COURSE INFORMATION PAGE
General Information
List of Precalculus Topics by Unit
List of Algebra and Trigonometry Topics by Unit
General Information
Each course is divided into 10 or more 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's concepts. Again detailed solutions are given for each question. Each of the units concludes with a unit summary and a test with full solutions.
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List of Precalculus Topics by Unit
- 1. Precalculus Prep
- The Real Number System
- Simplifying Radicals
- Polynomials
- Rational Expressions 1
- Rational Expressions 2-Multiplication & Division
- Rational Expressions 3-Addition & Subtraction
- Slope and 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, Absolute Value
- Translations
- Reflections
- Inverses
- Stretches and Compressions
- Combinations of Transformations
- Combining Functions-addition/subtraction/multiplication/division and composition of functions
- Summary & Test
- 3. Quadratics and Applications
- 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 and Logarithmic Functions and Applications
- Laws of Exponents
- Solving Exponential Equations I
- Exponential Functions and their Graphs
- Exponential Functions Base e
- Logarithmic Functions - Solving Exponential & Logarithmic Equations II
- 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 - trigonometric definitions using standard {x, y, r} method
- Standard Position - trigonometric definitions using Unit Circle method
- Graphs of Trigonometric Functions - Amplitude and Period
- Transformations y = a sink(x + d) + c & y = a cosk(x + d) + c
- Trigonometric Identities
- Trigonometric 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
- Trigonometric 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 and 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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List of Algebra and Trigonometry Topics by Unit
- 1. Algebra Prep: Exponents, polynomials, Rational Expressions
- Real Numbers and Radicals
- Basic Algebra and Polynomials
- Solving Linear Equations
- Inequalities and Absolute Value
- Rational Expressions 1
- Rational Expressions 2-Multiplication & Division
- Rational Expressions 3-Addition & Subtraction
- Exponents Review and Rational Exponents
- Slope and Equations of Lines
- Summary & Test
- 2. Systems of Equations
- Coordinates, Distance and Midpoint
- Linear Inequalities
- The Graphical Method
- Substitution and Elimination
- Solving Systems Using Matrices
- Problem Solving Using Systems
- Systems of Inequalities
- Solving Systems of 3 Equations in 3 Unknowns
- Summary & Test
- 3. Quadratics and Applications
- Quadratic Functions
- Quadratic Equations
- Problem Solving with Quadratic Functions including Max/Min Problems
- Problem Solving with Quadratic Equations
- Operations with Radicals - Irrational Expressions
- Complex Numbers as Roots of Quadratic Equations
- Operations with Complex Numbers
- Reciprocal Functions
- Summary & Test
- 4. Functions and Transformations
- Functions:Definition, Domain and Range
- Functions you should know - Linear, Quadratic, Reciprocal, Square Root, Domain Defined, Absolute Value
- Horizontal and Vertical Translations (Shifts)
- Reflections
- Inverses of Functions
- Stretches and Compressions
- Combinations of Transformations
- Combining Functions-addition/subtraction/multiplication/division and composition of functions
- Summary & Test
- 5. Exponential and Logarithmic Functions and Applications
- Laws of Exponents
- Solving Exponential Equations I
- Exponential Functions and their Graphs
- Exponential Functions Base e
- The Logarithmic Functions
- Laws of Logarithms - Solving Exponential & Logarithmic Equations II
- Applications - Growth and Decay
- Summary & Test
- 6. Trigonometry I: Right Triangles, Oblique Triangles
- Right Triangles
- Angles in Standard Position
- Sine Law & Ambiguous Case
- Cosine Law
- Problem Solving with Triangles
- Summary & Test
- 7. Trigonometry II: Trigonometric Functions - Graphs, Transformations, Identities and Trigonometric Equations
- Angle Measure - Radians & Degrees
- Standard Position - trigonometric definitions using standard {x, y, r} method
- Standard Position - trigonometric definitions using Unit Circle method
- Graphs of Trigonometric Functions - Amplitude and Period
- Transformations y = a sink(x + d) + c & y = a cosk(x + d) + c
- Trigonometric Identities
- Trigonometric Equations
- Summary & Test
- 8. Sequences and Series
- Arithmetic Sequences
- Geometric Sequences
- Arithmetic Series
- Geometric Series
- Sigma Notation
- Mathematical Induction
- Summary & Test
- 9. Investment Mathematics-Annuities
- Simple & Compound Interest
- Present Value
- Ordinary Annuities
- Present Value Annuities
- General Annuities & Equivalent Rates
- Mortgages
- Summary & Test
- 10. 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
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PRECALCULUS
ALGEBRA AND TRIGONOMETRY
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