Algebra Cheat Sheet Vocabulary

Algebra study tool covering order of operations, properties of real numbers, set definitions, statistical measures, and geometric formulas.

PEMDAS

The Order of Operations: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.

Commutative Property

A property of real numbers stating $a + b = b + a$ and $ab = ba$.

Associative Property

A property of real numbers stating $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$.

Distributive Property

A property of real numbers stating $a(b + c) = ab + ac$.

Zero Property

A property of real numbers where $a \times 0 = 0$.

Identity Property

A property of real numbers: $a + 0 = a$ for addition and $a \times 1 = a$ for multiplication.

Inverse Property

A property of real numbers: $a + -a = 0$ for addition and $a \times \frac{1}{a} = 1$ for multiplication.

GCF

Greatest Common Factor, a factoring method.

Quadratic Formula

$x = \frac{-b \text{±} \text{√}b^2 - 4ac}{2a}$.

DOTS

Difference of Two Squares, a method used for factoring.

Natural Numbers

The set of numbers starting from 1: $1, 2, 3, 4, 5, \text{…}$

Whole Numbers

The set of natural numbers including zero: $0, 1, 2, 3, 4, 5, \text{…}$

Integers

The set of whole numbers and their negatives: $\text{…} , -3, -2, -1, 0, 1, 2, 3, \text{…}$

Slope Formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$, which represents the vertical change over horizontal change.

Mean

The average of a set of numbers.

Median

The middle value when numbers are put in order.

Mode

The number that appears the most in a data set.

Exponential Growth

An exponential equation $y = ab^x$ where $b > 1$.

Exponential Decay

An exponential equation $y = ab^x$ where $0 < b < 1$.

Vertex Formula

$x = \frac{-b}{2a}$, used to find the x-coordinate of the vertex.

Vertex Form

$y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.

Compound Interest Formula

$A = P(1 + \frac{r}{n})^{nt}$, where $P$ is Principle, $r$ is Interest rate, $n$ is compounding per year, and $t$ is total years.

Geometric Sequence Formula

$a_n = a_1 r^{n-1}$, used when a sequence is formed by multiplying or dividing.

Arithmetic Sequence Formula

$a_n = a_1 + (n - 1)d$, used when a sequence is formed by adding or subtracting.

Vertical Shift Transformation

$y = f(x) + C$; moves up if $C > 0$ and moves down if $C < 0$.

Horizontal Shift Transformation

$y = f(x + C)$; moves left if $C > 0$ and moves right if $C < 0$.

Reflection in the x-axis

A transformation defined by the equation $y = -f(x)$.

Trapezoid Area Formula

$A = \frac{1}{2}(a + b)h$.

Circumference Mnemonic

Cherry Pie’s Delicious ($C = \text{π}d$).

Circle Area Mnemonic

Apple Pies Are Two ($A = \text{π}r^2$).