← All courses f − 1 f^{-1} f − 1 Algebra
Everything calculus assumes: functions in depth, polynomial and rational behavior, exponentials and logs, trigonometry, vectors, complex numbers, matrices, sequences, conics and the first limits.
Before this: Algebra 2 , Trigonometry What you'll be able to do
Analyze end behavior, asymptotes and zeros of any function Use trig identities fluently Work with vectors, polar forms and De Moivre Evaluate limits algebraically Start the course
Go through each topic step by step — prose, worked examples, quick checks, and a timed practice round after every section.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics 1. Core Ideas in Plain Terms
5 lessons The bridge to calculus, in everyday language
2. Sequences, Series, and the Binomial Theorem
10 lessons Explicit & recursive formulas, factorials, sigma notation, arithmetic & geometric series, induction, the Binomial Theorem, counting, and probability
3. Introduction to Limits
8 lessons The idea of a limit, evaluating limits, one-sided & infinite limits, limits at infinity, continuity, and a first look at the derivative
4. Functions and Their Graphs
10 lessons Notation, domain & range, graph analysis, parent functions, transformations, combinations, inverses, and piecewise functions
5. Polynomial and Rational Functions
8 lessons Quadratics, end behavior, zeros, division, complex numbers, and rational graphs
6. Exponential and Logarithmic Functions
8 lessons Graphs, properties, equations, and modeling — everything on one reference
7. Trigonometric Functions
9 lessons Angles, the unit circle, graphs, and inverse trig functions
8. Analytic Trigonometry
9 lessons Identities, verifications, trig equations, and the sum/difference & multiple-angle formulas
9. Triangle Trigonometry and Vectors
8 lessons Laws of Sines and Cosines, area, vectors, dot products, and applications
10. Polar Coordinates and Complex Numbers
9 lessons Complex plane, trig form, DeMoivre, roots, polar points, equations, and curves
11. Systems, Matrices, and Determinants
12 lessons Substitution, elimination, Gaussian elimination, matrix algebra, inverses, determinants, Cramer's Rule, partial fractions, and linear programming
12. Conic Sections and Parametric Equations
12 lessons Parabolas, ellipses, hyperbolas, classifying by completing the square, parametric curves, and polar conics
13. Course Review
11 lessons Functions, polynomials, exponentials, all of trigonometry, polar & complex numbers, matrices, conics, sequences, and an introduction to limits