Precollege Algebra Cheat Sheet
Your complete reference for algebra formulas, rules, and graphs. From basic arithmetic to trigonometric identities — everything you need in one place.
Fundamentals
5 topics
Arithmetic Operations
Basic rules for addition, subtraction, multiplication, and division including fractions and order of operations.
Exponents and Radicals
Laws of exponents, radical expressions, and simplification rules.
Absolute Value
Definition, properties, and equations involving absolute value.
Special Factorizations
Common factoring patterns including difference of squares, perfect square trinomials, and sum/difference of cubes.
Properties of Logarithms
Logarithm rules including product, quotient, power, and change of base formulas.
Equations & Formulas
2 topics
Geometry
3 topics
Geometry Formulas
Area and perimeter formulas for circles, triangles, rectangles, and polygons.
Common Conversion Factors
Unit conversions for length, area, volume, mass, time, speed, and temperature.
Heron's Formula
Calculate the area of a triangle using only the lengths of its three sides.
Functions
3 topics
Functions
Types of functions including constant, linear, quadratic, polynomial, rational, exponential, and logarithmic.
Graphs of Common Functions
Visual representations and key features of common function types.
Transformations
Translations, reflections, stretches, and compressions of function graphs.
Advanced Algebra
3 topics
Conic Sections
Equations and properties of parabolas, circles, ellipses, and hyperbolas.
Sequences and Series
Arithmetic and geometric sequences, summation formulas, and series notation.
The Binomial Theorem
Expansion of binomial expressions and Pascal's triangle.
Trigonometry
13 topics
Trigonometric Functions
Definitions of sine, cosine, tangent, cotangent, secant, and cosecant.
Graphs of Trigonometric Functions
Visual representations and key features of the six trigonometric functions.
Inverse Trigonometric Functions
Definitions, domains, and ranges of arcsin, arccos, arctan, and related functions.
Graphs of Inverse Trig Functions
Visual representations of inverse trigonometric function graphs.
Amplitude, Period, and Phase Shift
Parameters that control the shape and position of trigonometric graphs.
Right Triangle Trigonometry
SOH-CAH-TOA, special right triangles (30-60-90 and 45-45-90).
Trig Functions in Cartesian Plane
Unit circle approach to trigonometric functions.
Exact Values of Trig Functions
Common angle values and reference angle techniques.
Angle Measurement
Degrees, radians, and conversions between angle units.
Oblique Triangles
Law of Sines, Law of Cosines, and solving non-right triangles.
Circular Functions
Unit circle definition of sine and cosine with graphical representation.
Trigonometric Identities
Sum, difference, double angle, half angle, product-to-sum, and sum-to-product identities.
Basic Trigonometric Identities
Pythagorean, reciprocal, and quotient identities.
Vectors & Complex Numbers
3 topics
Vectors
Vector operations, magnitude, direction, dot product, and applications.
Polar Coordinates
Converting between rectangular and polar coordinates, polar equations.
Powers and Roots of Complex Numbers
De Moivre's theorem, complex number operations, and finding roots.