Algebra 1 EOC Review Flashcards

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Questions and Answers

What is a relation?

Single point on a graph

Graph of a function

Set of x-values

Set of ordered pairs (correct)

What are the coordinates of an ordered pair?

(x, y)

What is the coordinate plane?

A plane formed by 2 perpendicular lines called axes.

What defines a function?

Every x-value is paired with only one y-value Signup and view all the answers

What does the domain of a function represent?

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

What does the range of a function represent?

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

What is an independent variable?

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

What is a dependent variable?

The output or result in a situation. 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

What happens to the slope when 'm' changes in slope-intercept form?

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

What slope does a horizontal line have?

0 Signup and view all the answers

What slope does a vertical line have?

undefined Signup and view all the answers

What is the point where the graph crosses the x-axis called?

x-intercept Signup and view all the answers

What is the point where the graph crosses the y-axis called?

y-intercept Signup and view all the answers

What is a linear inequality?

An inequality representing a linear relationship. Signup and view all the answers

How do the slopes of parallel lines compare?

They are the same. Signup and view all the answers

How do the slopes of perpendicular lines compare?

They are opposite and the fractions are flipped. 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 can a system with 2 equations have?

No solutions, one solution, or infinitely many solutions. Signup and view all the answers

How do you multiply exponents of like variables?

Add them. Signup and view all the answers

How do you divide exponents of like variables?

Subtract them. Signup and view all the answers

What does the term 'rate of change' refer to?

Slope. Signup and view all the answers

What is the formula for compound interest?

A = (P + r/n)^(nt) Signup and view all the answers

How do you solve proportions?

Cross multiply. Signup and view all the answers

What is the quadratic formula for solving quadratics?

x = (-b ± sqrt(b^2 - 4ac)) / 2a Signup and view all the answers

What represents the standard form of a line?

Ax + By = C Signup and view all the answers

What are perfect squares?

1, 4, 9, 16, 25, etc. Signup and view all the answers

Study Notes

Algebra Concepts and Definitions

Relation: Set of ordered pairs.
Ordered pair: Represents coordinates on a coordinate plane, written as (x, y).
Coordinate plane: Formed by two perpendicular axes; x-axis runs horizontally and y-axis vertically.
Function: A specific type of relation where each x-value has one unique y-value, passing the vertical line test.
Mapping: Visual representation of x-values and their corresponding y-values.
Table: A method to illustrate ordered pairs clearly.

Domain and Range

Domain: The complete set of all possible x-values (inputs).
Range: The complete set of all possible y-values (outputs).

Variables

Variable: A letter/symbol that represents a numerical value (not a number itself).
Independent variable: The controlled input variable (x).
Dependent variable: The output variable that is influenced by the independent variable (y).

Functions and Their Characteristics

Vertical line test: Determines if a relation is a function; if a vertical line touches the graph only once, it is a function.
Discrete function: Graph displayed as individual points without connection.
Continuous function: Graph depicted as a smooth curve.

Linear Functions

Standard form: y = mx + b; where m = slope and b = y-intercept.
Slope: Measures the steepness; calculated as rise over run (change in y/change in x).
x-intercept: The point where the graph crosses the x-axis (x, 0).
y-intercept: The point where the graph crosses the y-axis (0, y).

System of Equations

System of equations: Consists of two or more equations/inequalities graphed on the same coordinate plane.
Solution of a system: The point where the lines intersect or cross.
Types of solutions: Can be no solution (parallel lines), one solution (intersection at one point), or infinitely many solutions (identical lines).

Quadratic Functions

Quadratic equation: Involves 'x-squared' as the highest exponent.
Solutions of a quadratic function: Found at x-intercepts, also known as roots or zeros.

Operations with Exponents

Multiplying exponents: Add exponents for like bases.
Dividing exponents: Subtract exponents for like bases.
Zero exponent: Any non-zero number raised to the power of zero equals one.

Solving Inequalities

Linear inequality: Involves inequalities (>, <, ≥, ≤) in place of an equal sign.
Graphing inequalities: determines whether to use a solid/dotted line (closed/open) based on the inequality's inclusiveness.

Special Formulas

Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a) for solving quadratic equations.
Compound interest formula: A = P(1 + r/n)^(nt), accounting for the compounding period.
Simple interest formula: I = PRT (interest = principal × rate × time).

Functions and Graphs

Function notation: f(x) indicates the function, interchangeable with y.
Increasing/Decreasing functions: Read graphs left to right to determine trends; upward indicates increasing, downward indicates decreasing.
Axis of symmetry: For parabolas, represented by the line x = -b/(2a) in standard form.

Sequences and Patterns

Arithmetic sequence: Sequence where each term increases by adding a constant.
Geometric sequence: Sequence where each term increases by multiplying/dividing by a constant.

Correlation and Causation

Correlation: Describes patterns among variables, range between -1 and 1 indicating strength/direction.
Causation: Indicates one event causes another; not to be confused with correlation.

General Concepts

Rate of change: Often synonymous with slope, representing how one variable changes in relation to another.
Perfect squares: Result from multiplying integers by themselves (e.g., 1, 4, 9, 16...).
Distinguishing functions: Linear functions increase at constant rates, while exponential functions increase at variable rates.

Important Terms

Absolute value: The distance a number is from zero on the number line, disregard sign.
Discriminant: In the quadratic formula, determines the nature of the roots: positive (two real solutions), zero (one real solution), negative (no real solution).

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Description

Prepare for your Algebra 1 End-of-Course (EOC) exam with these flashcards. Each card covers essential terms and concepts such as relations, ordered pairs, and functions. Perfect for quick reviews and mastering key algebraic ideas.