Precalculus Notes for Students and Future Teachers

Pre-Calc.com

Clear reference pages, worked examples, and interactive labs for algebra, functions, trigonometry, counting, matrices, and teacher certification review.

Functions Rational Functions Trigonometry Counting Matrices

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.

Review rational functions

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. Rational functionsDomain restrictions, holes, vertical asymptotes, horizontal asymptotes, slant asymptotes, and intercepts. Quadratic formulaDiscriminant cases, factoring guidance, quadratic formula solutions, and extraneous solution checks. Logarithmic functionsLog meaning, log rules, change of base, equations, and scale comparisons. Sequences and seriesArithmetic and geometric sequences, finite sums, infinite geometric series, recursion, and sigma notation. Right trianglesSOHCAHTOA, inverse trig, special right triangles, and applied triangles. Law of Sines and CosinesAAS, ASA, SAS, SSS, and ambiguous SSA triangles. Unit circleQuadrant signs, radians, reference angles, and exact sine and cosine values. Trigonometric identitiesReciprocal, quotient, Pythagorean, sum, difference, and double-angle identities. 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