Precalculus Plus Integrated Review

Paul Sisson

This courseware provides students with curriculum-level precalculus skills integrated with applicable review lessons. This course offers lessons familiar to students entering from a college algebra course, preparing them for the more advanced topics they will cover in a subsequent calculus course while also targeting specific remediation needs for just-in-time supplementation of foundational concepts.

Formats: Software, Textbook, Guided Notebook

Product ISBN
Courseware 978-1-64277-063-6
Courseware + Precalculus Textbook 978-1-64277-064-3
Courseware + Precalculus Guided Notebook 978-1-64277-065-0

Table of Contents

  1. Chapter 1.R: Integrated Review
    1. 1.R.1 Exponents, Prime Numbers, and LCM
    2. 1.R.2 Reducing Fractions
    3. 1.R.3 Multiplication and Division with Fractions
    4. 1.R.4 Addition and Subtraction with Fractions
    5. 1.R.5 Decimals and Percents
    6. 1.R.6 Applications: Number Problems and Consecutive Integers
    7. 1.R.7 Solving Equations: Ratios and Proportions
    8. 1.R.8 Simplifying Radicals
  2. Chapter 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
  3. Chapter 2.R: Integrated Review
    1. 2.R.1 Square Roots and the Pythagorean Theorem
    2. 2.R.2 Formulas in Geometry
  4. Chapter 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
  5. Chapter 3.R: Integrated Review
    1. 3.R.1 Order of Operations
    2. 3.R.2 Variables and Algebraic Expressions
    3. 3.R.3 Simplifying Expressions
    4. 3.R.4 Translating Phrases into Algebraic Expressions
  6. Chapter 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
  7. Chapter 4.R: Integrated Review
    1. 4.R.1 Greatest Common Factor of Two or More Terms
    2. 4.R.2 Factoring Trinomials by Grouping
    3. 4.R.3 Additional Factoring Practice
    4. 4.R.4 Defining Rational Expressions
  8. Chapter 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
  9. Chapter 5.R: Integrated Review
    1. 5.R.1 Simplifying Integer Exponents I
    2. 5.R.2 Simplifying Integer Exponents II
    3. 5.R.3 Rational Exponents
  10. Chapter 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
  11. Chapter 6.R: Integrated Review
    1. 6.R.1 Angles
    2. 6.R.2 Triangles
  12. Chapter 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
  13. Chapter 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
  14. Chapter 8. Additional Topics in Trigonometry
    1. 8.1a The Law of Sines and the Law of Cosines
    2. 8.1b Area 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
  15. Chapter 9.R: Integrated Review
    1. 9.R.1 Special Products
    2. 9.R.2 Special Factorizations - Squares
  16. Chapter 9. Conic Sections
    1. 9.1 The Ellipse
    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
  17. Chapter 10.R: Integrated Review
    1. 10.R.1 Solving Systems of Linear Equations by Graphing
    2. 10.R.2 Systems of Linear Inequalities
  18. Chapter 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
  19. Chapter 11. An Introduction to Sequences, Series, Combinatorics, 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