Precalculus

Created by: OpenStax, powered by Möbius

Description

The Precalculus Content Pack is an entire OpenStax textbook that you can use as a customizable starting point to a complete precalculus course in Möbius. This customizable resource includes all traditional OpenStax features such as chapter introductions, sections, review material, and practice tests, and has been enhanced with Möbius capabilities including algorithmic questions, in-lesson questions with unlimited practice, helpful hints, and immediate feedback. This Content Pack is adaptable and designed to fit the needs of a variety of precalculus courses; it’s a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way.

How does Möbius take OpenStax to the next level?

Course Structure

  • All content is organized into 13 units for easy navigation
  • Course materials provide a solid foundation for creating your course offering which include 98 lessons with illustrative visualizations, unlimited practice, helpful hints, and immediate feedback to promote Active Learning
  • Different forms of assessment materials are distributed across 97 assignments to evaluate student comprehension through a variety of different question types
  • Pull from a vast selection of over 2700 questions that you can use to create your own lessons and assignments or supplement existing ones
13 units
98 lessons
97 assignments
2700+ questions

Unit 0: Introductory Materials

Unit 1: Functions

  • Introduction

  • 1.1 Functions and Function Notation

  • 1.2 Domain and Range

  • 1.3 Rates of Change and Behavior of Graphs

  • 1.4 Composition of Functions

  • 1.5 Transformation of Functions

  • 1.6 Absolute Value Functions

  • 1.7 Inverse Functions

  • Chapter 1 Review

Unit 2: Linear Functions

  • Introduction

  • 2.1 Linear Functions

  • 2.2 Graphs of Linear Functions

  • 2.3 Modeling with Linear Functions

  • 2.4 Fitting Linear Models to Data

  • Chapter 2 Review

Unit 3: Polynomial and Rational Functions

  • Introduction

  • 3.1 Complex Numbers

  • 3.2 Quadratic Functions

  • 3.3 Power Functions and Polynomial Functions

  • 3.4 Graphs of Polynomial Functions

  • 3.5 Dividing Polynomials

  • 3.6 Zeros of Polynomial Functions

  • 3.7 Rational Functions

  • 3.8 Inverses and Radical Functions

  • 3.9 Modeling Using Variation

  • Chapter 3 Review

Unit 4: Exponential and Logarithmic Functions

  • Introduction

  • 4.1 Exponential Functions

  • 4.2 Graphs of Exponential Functions

  • 4.3 Logarithmic Functions

  • 4.4 Graphs of Logarithmic Functions

  • 4.5 Logarithmic Properties

  • 4.6 Exponential and Logarithmic Equations

  • 4.7 Exponential and Logarithmic Models

  • 4.8 Fitting Exponential Models to Data

  • Chapter 4 Review

Unit 5: Trigonometric Functions

  • Introduction

  • 5.1 Angles

  • 5.2 Unit Circle: Sine and Cosine Functions

  • 5.3 The Other Trigonometric Functions

  • 5.4 Right Triangle Trigonometry

  • Chapter 5 Review

Unit 6: Periodic Functions

  • Introduction

  • 6.1 Graphs of the Sine and Cosine Functions

  • 6.2 Graphs of the Other Trigonometric Functions

  • 6.3 Inverse Trigonometric Functions

  • Chapter 6 Review

Unit 7: Trigonometric Identities and Equations

  • Introduction

  • 7.1 Solving Trigonometric Equation With Identities

  • 7.2 Sum and Difference Identities

  • 7.3 Double-Angle, Half-Angle, and Reduction Formulas

  • 7.4 Sum-to-Product and Product-to-Sum Formulas

  • 7.5 Solving Trigonometric Equations

  • Chapter 7 Review

Unit 8: Further Applications of Trigonometry

  • Introduction

  • 8.1 Non-Right Triangles: Law of Sines

  • 8.2 Non-right Triangles: Law of Cosines

  • 8.3 Polar Coordinates

  • 8.4 Polar Coordinates: Graphs

  • 8.5 Polar Form of Complex Numbers

  • 8.6 Parametric Equations

  • 8.7 Parametric Equations: Graphs

  • 8.8 Vectors

  • Chapter 8 Review

Unit 9: Systems of Equations and Inequalities

  • Introduction

  • 9.1 Systems of Linear Equations: Two Variables

  • 9.2 Systems of Linear Equations: Three Variables

  • 9.3 Systems of Nonlinear Equations and Inequalities: Two Variables

  • 9.4 Partial Fractions

  • 9.5 Matrices and Matrix Operations

  • 9.6 Solving Systems with Gaussian Elimination

  • 9.7 Solving Systems with Inverses

  • 9.8 Solving Systems with Cramer's Rule

  • Chapter 9 Review

Unit 10: Analytic Geometry

  • Introduction

  • 10.1 The Ellipse

  • 10.2 The Hyperbola

  • 10.3 The Parabola

  • 10.4 Rotation of Axis

  • 10.5 Conic Sections in Polar Coordinates

  • Chapter 10 Review

Unit 11: Sequences, Probability and Counting Theory

  • Introduction

  • 11.1 Sequences and Their Notation

  • 11.2 Arithmetic Sequences

  • 11.3 Geometric Sequences

  • 11.4 Series and Their Notations

  • 11.5 Counting Principles

  • 11.6 Binomial Theorem

  • 11.7 Probability

  • Chapter 11 Review

Unit 12: Introduction to Calculus

  • Introduction

  • 12.1 Finding Limits: Numerical and Graphical Approaches Assignment

  • 12.2 Finding Limits: Properties of Limits

  • 12.3 Continuity

  • 12.4 Derivatives

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