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Pre-Calculus
1. Relations and Functions
1.1. Sets of Real Numbers and the Cartesian Coordinate Plane
1.2. Relations
1.3. Introduction to Functions
1.4. Function Notation
1.5. Function Arithmetic
1.6. Graphs of Functions
1.7. Transformations
Review
Test
2. Linear and Quadratic Functions
2.1. Linear Functions
2.2. Absolute Value Functions
2.3. Quadratic Functions
2.4. Inequalities with Absolute Value and Quadratic Functions
2.5. Regression
Review
Test
3. Polynomial Functions
3.1. Graphs of Polynomials
3.2. The Factor Theorem and the Remainder Theorem
3.3. Real Zeros of Polynomials
3.4. Complex Zeros and the Fundamental Theorem of Algebra
Review
Test
4. Rational Functions
4.1. Introduction to Rational Functions
4.2. Graphs of Rational Functions
4.3. Rational Inequalities and Applications
Review
Test
5. Further Topics in Functions
5.1. Function Composition
5.2. Inverse Functions
5.3. Other Algebraic Functions
Review
Test
6. Exponential and Logarithmic Functions
6.1. Introduction to Exponential and Logarithmic Functions
6.2. Properties of Logarithms
6.3 Exponential Equations and Inequalities
6.4. Logarithmic Equations and Inequalities
6.5. Applications of Exponential and Logarithmic Functions
Review
Test
7. Hooked on Conics
7.1. Introduction to Conics
7.2. Circles
7.3. Parabolas
7.4. Ellipses
7.5. Hyperbolas
Review
Test
8. Systems of Equations and Matrices
8.1. Systems of Linear Equations: Gaussian Elimination
8.2. Systems of Linear Equations: Augmented Matrices
8.3. Matrix Arithmetic
8.4. Systems of Linear Equations: Matrix Inverses
8.5. Determinants and Cramer's Rule
8.6. Partial Fraction Decomposition
8.7. Systems of Non-Linear Equations and Inequalities
Review
Test
9. Sequences and the Binomial Theorem
9.1. Sequences
9.2. Summation Notation
9.3. Mathematical Induction
9.4. The Binomial Theorem
Review
Test
10. Foundations of Trigonometry
10.1. Angles and their Measure
10.2. The Unit Circle: Cosine and Sine
10.3. The Six Circular Functions and Fundamental Identities
10.4. Trigonometric Functions
10.5. Graphs of the Trigonometric Functions
10.6. The Inverse Trigonometric Functions
10.7. Trigonometric Equations and Inequalities
Review
Test
11. Applications of Trigonometry
11.1. Applications of Sinusoids
11.2 The Law of Sines
11.3. The Law of Cosines
11.4. Polar Coordinates
11.5. Graphs of Polar Equations
11.6. Hooked on Conics Again
11.7. Polar Form of Complex Numbers
11.8. Vectors
11.9. The Dot Product and Projection
11.10. Parametric Equations
Review
Test
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2.2. Absolute Value Functions
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