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Precalculus

14 topics · study sheets, quizzes, and tests.

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Go through each topic step by step, with 10 timed practice problems after every section.

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Topics

1.

Core Ideas in Plain Terms

The bridge to calculus, in everyday language

Study PracticeQuizUnit Test
2.

Sequences, Series, and the Binomial Theorem

Explicit & recursive formulas, factorials, sigma notation, arithmetic & geometric series, induction, the Binomial Theorem, counting, and probability

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3.

Introduction to Limits

The idea of a limit, evaluating limits, one-sided & infinite limits, limits at infinity, continuity, and a first look at the derivative

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4.

Functions and Their Graphs

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

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5.

Polynomial and Rational Functions

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

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6.

Exponential and Logarithmic Functions

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

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7.

Trigonometric Functions

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

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8.

Analytic Trigonometry

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

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9.

Triangle Trigonometry and Vectors

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

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10.

Polar Coordinates and Complex Numbers

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

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11.

Systems, Matrices, and Determinants

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

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12.

Conic Sections and Parametric Equations

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

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13.

Conic Sections

Slice a cone, get every curve: circle, ellipse, parabola, hyperbola

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14.

Course Review

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

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