What is an irrational number?
Any real number that cannot be expressed as a ratio of integers.
Define integers.
Define integers.
Whole numbers that include all the positives and negatives.
What is a whole number?
What is a whole number?
What are natural numbers?
What are natural numbers?
What is an algebraic expression?
What is an algebraic expression?
What is a variable?
What is a variable?
What is a coefficient?
What is a coefficient?
What is an equation?
What is an equation?
Give an example of a solution to an equation with one variable.
Give an example of a solution to an equation with one variable.
What are like terms?
What are like terms?
What is a literal equation?
What is a literal equation?
What is a proportion?
What is a proportion?
What is an inequality?
What is an inequality?
What does 'at least' mean?
What does 'at least' mean?
What does 'at most' mean?
What does 'at most' mean?
What is a compound inequality?
What is a compound inequality?
Define relation in mathematical terms.
Define relation in mathematical terms.
What is a function?
What is a function?
Define domain.
Define domain.
Define range.
Define range.
What is an independent variable?
What is an independent variable?
What is a dependent variable?
What is a dependent variable?
Provide an example of a linear function.
Provide an example of a linear function.
What is the standard form of a linear equation?
What is the standard form of a linear equation?
Define slope.
Define slope.
What is the slope formula?
What is the slope formula?
What is the x-intercept?
What is the x-intercept?
What is the y-intercept?
What is the y-intercept?
What is slope-intercept form?
What is slope-intercept form?
What is point-slope form?
What is point-slope form?
What is an absolute value function?
What is an absolute value function?
Define scatter plot.
Define scatter plot.
What is a solution of a system of linear equations?
What is a solution of a system of linear equations?
Provide an example of a system with one solution.
Provide an example of a system with one solution.
What is a system with no solutions?
What is a system with no solutions?
What is a system with many solutions?
What is a system with many solutions?
What is an exponential function?
What is an exponential function?
What is an exponent?
What is an exponent?
Define monomial.
Define monomial.
What is a binomial?
What is a binomial?
What is a trinomial?
What is a trinomial?
Define polynomial.
Define polynomial.
The rules of exponents govern the manipulation of _____ in expressions.
The rules of exponents govern the manipulation of _____ in expressions.
What does multiplying powers entail?
What does multiplying powers entail?
What is the power of power rule?
What is the power of power rule?
What is the power of product rule?
What is the power of product rule?
What is a negative exponent?
What is a negative exponent?
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!
