Advanced Algebra with Trigonometry

Notes

Ch 1: Review of the Real Number System

1. Basic Concepts

2. Operations on Real Numbers

3. Exponent, Roots, and Order of Operation

4. Properties of Real Numbers

Ch 2: Linear Equations, Inequalities, and Applications

1. Linear Equations in One Variable

2. Formulas

3. Applications of Linear Equations

4. Linear Inequalities in One Variable

5. Set Operations and Compound Inequalities

6. Absolute Value Equations and Inequalities

Ch 3: Graphs, Linear Equations, and Functions

1. The Rectangular Coordinate System

2. The Slope of a Line

3. Linear Equation in Two Variables

4. Linear Inequalities in Two Variables

5. Introduction to Functions

Ch 4: Systems and Matrices

1. Systems of Linear Equations in Two Variables

2. Systems of Linear Equations in Three Variables

3. Solving Systems of Linear Equations by Matrix Methods

4. Properties of Matrices

5. Matrix Inverses

6. Determinants and Cramer’s Rule

Ch 5: Exponents, Polynomials, and Polynomial Functions

1. Integer Exponents and Scientific Notation

2. Adding and Subtracting Polynomials

3. Polynomial Functions, Graphs, and Composition

4. Multiply Polynomials

5. Dividing Polynomials

Ch 6: Factoring

1. Greatest Common Factors; Factoring by Grouping

2. Factoring Trinomials

3. Special Factoring

4. A General Approach to Factoring

5. Solving Equations by Factoring

Ch 7: Rational Expressions and Functions

1. Part 1: Rational Expressions and Functions;  Part 2: Multiplying and Dividing

2. Adding and Subtracting Rational Expressions

3. Complex Fractions

4. Equations with Rational Expressions and Graphs

5. Applications of Rational Expressions

6. Variation

Ch 8: Roots, Radicals, and Root Functions

1. Radical Expressions and Graphs

2. Rational Exponents

3. Simplifying Radical Expressions

4. Adding and Subtracting Radical Expressions

5. Multiplying and Dividing Radical Expressions

6. Solving Equations with Radicals

7. Complex Numbers

Ch 9: Quadratic Equations and Inequalities

1. The Square Root Property and Completing the Square

2. The Quadratic Formula

3. Equations in Quadratic Form

4. Formulas and Further Applications

5. Quadratic and Rational Inequalities

Ch 10: Additional Graphs of Functions and Relations

1. Review of Operations and Composition

2. Graphs of Quadratic Functions

3. More about Parabolas and Their Applications

4. Symmetry; Increasing and Decreasing Functions

5. Piecewise Linear Functions

Ch 11: Inverse, Exponential, and Logarithmic Functions

1. Inverse Functions

2. Exponential Functions

3. Logarithmic Functions

4. Properties of Logarithms

5. Common and Natural Logarithms

6. Exponential and Logarithmic Equations; Further Applications

Ch 12: Polynomial and Rational Functions

1. Synthetic Division

2. Zeros of Polynomial Functions

3. Graphs and Applications of Polynomial Functions

4. Graphs and Applications of Rational Functions

Ch 13: Conic Sections and Nonlinear Systems

1. The Circle and the Ellipse

2. The Hyperbola and Functions Defined by Radicals

3. Nonlinear Systems of Equations

Ch 14: Trigonometric Functions

1. Angles

2. Angle Relationships and Similar Triangles

3. Trigonometric Functions

4. Using the Definitions of the Trigonometric Functions

Ch 15: Acute Angles and Right Triangles

1. Trigonometric Functions of Acute Angles

2. Trigonometric Functions of Non-Acute Angles

3. Finding Trigonometric Function Values Using a Calculator

4. Solving Right Triangles

Ch 16: Radian Measure and Circular Functions

1. Radian Measure

2. Applications of Radian Measure

3. The Unit Circle and Circular Functions

4. Linear and Angular Speed

Ch 17: Graphs of the Circular Functions

1. Graphs of the Sine and Cosine Functions

2. Translations of the Graphs of the Sine and Cosine Functions

3. Graphs of the Tangent and Cotangent Functions

4. Graphs of the Secant and Cosecant Functions

Ch 18: Trigonometric Identities

1. Fundamental Identities

2. Verifying Trigonometric Identities

3. Sum and Difference Identities for Cosine

4. Sum and Difference Identities for Sine and Tangent

5. Double-Angle Identities

6. Half-Angle Identities

Ch 19: Inverse Circular Functions and Trigonometric Equations

1. Inverse Circular Functions

2. Trigonometric Equations I

3. Trigonometric Equations II

Ch 20: Oblique Triangles and Vectors

1. Oblique Triangles and the Law of Sines

2. The Ambiguous Case of the Law of Sines

3. The Law of Cosines

4. Vectors