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COURSE INFORMATION PAGE

This course is divided into 12 Units, each containing several lessons (see list of topics by unit below). Each lesson has several fully explained examples. At the bottom of each lesson page is a link which takes you to a set of homework questions which allow you to practice the lesson concepts. Again detailed solutions are given for each question. Each of the twelve units concludes with a review/summary and a test with full solutions.

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• 1. Precalculus Prep
  • The Real Number System
  • Simplifying Radicals
  • Polynomials
  • Rational Expressions 1
  • Rational Expressions 2-Multiplication & Division
  • Rational Expressions 3-Addition & Subtraction
  • Slope & Equations of Lines
  • Summary/Test
• 2. Functions and Transformations
  • Functions:Definition, Domain and Range
  • Functions you should know - Linear, Quadratic, Reciprocal, Square Root, domain defined etc.
  • Translations
  • Reflections
  • Inverses
  • Stretches and Compressions
  • Combinations of Transformations
  • Combining Functions-addition/subtraction/multiplication/division and composition of functions
  • Summary/Test
• 3. Quadratics
  • Quadratic Functions
  • Quadratic Equations
  • Problem Solving with Quadratic Functions including Max/Min Problems
  • Problem Solving with Quadratic Equations
  • Operations with Radicals
  • Complex Numbers as Roots of Quadratic Equations
  • Operations with Complex Numbers
  • Reciprocal Functions
  • Summary/Test
• 4. Polynomial Functions
  • Polynomial Functions Introduction
  • Investigating Polynomial Functions
  • Polynomial Division - Long Division and Synthetic Division
  • Remainder and Factor Theorems
  • Polynomial Equations
  • Polynomial Inequalities
  • Rational Functions
  • Summary/Test
• 5. Exponential & Logarithmic Functions
  • Laws of Exponents
  • Solving Exponential Equations
  • Exponential Functions and their Graphs
  • Exponential Functions Base e
  • Logarithmic Functions - Solving Exponential & Logarithmic Equations
  • Laws of Logarithms - Solving Exponential & Logarithmic Equations cont'd
  • Applications - Growth and Decay
  • Summary/Test
• 6. Trigonometry with Triangles
  • Right Triangles
  • Angles in Standard Position
  • Sine Law & Ambiguous Case
  • Cosine Law
  • Problem Solving with Triangles
  • Summary/Test
• 7. Trigonometry Functions and Their Graphs
  • Angle Measure - Radians & Degrees
  • Standard Position - trig definitions using standard {x, y, r} method
  • Standard Position - trig definitions using Unit Circle method
  • Graphs of Trig. Functions - Amplitude and Period
  • Transformations y = a sink(x + d) + c & y = a cosk(x + d) + c
  • Trig. Identities
  • Trig. Equations
  • Summary/Test
• 8. Analytic Trigonometry
  • Trigonometric Functions of Real Numbers
  • Compound Angle Formulas
  • Sum to Product and Product to Sum Formulas
  • Double Angle Formulas
  • Trig. Equations
  • Inverse Trigonometric Functions
  • Summary/Test
• 9. Analytic Geometry - The Conics
  • Locus
  • The Circle
  • The Ellipse
  • The Parabola
  • The Hyperbola
  • General Form of the Equation of a Conic
  • Intersection of Lines & Conics
  • Summary/Test
• 10. Sequences and Series
  • Arithmetic Sequences
  • Geometric Sequences
  • Arithmetic Series
  • Geometric Series
  • Sigma Notation
  • Mathematical Induction
  • Summary/Test
• 11. Investment Mathematics-Annuities
  • Simple & Compound Interest
  • Present Value
  • Ordinary Annuities
  • Present Value Annuities
  • General Annuities & Equivalent Rates
  • Mortgages
  • Summary/Test
• 12. Parametric Equations & Polar Coordinates
  • Parametric Equations of Curves Defined
  • The Polar Coordinate System
  • Complex Numbers in Polar Form
  • Multiplication and Division of Complex Numbers
  • Powers and Roots of Complex Numbers
  • Summary/Test

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