Grammar Hero's Math Reference Sheet Vocabulary

Vocabulary and formulas covering geometry, algebra, statistics, and arithmetic based on the Grammar Hero reference sheet.

Triangle Sum Theorem

The theorem stating that the sum of the three interior angles in a triangle is always $180^{\circ}$, represented as $\angle a + \angle b + \angle c = 180^{\circ}$.

Slope of a Line ($m$)

The ratio of the change in $y$ to the change in $x$ between two points $(x_1, y_1)$ and $(x_2, y_2)$, calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Quadratic Formula

The formula used to solve equations in the form $ax^2 + bx + c = 0$: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Pythagorean Theorem

In a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse: $a^2 + b^2 = c^2$.

Slope-Intercept Form

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

Point-Slope Form

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

Distance Formula

The formula to find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$, defined as $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Midpoint Formula ($M$)

The formula used to find the point halfway between two coordinates: $M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.

Simple Interest Formula

$I = prt$, where $p$ is the Principal, $r$ is the Rate of interest per year in decimal form, and $t$ is Time in years.

PEMDAS

An acronym for the order of operations: Parenthesis, Exponents, Multiplication and Division (Left to Right), and Addition and Subtraction (Left to Right).

Percent Change ($PC$)

The formula $\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$; a positive result indicates an increase, while a negative result indicates a decrease.

Mean

The average of a data set, calculated by dividing the sum of all data points by the total number of data points.

Median

The middle value of a data set arranged from smallest to largest; if there is an even number of observations, it is the average of the two middle values.

Mode

The specific value in a data set that occurs most frequently.

Range

The difference between the highest and lowest values in a data set: $\text{Maximum Value} - \text{Minimum Value}$.

Circumference

The perimeter of a circle, calculated using the formulas $C = \pi d$ or $C = 2\pi r$.

Sum of Interior Angles (Polygon)

The sum of the interior angles of any polygon with $n$ sides is given by the formula $S = 180(n - 2)$.

Volume of a Sphere

The formula for the space inside a sphere: $V = \frac{4}{3} \pi r^3$.

Fundamental Counting Principle

A method to determine the total number of ways different events can occur by multiplying the number of ways for each event ($m \times n$).

Zero-Exponent Rule

The mathematical rule stating that anything raised to the zero power is 1: $a^0 = 1$.

Factorial ($n!$)

The product of an integer and all positive integers below it: $n! = n \times (n - 1) \times (n - 2) \times \dots \times 1$.

Like Terms

Algebraic terms that share the same letter variables raised to the same powers.

Prime Number

A number that is only divisible by one and itself; numbers divisible by 2, 3, 4, 5, 6, 9, or 10 cannot be prime.

Reciprocal

The result of swapping the numerator and denominator of a fraction.

Acute Angle

An angle whose measure is less than $90^{\circ}$.

Obtuse Angle

An angle whose measure is greater than $90^{\circ}$ but less than $180^{\circ}$.

Complementary Angles

Two angles whose measures add up to a sum of $90^{\circ}$.

Supplementary Angles

Two angles whose measures add up to a sum of $180^{\circ}$.