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