# Topics Covered By Infinite Precalculus

Infinite Precalculus covers all typical Precalculus material and more: trigonometric functions, equations, and identities; parametric equations; polar coordinates; vectors; limits; and more. Over 100 individual topics extend skills from Algebra 2 and introduce Calculus.

Functions

Continuity

Extrema, intervals of increase and decrease

Power functions

Average rates of change

Transformations of graphs

Piecewise functions

Operations

Inverses

Power,
Polynomial, and Rational Functions

Graphs, real zeros, and end behavior of polynomial functions

Dividing polynomial functions

The Remainder Theorem and bounds of real zeros

Writing polynomial functions and conjugate roots

Complex zeros and The Fundamental Theorem of Algebra

Graphs of rational functions

Rational equations

Polynomial inequalities

Rational inequalities

Exponential
and Logarithmic Expressions

Graphing exponential functions

Exponential equations not requiring logarithms

Exponents and logarithms

Evaluating logarithms

Logarithms and exponents as inverses

Properties of logarithms

Writing logs in terms of others

Exponential equations requiring logarithms

Logarithmic equations, simple

Logarithmic equations, hard

Graphing logarithmic functions

Compound interest

Trigonometry

Angles and angle measure

Radians and degrees

Right triangle trig: Finding ratios

Right triangle trig: Finding angles and sides

Trig functions of any angle

Graphing trig functions

Simple trig equations

Inverse trig functions

Fundamental identities

Equations with factoring and fundamental identities

Sum and Difference Identities

Multiple-Angle Identities

Product-to-Sum Identities

Equations and Multiple-Angle Identities

The Law of Sines

The Law of Cosines

Area and Laws of Sines and Cosines

Parametric
Equations

Parametric equations

Projectile motion

Polar
Coordinates

Polar coordinates

Graphs of polar equations

Polar and rectangular forms of equations

Polar forms of conic section

Complex numbers in polar form

Vectors

Basics

Diagrams

Operations

Dot products

Three-Dimensional Vectors

Points in three dimensions

Basics

Operations

Cross products

Matrices and
Systems

Operations

Determinants

Inverses

Cramer's Rule

Equations

Multivariable linear systems and row operations

Partial fraction decomposition

Conic
Sections

Parabolas, graphing & properties

Parabolas, writing equations

Circles, graphing & properties

Circles, writing equations

Ellipses, graphing & properties

Ellipses, writing equations

Hyperbolas, graphing & properties

Hyperbolas, writing equations

Rotations of conic sections

Discrete
Mathematics

Sample spaces and The Fundamental Counting Principle

Permutations

Combinations

Permutations vs combinations

The Binomial Theorem

Mathematical induction

Probability

Probability of independent and dependent events, word problems

Probability of independent and dependent events

Probability of mutually exclusive events, word problems

Probability of mutually exclusive events

Probability with permutations and combinations

Sequences
and Series

General sequences

Arithmetic sequences

Geometric sequences

Arithmetic and geometric mean

General series

Arithmetic series

Geometric series

Power series

Introduction
to Calculus

Limits by direct evaluation

Limits at kinks and jumps

Limits at removable discontinuities

Limits at essential discontinuities

Limits at infinity

Definition of the derivative

Instantaneous rates of change

Power rule for differentiation

Motion along a line

Approximating area under a curve

Area under a curve by limit of sums

Indefinite integrals