Algebra 1 EOC Review Flashcards

Questions and Answers

What is a relation?

Set of ordered pairs

What are the coordinates of a point on the coordinate plane?

(x,y)

What is a coordinate plane?

A plane formed by 2 perpendicular lines called axes

What is a function?

A special relation where each x-value is paired with only one y-value. Signup and view all the answers

What does a Mapping Diagram represent?

Bubbles that represent the x-values and the y-values. Signup and view all the answers

What is a Table in mathematics?

A way to represent ordered pairs. Signup and view all the answers

What is the domain in a function?

Set of all of the possible x-values. Signup and view all the answers

What is the range in a function?

Set of all the possible y-values. Signup and view all the answers

What is a variable?

Not a number; a letter or symbol that stands for a number. Signup and view all the answers

What is an independent variable?

The input or cause in a situation or problem. Signup and view all the answers

What is a dependent variable?

The output or result in a situation or problem. Signup and view all the answers

What is the vertical line test?

A relation is a function if a vertical line drawn through the graph touches the graph only once. Signup and view all the answers

What does the slope represent?

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

In the equation y = mx + b, 'm' stands for __________.

slope Signup and view all the answers

In the equation y = mx + b, 'b' stands for __________.

the y-intercept Signup and view all the answers

How do you combine like terms?

Add their coefficients. Signup and view all the answers

What is the difference between a whole number and an integer?

Whole numbers start at 0 while integers include all positive and negative numbers. Signup and view all the answers

The slopes of parallel lines are different.

False Signup and view all the answers

What is the solution of a system of equations?

Where the lines touch or cross. Signup and view all the answers

What do you call a data point that does not fit in with the rest of the data?

Outlier Signup and view all the answers

What is the maximum or minimum in a box and whisker plot?

The largest and smallest numbers shown. Signup and view all the answers

What is the geometric sequence?

A pattern in which you multiply or divide by a common number. Signup and view all the answers

What is the arithmetic sequence?

A pattern in which you add a number each time. Signup and view all the answers

When multiplying fractions, you should __________.

Cancel or reduce if possible, then multiply straight across. Signup and view all the answers

How do you convert an improper fraction to a mixed number?

Determine how many times the denominator goes into the numerator, then note the remainder. Signup and view all the answers

Study Notes

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.

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Description

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!