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# 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.

View as text in:   Index Order     Suggested Order

Comparison of topics in each program

### 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
• 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

• 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
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Infinite Precalculus
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