Algebra I Regents High School Examination Practice

This set of vocabulary flashcards covers essential algebraic concepts, formulas, and statistical terms derived from the June 2025 Algebra I Regents Examination transcript.

Exponential relationship

A scenario where a quantity changes by a consistent percentage over time, such as a business growing by $5\%$ each month.

Polynomial degree

The value of the highest exponent in a polynomial expression.

Leading coefficient

The coefficient of the term with the highest degree in a polynomial expression.

Average rate of change

The change in the dependent variable divided by the change in the independent variable over a specific interval, calculated as $\frac{y_2 - y_1}{x_2 - x_1}$.

Subtraction property of equality

A mathematical property that allows subtracting the same value from both sides of an equation to maintain equality.

Interquartile Range (IQR)

A measure of statistical spread calculated as the difference between the third quartile and the first quartile, represented as $IQR = Q_3 - Q_1$.

Domain

The set of all possible input values ($x$-values) for which a function is defined.

Irrational number

A number that cannot be expressed as a ratio of two integers and cannot be written as a terminating or repeating decimal.

Kinetic energy formula

The physical formula $K = \frac{1}{2}mv^2$, where $K$ is kinetic energy, $m$ is mass, and $v$ is velocity.

Arithmetic sequence

A sequence of numbers in which the difference between consecutive terms is constant, defined by $a_n = a_1 + d(n - 1)$.

Geometric sequence

A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio, defined by $a_n = a_1r^{n - 1}$.

Axis of symmetry

A vertical line that passes through the vertex of a parabola, calculated using the formula $x = -\frac{b}{2a}$.

Standard form of a quadratic equation

An algebraic expression written in the form $y = ax^2 + bx + c$.

Quadratic formula

The formula used to find the solutions of a quadratic equation: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Correlation coefficient ($r$)

A numerical value that indicates the strength and direction of a linear relationship between two variables.

Slope-intercept form

The linear equation format $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.