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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.
 

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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
  • 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
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Infinite Precalculus
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