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Precalculus

Paul Sisson

Precalculus starts off with several lessons familiar to students coming from a college algebra course—reviewing topics like linear inequalities, quadratic equations, and inverses of functions—before covering more advanced topics to prepare them for calculus. The text explains elements of trigonometry in detail.

Formats: Software, Textbook, eBook, Guided Notebook

Product ISBN
Software + eBook 978-1-941552-91-9
Software + eBook + Guided Notebook 978-1-946158-43-7
Software + eBook + Textbook 978-1-941552-90-2

Resources

  1. Formulas

Table of Contents

  1. 1 Number Systems and Equations of One Variable
    1. 1.1a The Real Number System
    2. 1.1b The Arithmetic of Algebraic Expressions
    3. 1.2a Properties of Exponents
    4. 1.2b Scientific Notation and Geometric Problems Using Exponents
    5. 1.2c Properties of Radicals
    6. 1.2d Rational Number Exponents
    7. 1.3 Polynomials and Factoring
    8. 1.4 The Complex Number System
    9. 1.5a Linear Equations in One Variable
    10. 1.5b Applications of Linear Equations in One Variable
    11. 1.6 Linear Inequalities in One Variable
    12. 1.7a Quadratic Equations in One Variable
    13. 1.7b Higher Degree Polynomial Equations
    14. 1.8a Rational Expressions and Equations
    15. 1.8b Radical Equations
    16. Chapter 1 Review and Test
  2. 2 Introduction to Equations and Inequalities of Two Variables
    1. 2.1 The Cartesian Coordinate System
    2. 2.2 Linear Equations in Two Variables
    3. 2.3 Forms of Linear Equations
    4. 2.4 Parallel and Perpendicular Lines
    5. 2.5 Linear Inequalities in Two Variables
    6. 2.6 Introduction to Circles
    7. Chapter 2 Review and Tes
  3. 3 Relations, Functions, and Their Graphs
    1. 3.1 Relations and Functions
    2. 3.2a Linear and Quadratic Functions
    3. 3.2b Max/Min Applications of Quadratic Functions
    4. 3.3 Other Common Functions
    5. 3.4 Variation and Multi-Variable Functions
    6. 3.5 Transformations of Functions
    7. 3.6 Combining Functions
    8. 3.7 Inverses of Functions
    9. Chapter 3 Review and Test
  4. 4 Polynomial Functions
    1. 4.1 Introduction to Polynomial Equations and Graphs
    2. 4.2 Polynomial Division and the Division Algorithm
    3. 4.3 Locating Real Zeros of Polynomials
    4. 4.4 The Fundamental Theorem of Algebra
    5. 4.5a Rational Functions
    6. 4.5b Rational Inequalities
    7. Chapter 4 Review and Test
  5. 5 Exponential and Logarithmic Functions
    1. 5.1 Exponential Functions and Their Graphs
    2. 5.2 Applications of Exponential Functions
    3. 5.3 Logarithmic Functions and Their Graphs
    4. 5.4 Properties and Applications of Logarithms
    5. 5.5 Exponential and Logarithmic Equations
    6. Chapter 5 Review and Test
  6. Unit 6 Trigonometric Functions
    1. 6.1 Radian and Degree Measure of Angles
    2. 6.2 Trigonometric Functions of Acute Angles
    3. 6.3 Trigonometric Functions of Any Angle
    4. 6.4 Graphs of Trigonometric Functions
    5. 6.5 Inverse Trigonometric Functions
    6. Chapter 6 Review and Test
  7. Unit 7 Trigonometric Identities and Equations
    1. 7.1 Fundamental Identities and Their Uses
    2. 7.2 Sum and Difference Identities
    3. 7.3 Product - Sum Identities
    4. 7.4 Trigonometric Equations
    5. Chapter 7 Review and Test
  8. Unit 8 Additional Topics in Trigonometry
    1. 8.1a The Law of Sines and the Law of Cosines
    2. 8.1b Areas of Triangles
    3. 8.2 Polar Coordinates and Polar Equations
    4. 8.3a Parametric Equations - Graphing and Applications
    5. 8.3b Parametric Equations - Eliminating the Parameter
    6. 8.3c Parametric Equations - Constructing Equations
    7. 8.4a Trigonometric Form of Complex Numbers
    8. 8.4b Operations with Complex Numbers
    9. 8.5 Vectors in the Cartesian Plane
    10. 8.6 The Dot Product and Its Uses
    11. Chapter 8 Review and Test
  9. 9 Conic Sections
    1. 9.1 Solving Systems by Substitution and Elimination
    2. 9.2 The Parabola
    3. 9.3 The Hyperbola
    4. 9.4 Rotation of Conics
    5. 9.5 Polar Form of Conic Sections
    6. Chapter 9 Review and Test
  10. 10 Systems of Equations
    1. 10.1 Solving Systems by Substitution and Elimination
    2. 10.2 Matrix Notation and Gaussian Elimination
    3. 10.3 Determinants and Cramer's Rule
    4. 10.4 The Algebra of Matrices
    5. 10.5 Inverses of Matrices
    6. 10.6 Partial Fraction Decomposition
    7. 10.7 Linear Programming
    8. 10.8 Nonlinear Systems of Equations
    9. Chapter 10 Review and Test
  11. 11 An Introduction to Sequences, Series, and Probability
    1. 11.1 Sequences and Series
    2. 11.2 Arithmetic Sequences and Series
    3. 11.3 Geometric Sequences and Series
    4. 11.4 Mathematical Induction
    5. 11.5a An Introduction to Combinatorics - Counting, Permutations, and Combinations
    6. 11.5b An Introduction to Combinatorics - The Binomial and Multinomial Theorems
    7. 11.6 An Introduction to Probability
    8. Chapter 11 Review and Test
  12. Appendix
    1. A.1 Mathematical Models
    2. A.2 Properties of Functions
    3. A.3 Trigonometric Functions and the Unit Circle
    4. A.4 Limits in the Plane