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Precalculus, American: syllabus

The lessons in book order, one card per unit. Open any lesson that has an episode if you have access; locked lessons are greyed out.

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Chapter 1: Functions

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  1. Functions and Function Notation

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  2. Domain and Range

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  3. Rates of Change and Behavior of Graphs

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  4. Composition of Functions

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  5. Transformation of Functions

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  6. Absolute Value Functions

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  7. Inverse Functions

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Chapter 2: Linear Functions

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  1. Linear Functions

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  2. Graphs of Linear Functions

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  3. Modeling with Linear Functions

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  4. Fitting Linear Models to Data

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Chapter 3: Polynomial and Rational Functions

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  1. Complex Numbers

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  2. Quadratic Functions

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  3. Power Functions and Polynomial Functions

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  4. Graphs of Polynomial Functions

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  5. Dividing Polynomials

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  6. Zeros of Polynomial Functions

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  7. Rational Functions

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  8. Inverses and Radical Functions

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  9. Modeling Using Variation

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Chapter 4: Exponential and Logarithmic Functions

8 lessonsno episodes yet
  1. Exponential Functions

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  2. Graphs of Exponential Functions

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  3. Logarithmic Functions

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  4. Graphs of Logarithmic Functions

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  5. Logarithmic Properties

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  6. Exponential and Logarithmic Equations

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  7. Exponential and Logarithmic Models

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  8. Fitting Exponential Models to Data

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Chapter 5: Trigonometric Functions

4 lessonsno episodes yet
  1. Angles (degrees and radians)

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  2. Unit Circle: Sine and Cosine Functions

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  3. The Other Trigonometric Functions

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  4. Right Triangle Trigonometry

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Chapter 6: Periodic Functions

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  1. Graphs of the Sine and Cosine Functions

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  2. Graphs of the Other Trigonometric Functions

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  3. Inverse Trigonometric Functions

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Chapter 7: Trigonometric Identities and Equations

6 lessonsno episodes yet
  1. Simplifying and Verifying Trigonometric Identities

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  2. Sum and Difference Identities

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  3. Double-Angle, Half-Angle, and Reduction Formulas

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  4. Sum-to-Product and Product-to-Sum Formulas

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  5. Solving Trigonometric Equations

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  6. Modeling with Trigonometric Functions

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Chapter 8: Further Applications of Trigonometry

8 lessonsno episodes yet
  1. Non-right Triangles: Law of Sines

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  2. Non-right Triangles: Law of Cosines

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  3. Polar Coordinates

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  4. Polar Coordinates: Graphs

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  5. Polar Form of Complex Numbers

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  6. Parametric Equations

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  7. Parametric Equations: Graphs

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  8. Vectors

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Chapter 9: Systems of Equations and Inequalities

8 lessonsno episodes yet
  1. Systems of Linear Equations: Two Variables

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  2. Systems of Linear Equations: Three Variables

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  3. Systems of Nonlinear Equations and Inequalities: Two Variables

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  4. Partial Fractions

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  5. Matrices and Matrix Operations

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  6. Solving Systems with Gaussian Elimination

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  7. Solving Systems with Inverses

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  8. Solving Systems with Cramer's Rule

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Chapter 10: Analytic Geometry

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  1. The Ellipse

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  2. The Hyperbola

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  3. The Parabola

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  4. Rotation of Axes

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  5. Conic Sections in Polar Coordinates

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Chapter 11: Sequences, Probability and Counting Theory

7 lessonsno episodes yet
  1. Sequences and Their Notations

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  2. Arithmetic Sequences

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  3. Geometric Sequences

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  4. Series and Their Notations (sigma notation)

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  5. Counting Principles (permutations and combinations)

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  6. Binomial Theorem

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  7. Probability

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Chapter 12: Introduction to Calculus

4 lessonsno episodes yet
  1. Finding Limits: Numerical and Graphical Approaches

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  2. Finding Limits: Properties of Limits

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  3. Continuity

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  4. Derivatives

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