← Precalculus course

Precalculus· Study notes

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.

11 topics · 103 lessons about 47 hoursBefore 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

Read the notes as a guided lesson

Walk the notes one box at a time — prose, worked examples, quick checks — with a timed practice round after every section. For the full course with interactive lessons, go back to the course.

The course Guided reading
Final Test (30) Big Test (50) Search & glossary Flashcards Print the course (PDF)Suggest a problem

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

Study PracticeQuizUnit Test
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

Interactive Study PracticeQuizUnit TestTest out
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

Interactive Study PracticeQuizUnit TestTest outReview so far
4.

Functions and Their Graphs

10 lessons

Notation, domain & range, graph analysis, parent functions, transformations, combinations, inverses, and piecewise functions

Interactive Study PracticeQuizUnit TestTest outReview so far
5.

Polynomial and Rational Functions

8 lessons

Quadratics, end behavior, zeros, division, complex numbers, and rational graphs

Interactive Study PracticeQuizUnit TestTest outReview so far
6.

Exponential and Logarithmic Functions

8 lessons

Graphs, properties, equations, and modeling — everything on one reference

Interactive Study PracticeQuizUnit TestTest outReview so far
7.

Trigonometric Functions

9 lessons

Angles, the unit circle, graphs, and inverse trig functions

Interactive Study PracticeQuizUnit TestTest outReview so far
8.

Analytic Trigonometry

9 lessons

Identities, verifications, trig equations, and the sum/difference & multiple-angle formulas

Interactive Study PracticeQuizUnit TestTest outReview so far
9.

Triangle Trigonometry and Vectors

8 lessons

Laws of Sines and Cosines, area, vectors, dot products, and applications

Interactive Study PracticeQuizUnit TestTest outReview so far
10.

Polar Coordinates and Complex Numbers

9 lessons

Complex plane, trig form, DeMoivre, roots, polar points, equations, and curves

Interactive Study PracticeQuizUnit TestTest outReview so far
11.

Systems, Matrices, and Determinants

12 lessons

Substitution, elimination, Gaussian elimination, matrix algebra, inverses, determinants, Cramer's Rule, partial fractions, and linear programming

Interactive Study PracticeQuizUnit TestTest outReview so far
12.

Conic Sections and Parametric Equations

12 lessons

Parabolas, ellipses, hyperbolas, classifying by completing the square, parametric curves, and polar conics

Interactive Study PracticeQuizUnit TestTest outReview so far
13.

Course Review

11 lessons

Functions, polynomials, exponentials, all of trigonometry, polar & complex numbers, matrices, conics, sequences, and an introduction to limits

Study PracticeQuizUnit Test