Algebra EOC Study Guide

These flashcards cover key vocabulary, formulas, and concepts from the Algebra EOC Study Guide, including functions, statistics, sequences, number properties, and equation solving.

f(x)

A fancy way of saying "y" in function notation.

Domain

A list of all $x$ values.

Range

A list of all $y$ values.

Roots

A list of $x$ intercepts where the $y$ value is equal to $0$.

Independent Variable

The horizontal quantity represented by $x$; often used for time.

Dependent Variable

The vertical quantity represented by $y$ that depends on the independent variable.

Stem and Leaf Plot

An organized chart used to arrange data by finding least and greatest values and writing stems in a column.

Positive Correlation

A relationship where both sets of data increase together.

Negative Correlation

A relationship where one set of data decreases as the other set increases.

No Correlation

A situation where data sets are not related to each other.

Line of Best Fit

The best trend line representing data on a scatter plot.

Mode

The most common number in a data set; there may be more than one or none at all.

Median

The middle number in an ordered list; if two middle numbers exist, it is their average.

Mean

The average of a data set calculated by adding all numbers and dividing by the number of items.

Range (Data)

The difference between the largest number on a list and the smallest number.

Box and Whisker Plot

A display that shows how data is spread out by dividing it into four groups using the minimum, maximum, and quartiles.

Parent Function: Linear

$$y = mx + b$$

Parent Function: Absolute Value

$$y = a|x - h| + k$$

Parent Function: Exponential

$$y = a \times b^x$$

Parent Function: Quadratic

$$y = a(x - h)^2 + k$$

Parent Function: Rational

$$y = \frac{1}{x} + k$$

Arithmetic Sequence

A sequence where each term is created by adding a common difference, denoted as $d$.

Recursive Form

A sequence formula for the nth term that uses the prior term ($a_{n-1}$).

Geometric Sequence

A sequence where each term is created by multiplying by a common ratio, denoted as $r$.

Rational Number

Any number that can be written as a fraction in the form $\frac{a}{b}$; including counting numbers, whole numbers, and integers.

Irrational Number

Numbers that cannot be written as a fraction, such as non-repeating decimals and radicals.

Commutative Property

$a + b = b + a$ or $ab = ba$

Associative Property

$(a + b) + c = a + (b + c)$ or $(ab)c = a(bc)$

Proportion

An equation showing that two ratios are equal, where the cross products are equal.

Percent Change

The difference between two amounts divided by the original amount.

Inconsistent System

A system of equations with no solution where the lines are parallel.

Dependent System

A consistent system with infinitely many solutions where the equations represent the same line.

Scientific Notation

A number written as a product of a number between $0$ and $9$ and a power of $10$.

Slope Formula

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Parallel Lines

Lines that have the exact same slope.

Perpendicular Lines

Lines with slopes that are the reciprocal opposite of each other.

Standard Form

A linear equation in the form $Ax + By = C$, where $x$ is positive and there are no fractions.

Substitution Method

A method used to solve systems by replacing one variable with an expression found from the other equation.

Elimination Method

A method used to solve systems by multiplying equations by factors to create opposites that can be added together to cancel a variable.