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 and probability
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 algebra 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
Algebra foundationsEquations, expressions, factoring, radicals, exponents, and notation fluency.
Functions and graphsDomain, range, transformations, inverse functions, and interpreting graphs.
Polynomial and rational functionsZeros, asymptotes, end behavior, graph shape, and function operations.
Exponential and logarithmic functionsGrowth models, log rules, equations, and inverse relationships.
Right triangle trigonometrySOH-CAH-TOA, inverse trig, Law of Sines, Law of Cosines, and applied triangles.
Trig identities and graphsUnit circle facts, identities, equations, amplitude, period, and phase shift.
Permutations and arrangementsSlot method, ordered selections, circular arrangements, keyrings, and word problems.
Combinations and group selectionBinomial coefficients, unordered groups, stars and bars, and calculator support.
Interactive Labs
2x2 Matrix Transform Lab
Drag points and apply live matrices to see rotations, reflections, scaling, projections, and shears on the coordinate plane.
Open the 2x2 lab
3x3 Matrix Transform Lab
Explore 3D linear transformations with basis vectors, shape presets, and live matrix controls.
Open the 3x3 lab
Animated 2D Transform Patterns
Watch common transformation matrices animate so the geometric meaning becomes easier to remember.
Open the transform patterns