Algebra 1 EOC Review Flashcards

Algebraic Concepts and Definitions

• Relation: A set of ordered pairs.
• Ordered Pair: Represents coordinates of a point in the coordinate plane, denoted as (x, y).
• Coordinate Plane: Formed by two perpendicular lines called axes; x-axis (horizontal) and y-axis (vertical).
• Function: A specific relation where each x-value is linked to only one y-value; it must pass the vertical line test.
• Mapping Diagram: Visual representation where bubbles represent corresponding x-values and y-values.

Key Components

• Domain: The set of all possible x-values (inputs) in a function.
• Range: The set of all possible y-values (outputs) in a function.
• Variable: A letter or symbol representing a number; not a fixed number.
• Independent Variable: The input in a function, often represented as x; controlled by the user.
• Dependent Variable: The output in a function, represented as y; cannot be controlled by the user.
• Other Names: x can be referred to as domain, independent variable, or input; y can be known as range, dependent variable, or output.

Functions and Tests

• Vertical Line Test: A graphical method for determining if a relation is a function; a vertical line must intersect the graph at most once.
• Discrete Function: Data represented by individual points on a graph; cannot be broken down further.
• Examples of Functions: Linear functions, quadratic functions, and inverse functions.

Slope and Intercepts

• Slope (m): Indicates the steepness of a line; calculated as the change in y (rise) divided by the change in x (run).
• Y-intercept (b): The point where a line crosses the y-axis, represented as (0, y).
• Slope of Horizontal Line: Always equal to 0.
• Slope of Vertical Line: Undefined.

Equations and Inequalities

• Slope-Intercept Form: Represents a line as y = mx + b.
• Linear Inequality: Similar to linear equations but includes symbols like <, > for inequalities.
• System of Equations: Two or more equations graphed on the same plane; can have no solution, one solution, or infinitely many solutions.

Special Terms and Properties

• Factoring: Breaking down expressions into simpler factors.
• Like Terms: Terms in an expression that have the same variables raised to the same exponents.
• Combining Like Terms: Involves adding their coefficients.
• Associative, Distributive, and Commutative Properties: Rules governing operations in math.

Data and Statistics

• Mean (Average): Total of data points divided by the number of points.
• Median: Middle value when data is ordered; average of two middle values if needed.
• Mode: The most frequently occurring number in a data set.
• Range: Difference between the largest and smallest value in a data set.

Fraction and Decimal Operations

• Adding/Subtracting Fractions: Requires a common denominator.
• Multiplying Fractions: Multiply numerators together and denominators together, then simplify if possible.
• Dividing Fractions: Use the "Keep, Change, Flip" method.
• Converting Between Fractions and Decimals: Divide numerator by the denominator or recognize decimal places.

Graphs and Visuals

• Histograms: Bar graph showing frequency distribution across value ranges.
• Box and Whisker Plots: Visual representation showing median, quartiles, and potential outliers.

Miscellaneous Concepts

• Maximum/Minimum: Highest and lowest values in data representation like box plots.
• Percent Conversion: Understanding how to convert between decimal, fraction, and percentage forms.
• Perfect Squares: Results of integers multiplied by themselves. Examples include 1, 4, 9, 16, etc.

Final Notes

• Solving Proportions: Involves cross-multiplication.
• Radicals: Refers to square roots; methods of simplifying need careful attention to detail.
• Standard Form of a Line: Written as Ax + By = C; requires no fractions or decimals with A positive.

Review essential algebra concepts with these flashcards. Each card includes a term related to relations, ordered pairs, the coordinate plane, and functions. Enhance your understanding and prepare effectively for the EOC exam!