sat math

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Slope Formula

m = (y₂ - y₁) / (x₂ - x₁)

Integers

…, -3, -2, -1, 0, 1, 2, 3, …

Rationals

Fractions (anything expressible as a ratio of integers).

Reals

Integers, rationals, plus special numbers (like √2 or π).

Order of Operations

PEMDAS (Parentheses, Exponents, Multiply/Divide, Add/Subtract).

Arithmetic Sequences

t₁, t₁ + d, t₁ + 2d, …

Geometric Sequences

t₁, t₁ · r, t₁ · r², …

Factors

Numbers that divide evenly into a target (e.g., factors of 52 are 1, 2, 4, 13, 26, 52).

Multiples

Numbers formed by multiplying by integers (e.g., multiples of 20 are 20, 40, 60, 80, 100…).

Percentages Formula

part = (percent / 100) * whole

Average Formula

Average = Sum of terms / Number of terms

Average Speed Formula

Average Speed = Total distance / Total time

Sum Formula

Sum = Average * (Number of terms)

Mode

The value in a list that appears most often.

Median

The middle value in an ordered list.

Fundamental Counting Principle

If event 1 has N ways and independent event 2 has M ways, both together can happen in N * M ways.

Probability Formula

Probability = Number of desired outcomes / Total number of outcomes

Adding Exponents

xᵃ · xᵇ = xᵃ⁺ᵇ

Subtracting Exponents

xᵃ / xᵇ = xᵃ⁻ᵇ

Negative Exponents

1 / xᵇ = x⁻ᵇ

Multiplying Exponents

(xᵃ)ᵇ = xᵃᵇ

Zero Exponent (x⁰)

x⁰ = 1

Roots Multiplication Rule

√(x · y) = √x · √y

FOIL Method

(x + a)(x + b) = x² + (a + b)x + ab

Difference of Squares

a² - b² = (a + b)(a - b)

Square of a Sum

a² + 2ab + b² = (a + b)²

Square of a Difference

a² - 2ab - b² = (a - b)²

Distance Formula

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Midpoint Formula

Midpoint = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Intersecting Lines

Opposite (vertical) angles are equal; adjacent angles along a line add to 180°.

Area of Triangle

Area = (1/2) * base * height

Triangle Angles Sum

All interior angles add up to 180 degrees.

Triangle Inequality Theorem

The length of any 1 side is always less than the sum of the other 2 sides.

Equilateral Triangle

Three equal sides; all interior angles = 60 degrees.

Isosceles Triangle

2 equal sides; 2 equal angles opposite those sides.

Similar Triangles

Same shape, corresponding angles are equal, corresponding sides are in proportion.

Area of Circle

Area = π * r²

Circumference of Circle

Circumference = 2 * π * r

Degrees in a Circle

A full circle = 360 degrees.

Arc Length Formula

Arc Length = (n° / 360°) * 2πr

Area of Sector Formula

Sector Area = (n° / 360°) * πr²

Area of Rectangle

Area = length * width

Area of Parallelogram

Area = base * height

Volume of Rectangular Solid

Volume = length * width * height

Volume of Right Cylinder

Volume = π * r² * h

Prime Numbers

Numbers greater than 1 with no positive divisors other than 1 and itself (2, 3, 5, 7, 11…).

Greatest Common Factor (GCF)

The largest factor shared by numbers (e.g., GCF of 200 and 60 is 20).

Least Common Multiple (LCM)

The smallest multiple shared by numbers (e.g., LCM of 200 and 60 is 600).

Equation of Circle

(x - h)² + (y - k)² = r², center at (h, k) and radius r.

Area of Trapezoid

Area = [(base₁ + base₂) / 2] * height

Direct Variation

y = kx

Inverse Variation

y = k / x

Slope-Intercept Form

y = mx + b

Point-Slope Form

y - y₁ = m(x - x₁)

Standard Form of Linear Equation

Ax + By = C (where A, B, C are integers and A ≥ 0).

Dividing Inequality by Negative

Must FLIP the inequality sign (< becomes >, etc.).

Graphing < or > on Coordinate Plane

Dotted / dashed line.

Graphing ≤ or ≥ on Coordinate Plane

Solid line.

Graphing > or ≥ on Coordinate Plane

Shade upwards or to the right.

Graphing < or ≤ on Coordinate Plane

Shade downwards or to the left.

Circle Perimeter

Same as circumference = 2πr

Chord

A line segment connecting two points on a circle.

Sector

The region of a circle bounded by two radii and an arc (looks like a slice of pie).

Arc

A portion of the circumference connecting two points on a circle.

Central Angle

An angle whose vertex lies at the center of the circle.