Algebra I Regents Examination Review

Vocabulary and key concepts from the Algebra I Regents High School Examination transcript (June 2025).

Exponential relationship

A relationship where a quantity increases or decreases by a constant percentage over equal time intervals, such as a business growing by $5\%$ each month.

Standard deviation

A measure of how spread out numbers are from the mean; in the exam, used to compare the consistency of test scores between individuals like Andrea and Joe.

Leading coefficient

The coefficient of the term with the highest degree in a polynomial; for example, the leading coefficient of $2x^3 + x^2 + 4x$ is $2$.

Polynomial degree

The highest power of the variable in a polynomial expression; for example, $2x^3 + x^2 + 4x$ has a degree of $3$.

Average rate of change

The ratio of the change in the output value to the change in the input value over a specific interval, calculated as $\frac{h(x_2) - h(x_1)}{x_2 - x_1}$.

Subtraction property of equality

The algebraic property used to justify moving a term from one side of an equation to the other by subtracting it from both sides, as seen in Chloe's first step solving $x^2 + 5x = 3x + 3$.

Substitution method

An algebraic process for solving systems of equations by replacing one variable with an equivalent expression from the other equation, such as substituting $5 - 4x$ for $y$ in the equation $2x - 3y = 10$.

Interquartile Range (IQR)

A measure of statistical dispersion calculated as the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$), represented by the length of the box in a box plot.

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 terminating or repeating decimal, such as the sum of $\sqrt{3}$ and $\sqrt{5}$.

Kinetic energy formula

The expression $K = \frac{1}{2}mv^2$, 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, represented by the formula $a_n = a_1 + d(n - 1)$.

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, represented by $a_n = a_1r^{n-1}$.

Axis of symmetry

The vertical line that divides a parabola into two symmetrical halves, determined by the formula $x = -\frac{b}{2a}$.

Trinomial in standard form

A polynomial with three terms written in descending order of exponents, such as $-10x^2 + 41x - 21$.

Slope-intercept form

The equation of a straight line in the form $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Quadratic formula

The formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ used to find the solutions of a quadratic equation in the form $ax^2 + bx + c = 0$.

Correlation coefficient

A numerical value ($r$) ranging from $-1$ to $1$ that indicates the strength and direction of the linear relationship between two variables; for example, $-0.99$ indicates a strong negative correlation.

System of inequalities

A set of two or more inequalities with the same variables that are solved simultaneously to find a common region of solutions on a graph.

Leading coefficient of 2

In the context of the polynomial $2x^3 + x^2 + 4x$, the number $2$ acts as the leading coefficient because it is attached to the highest power, $x^3$.