Digital SAT Math Formula Sheet Vocabulary Flashcards

Flashcards covering essential key terms, rules, and formulas for the Digital SAT Math section directly derived from the transcript.

Slope Formula

Calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$, where the point used first in the numerator must also be used first in the denominator.

Slope-intercept Form

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

Point-slope Form

The linear equation form $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

Standard Form (Linear)

The linear equation form $Ax + By = C$, which gives an x-intercept of $\frac{C}{A}$, a y-intercept of $\frac{C}{B}$, and a slope of $-\frac{A}{B}$.

Parallel Lines

Lines that have the exact same slope ($m_1 = m_2$).

Perpendicular Lines

Lines that have opposite reciprocal slopes, satisfying $m_1 \cdot m_2 = -1$.

Midpoint Formula

The formula used to find the midpoint between two coordinates, given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Distance Formula

The formula given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, which represents the Pythagorean theorem applied to coordinate geometry.

Absolute Value Equations

Equations formatted as $|ax + b| = c$, which split into $ax + b = c$ and $ax + b = -c$ (yielding no solution if $c$ is negative).

Percent Change

Calculated using the formula $\frac{\text{final} - \text{initial}}{\text{initial}} \times 100$, where the denominator is always the original value.

Difference of Squares

An algebraic factoring shortcut defined by the identity $a^2 - b^2 = (a + b)(a - b)$.

Remainder Theorem

States that the remainder when a polynomial $P(x)$ is divided by $(x - a)$ is equal to $P(a)$.

Factor Theorem

States that $(x - a)$ is a factor of polynomial $P(x)$ if and only if $P(a) = 0$.

Quadratic Formula

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

Vertex Form

The quadratic equation form $y = a(x - h)^2 + k$, which directly displays the parabola's vertex at $(h, k)$ and minimum/maximum value as $k$.

Sum and Product of Roots

For a quadratic in standard form, the sum of roots equals $-\frac{b}{a}$ and the product of roots equals $\frac{c}{a}$.

Discriminant

Calculated as $D = b^2 - 4ac$; $D > 0$ indicates 2 real solutions, $D = 0$ indicates 1 real solution, and $D < 0$ indicates 0 real solutions.

General Exponential Model

Formulated as $y = a(1 \pm r)^t$, where $a$ is the initial amount, $r$ is the rate per period as a decimal, and $t$ is the number of periods.

Equation of a Circle

Defined as $(x - h)^2 + (y - k)^2 = r^2$, representing a circle with center $(h, k)$ and radius $r$.

Complementary Angle Identity

Trigonometric identities stating that $\sin(x) = \cos(90^\circ - x)$ and $\cos(x) = \sin(90^\circ - x)$.

Interquartile Range (IQR)

A measure of statistical spread calculated as $\text{IQR} = Q3 - Q1$.