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- Polynomial and Rational Inequalities
- One-to-One and Inverse Functions
- Exponential Functions
- Logarithms and Logarithmic Functions
- Properties of Logarithms; solving Exponential/Logarithmic Equations
- Angle Measure, Special Triangles, and Special Angles
- Unit Circles and the Trigonometry of Real Numbers
- Graphs of Sine and Cosine Functions; Cosecant and Secant Functions
- Graphs of Tangent and Cotangent Functions
- Transformations and Applications of Trigonometric Graphs
- The Trigonometry of Right Triangles
- Trigonometry and the Coordinate Plane
- Fundamental identities and Families of Identities
- Constructing and Verifying Identities
- The Sum and Difference Identities
- The Double-Angle, Half-Angle, and Product-to-Sum Identities
- The Inverse Trig Functions and Their Applications
- Solving Basic Trig Equations
- General Trig Equations and Applications
- Oblique Triangles and the Law of Sines
- The Law of Cosines; the Area of a Triangle
- Linear Systems in Two Variables with Applications
- Linear Systems in Three Variables with Applications
- Partial Fraction Decomposition
- Solving Linear Systems Using matrices and Row Operations
- Solving Linear Systems Using Matrix Equations (Use determinants to find whether a matrix is invertible)
- Applications of Matrices and Determinants: Cramer’s Rule, Geometry, and More
- The Circle and the Ellipse
- The Hyperbola
- The Analytic Parabola
- Sequences and Series
- Arithmetic Sequences
- Geometric Sequences
- Mathematical Induction
- The Binomial Theorem