SAT Math Study Guide Part 1: Foundations, Numbers, Algebra, and Functions

Vocabulary and formula review flashcards based on foundations of algebra, numbers, operations, and functions for SAT Math preparation.

PEMDAS

The order of operations used when solving expressions: 1. Parentheses, 2. Exponents, 3. Multiplication and Division (left to right), 4. Addition and Subtraction (left to right).

Adding/Subtracting Fractions

Find a common denominator, add or subtract the numerators, and simplify.

Multiplying Fractions

Multiply straight across.

Dividing Fractions

Follow the sequence: Keep, Change, Flip.

Percent

Means "out of 100."

Percent of a number formula

$$\text{Part} = \text{Percent} \times \text{Whole}$$

Percent Increase formula

$$\frac{\text{New} - \text{Old}}{\text{Old}}$$

Ratio

A comparison of two quantities.

Proportions

Equations where you cross multiply to solve for a variable.

Scientific Notation (Large Numbers)

$$5,400,000 = 5.4 \times 10^{6}$$

Scientific Notation (Small Numbers)

$$0.00042 = 4.2 \times 10^{-4}$$

Absolute Value

The distance from zero; it is always positive, e.g., $|-5| = 5$.

Product of Powers Rule

$$a^{m} \times a^{n} = a^{m+n}$$

Quotient of Powers Rule

$$a^{m} / a^{n} = a^{m-n}$$

Power of a Power Rule

$$(a^{m})^{n} = a^{mn}$$

Zero Exponent Rule

$$a^{0} = 1$$

Negative Exponent Rule

$$a^{-2} = \frac{1}{a^{2}}$$

Perfect Squares

The sequence of numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.

Combining Like Terms

Only combine terms with the same variable and exponent.

Distributive Property

$$a(b+c) = ab+ac$$

Standard Form (Linear)

$$Ax + By = C$$

Slope-intercept Form

$y = mx + b$ where $m$ is slope and $b$ is y-intercept.

Slope Formula

$$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

Zero Slope

Describes a horizontal line.

Undefined Slope

Describes a vertical line.

Parallel Lines

Lines that have the same slope but different y-intercepts.

Perpendicular Lines

Lines with slopes that are opposite reciprocals, such as $2$ and $- \frac{1}{2}$.

Inequalities Rule

When multiplying or dividing by a negative number, you must flip the inequality sign.

Systems of Equations Methods

Substitution, Elimination, and Graphing.

Function

A relation that gives exactly one output for each input.

Domain

The set of all possible x-values for a function.

Range

The set of all possible y-values for a function.

Standard Form (Quadratic)

$$ax^{2}+bx+c$$

Parabola

The name of the graph of a quadratic equation.

Quadratic Formula

$$x = \frac{-b \neq \text{v}(b^{2}-4ac)}{2a}$$

Vertex Form

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

common mistake Distributing

Forgetting to distribute accurately across a set of parentheses.

Estimation

Estimate the answer before calculating to ensure the result is reasonable.