SAT Math Flashcards

Absolute Value

The distance of a number from zero on a number line, always positive. Written as |x|. For example, |-5| = 5 and |5| = 5.

Quadratic Formula

Used to solve quadratic equations: x = (-b ± √(b² - 4ac)) / 2a, where the equation is ax² + bx + c = 0.

Slope

The rate of change of a line, calculated as (y₂ - y₁) / (x₂ - x₁). Tells you how steep a line is.

Linear Equation

An equation that creates a straight line when graphed. Standard form: ax + by = c or slope-intercept form: y = mx + b.

System of Equations

Two or more equations with multiple variables that are solved together. The solution is the point where all equations intersect.

Exponent Rules

Key rules include: x^a · x^b = x^(a+b), x^a / x^b = x^(a-b), and (x^a)^b = x^(ab).

Polynomial

An expression with variables and coefficients using addition, subtraction, and multiplication. Example: 3x² + 2x - 5.

Factoring

Breaking down an expression into simpler parts that multiply together. Example: x² + 5x + 6 = (x + 2)(x + 3).

Rational Expression

A fraction containing polynomials in the numerator and denominator. Must simplify and note restrictions where denominator ≠ 0.

Radical or Square Root

The opposite of squaring a number. √x means 'what number multiplied by itself equals x?' Example: √16 = 4.

Pythagorean Theorem

In a right triangle: a² + b² = c², where c is the hypotenuse (longest side) and a and b are the other sides.

Distance Formula

Finds the distance between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²).

Midpoint Formula

Finds the center point between two points: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

Percent Change

Calculated as (new value - old value) / old value × 100%. Shows how much something increased or decreased.

Probability

The likelihood that an event occurs. Calculated as (number of favorable outcomes) / (total number of possible outcomes).

Mean, Median, Mode

Mean is the average (sum ÷ count). Median is the middle value when ordered. Mode is the most frequent value.

Standard Deviation

Measures how spread out data is from the mean. Higher standard deviation means data points are more scattered.

Circle Equation

Standard form: (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Area of Circle

A = πr², where r is the radius. Remember that the diameter is twice the radius.

Circumference of Circle

C = 2πr or C = πd, where r is radius and d is diameter. The distance around the circle.

Volume of Rectangular Prism

V = length × width × height. Measures the space inside a 3D box.

Volume of Cylinder

V = πr²h, where r is the radius of the base and h is the height.

Similar Triangles

Triangles with the same shape but different sizes. Corresponding angles are equal and corresponding sides are proportional.

Arithmetic Sequence

A sequence where each term increases by the same amount. Formula: aₙ = a₁ + (n - 1)d, where d is the common difference.

Geometric Sequence

A sequence where each term is multiplied by the same number. Formula: aₙ = a₁ · r^(n-1), where r is the common ratio.

Function Notation

Written as f(x), represents the output when x is the input. Means 'f of x' or 'the function f evaluated at x'.

Domain and Range

Domain is all possible input values (x-values). Range is all possible output values (y-values).

Compound Interest

Formula: A = P(1 + r/n)^(nt), where P is principal, r is rate, n is compounding periods per year, and t is time in years.

Matrix

A rectangular array of numbers arranged in rows and columns. Used to organize data or solve systems of equations.

Logarithm

The inverse of an exponent. log_b(x) = y means b^y = x. Common logs use base 10; natural logs use base e.