Precalculus notes for students and future teachers
Pre-Calc.com
Clear reference pages, worked examples, and interactive labs for algebra, functions, trigonometry, combinatorics, matrices, and teacher certification review.
Study Paths
MTTC Mathematics Review
Review the precalculus skills that often sit underneath teacher certification questions: functions, graph interpretation, trigonometry, sequences, probability, combinatorics, vectors, and algebraic reasoning.
Start with counting theory
State Teacher Certification Notes
Use these pages as compact notes for certification exams beyond Michigan too, especially when you need quick refreshers before practice tests or content-area review sessions.
Review foundations
Precalculus Reference Pages
Jump straight to definitions, formulas, examples, and common decision rules for the topics that bridge advanced algebra, trigonometry, and calculus readiness.
Browse functions and graphs
Core Topics
Order of operationsGrouping, exponents, left-to-right rules, fractions, radicals, and signs.
FunctionsDomain, range, notation, composition, inverses, and transformations.
InequalitiesInterval notation, compound inequalities, absolute value, and sign charts.
SystemsSubstitution, elimination, matrix form, no solution, infinite solutions, and regions.
Factoring polynomialsGCF, grouping, trinomials, cubes, SOAP, and completing the square.
Logarithmic functionsLog meaning, log rules, change of base, equations, and scale comparisons.
Right trianglesSOHCAHTOA, inverse trig, special right triangles, and applied triangles.
Law of Sines and CosinesAAS, ASA, SAS, SSS, and ambiguous SSA triangles.
Permutations and combinationsSlot method, ordered selections, groups, grid paths, stars and bars, and restrictions.
2x2 matricesMatrix operations, determinants, inverses, systems, and plane transformations.
Interactive Labs
2x2 Matrices
Review matrix operations, determinants, inverses, systems, and coordinate transformations.
Open 2x2 matrices
3x3 Matrices
Review row operations, REF, RREF, determinants, 3-variable systems, inverses, and volume scaling.
Open 3x3 matrices
Animated 2D Transform Patterns
Watch common transformation matrices animate so the geometric meaning becomes easier to remember.
Open the transform patterns