Algebra 1 EOC Comprehensive Everything Most Likely on the Test Review Guide

Slope Formula: The slope ( $m$ ) of a line passing through two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is calculated using the formula: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .
Slope-Intercept Form: The linear equation written in the form $y = mx + b$ , where $m$ represents the slope and $b$ represents the y-intercept (the point where the line crosses the y-axis).
Point-Slope Form: A linear equation that is useful when given a point $(x_{1}, y_{1})$ and the slope $m$ , expressed as: $y - y_{1} = m(x - x_{1})$ .

One-step Equations: Algebraic equations that require only one operation (addition, subtraction, multiplication, or division) to isolate the variable.
Multi-step Equations: Equations that require multiple operations and steps to solve for the variable, including combining like terms and isolating the variable term.
Variables on Both Sides: Equations where the variable term appears on both the left and right sides of the equal sign. To solve, terms containing the variable must be moved to one side using inverse operations.

Flipping the Inequality Sign: An essential rule that requires the inequality sign (<, >, ≤, ≥) to be reversed whenever both sides of the inequality are multiplied or divided by a negative number.

Defining the Solution: In a coordinate plane, the solution to a system of equations is the specific coordinate where the lines intersect or cross.
Elimination Method: A technique for solving systems of equations by adding or subtracting the equations to eliminate one of the variables, making it possible to solve for the remaining variable.
Possible Solutions: * One solution: The lines intersect at exactly one point. * No solution: The lines are parallel and never intersect. * Infinite solutions: The equations represent the same line, overlapping at every point.

Function Notation: Functions are typically represented using the notation $f(x)$ , read as "f of x," which indicates that the output depends on the value of the input variable $x$ .
Vertical Line Test: A graphical method used to determine if a curve is a function. If any vertical line passes through more than one point on the graph, the relation is not a function.

Product Rule: When multiplying two powers with the same base, add their exponents: $a^{m} \times a^{n} = a^{m+n}$ .
Quotient Rule: When dividing two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator: $\frac{a^{m}}{a^{n}} = a^{m-n}$ .
Power Rule: When raising a power to another power, multiply the exponents: $(a^{m})^{n} = a^{mn}$ .
Negative Exponents: A base with a negative exponent is equal to the reciprocal of the base with a positive exponent: $a^{-n} = \frac{1}{a^{n}}$ .

Combining Like Terms: The process of simplifying expressions by adding or subtracting terms that have the same variables raised to the same powers.
Distributive Property: The rule stating that $a(b + c) = ab + ac$ , used to eliminate parentheses in an expression.
FOIL: A mnemonic for expanding the product of two binomials by multiplying the First, Outer, Inner, and Last terms.

GCF Factoring: The method of finding the Greatest Common Factor (GCF) among all terms in a polynomial and factoring it out.
Factoring Trinomials: The process of breaking down a three-term polynomial, such as $ax^{2} + bx + c$ , into the product of two binomials.

Standard Form: The representation of a quadratic function as $y = ax^{2} + bx + c$ .
Vertex Form: The representation of a quadratic function as $y = a(x - h)^{2} + k$ , where $(h, k)$ is the vertex of the parabola.
Quadratic Formula: The formula used to find the solutions (roots) of a quadratic equation: $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$ .
Zero Product Property: The principle stating that if the product of two or more factors is zero (e.g., $a \times b = 0$ ), then at least one of the factors must be zero ( $a = 0$ or $b = 0$ ).

Vertex: The highest or lowest point on a parabola, depending on whether it opens upward or downward.
Axis of Symmetry: The vertical line that passes through the vertex and divides the parabola into two symmetrical halves.
Intercepts: * x-intercepts: The points where the parabola crosses the x-axis, also known as zeros, roots, or solutions. * y-intercepts: The point where the parabola crosses the y-axis.

Distance Formula: Used for problems involving movement, defined as distance equals rate times time: $d = r \times t$ .
Percent Problems: Calculations involving finding a part of a whole, percentages of change, or other proportional relationships.

Correlation Types: Descriptions of the relationship between two variables on a scatter plot: * Positive Correlation: Both variables increase together. * Negative Correlation: As one variable increases, the other decreases. * No Correlation: There is no apparent relationship between the variables.
Line of Best Fit: A straight line drawn through the center of the data points on a scatter plot to represent the overall trend of the data.

Watch negative signs carefully: Many errors occur due to simple mistakes in distributing or calculating with negative numbers.
Show your work: Documenting steps helps prevent errors and allows for tracking mistakes.
Memorize formulas: Having formulas like the quadratic formula and slope-intercept form memorized is crucial for efficiency.
Practice graphing: Ensure familiarity with plotting points and identifying key features of both linear and quadratic graphs.
Sleep well before the test: Mental alertness is essential for performing well on the exam.