Algebra and Trigonometry

Description

The Algebra and Trigonometry Content Pack is an entire OpenStax textbook that you can use as a customizable starting point to a complete algebra and trigonometry 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. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses, and is also ideal for an introductory algebra and trigonometry course. This Content Pack explores algebraic principles through a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

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Course Structure

All content is organized into 14 units for easy navigation
Course materials provide a solid foundation for creating your course offering which include 106 lessons with illustrative visualizations, unlimited practice, helpful hints, and immediate feedback to promote Active Learning
Different forms of assessment materials are distributed across 105 assignments to evaluate student comprehension through a variety of different question types
Pull from a vast selection of 3000 questions that you can use to create your own lessons and assignments or supplement existing ones

14 units

106 lessons

105 assignments

3000+ questions

Introductory Materials

Unit 1: Prerequisites

1.1 Real Numbers: Algebra Essentials
1.2 Exponents and Scientific Notation
1.3 Radicals and Rational Expressions
1.4 Polynomials
1.5 Factoring Polynomials
1.6 Rational Expressions

Unit 2: Equations and Inequalities

2.1 The Rectangular Coordinate Systems and Graphs
2.2 Linear Equations in One Variable
2.3 Models and Applications
2.4 Complex Numbers
2.5 Quadratic Equations
2.6 Other Types of Equations
2.7 Linear Inequalities and Absolute Value Inequalities

Unit 3: Functions

3.1 Functions and Function Notation
3.2 Domain and Range
3.3 Rates of Change and Behavior of Graphs
3.4 Composition of Functions
3.5 Transformation of Functions
3.6 Absolute Value Functions
3.7 Inverse Functions

Unit 4: Linear Functions

4.1 Linear Functions
4.2 Modeling with Linear Functions
4.3 Fitting Linear Models to Data

Unit 5: Polynomial and Rational Functions

5.1 Quadratic Functions
5.2 Power Functions and Polynomial Functions
5.3 Graphs of Polynomial Functions
5.4 Dividing Polynomials
5.5 Zeros of Polynomial Functions
5.6 Rational Functions
5.7 Inverses and Radical Functions
5.8 Modeling Using Variation

Unit 6: Exponential and Logarithmic Functions

6.1 Exponential Functions
6.2 Graphs of Exponential Functions
6.3 Logarithmic Functions
6.4 Graphs of Logarithmic Functions
6.5 Logarithmic Properties
6.6 Exponential and Logarithmic Equations
6.7 Exponential and Logarithmic Models
6.8 Fitting Exponential Models to Data

Unit 7: The Unit Circle: Sine and Cosine Functions

7.1 Angles
7.2 Right Angle Trigonometry
7.3 Unit Circle
7.4 The Other Trigonometric Functions

Unit 8: Periodic Functions

8.1 Graphs of the Sine and Cosine Functions
8.2 Graphs of the Other Trigonometric Functions
8.3 Inverse Trigonometric Functions

Unit 9: Trigonometric Identities and Equations

9.1 Solving Trigonometric Equations with Identities
9.2 Sum and Difference Identities
9.3 Double-Angle, Half-Angle, and Reduction Formulas
9.4 Sum-to-Product and Product-to-Sum Formulas
9.5 Solving Trigonometric Equations

Unit 10: Further Applications of Trigonometry

10.1 Non-right Triangles: Law of Sines
10.2 Non-right Triangles: Law of Cosines
10.3 Polar Coordinates
10.4 Polar Coordinates: Graphs
10.5 Polar Form of Complex Numbers
10.6 Parametric Equations
10.7 Parametric Equations: Graphs
10.8 Vectors

Unit 11: Systems of Equations and Inequalities

11.1 Systems of Linear Equations: Two Variables
11.2 Systems of Linear Equations: Three Variables
11.3 Systems of Nonlinear Equations and Inequalities: Two Variables
11.4 Partial Fractions
11.5 Matrices and Matrix Operations
11.6 Solving Systems with Gaussian Elimination
11.7 Solving Systems with Inverses
11.8 Solving Systems with Cramer's Rule

Unit 12: Analytic Geometry

12.1 The Ellipse
12.2 The Hyperbola
12.3 The Parabola
12.4 Rotation of Axis
12.5 Conic Sections in Polar Coordinates

Unit 13: Sequences, Probability and Counting Theory

13.1 Sequences and Their Notations
13.2 Arithmetic Sequences
13.3 Geometric Sequences
13.4 Series and Their Notations
13.5 Counting Principles
13.6 Binomial Theorem
13.7 Probability

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Algebra and Trigonometry

Description

How does Möbius take OpenStax to the next level?

Course Structure

Introductory Materials

Unit 1: Prerequisites

1.1 Real Numbers: Algebra Essentials

1.2 Exponents and Scientific Notation

1.3 Radicals and Rational Expressions

1.4 Polynomials

1.5 Factoring Polynomials

1.6 Rational Expressions

Unit 2: Equations and Inequalities

2.1 The Rectangular Coordinate Systems and Graphs

2.2 Linear Equations in One Variable

2.3 Models and Applications

2.4 Complex Numbers

2.5 Quadratic Equations

2.6 Other Types of Equations

2.7 Linear Inequalities and Absolute Value Inequalities

Unit 3: Functions

3.1 Functions and Function Notation

3.2 Domain and Range

3.3 Rates of Change and Behavior of Graphs

3.4 Composition of Functions

3.5 Transformation of Functions

3.6 Absolute Value Functions

3.7 Inverse Functions

Unit 4: Linear Functions

4.1 Linear Functions

4.2 Modeling with Linear Functions

4.3 Fitting Linear Models to Data

Unit 5: Polynomial and Rational Functions

5.1 Quadratic Functions

5.2 Power Functions and Polynomial Functions

5.3 Graphs of Polynomial Functions

5.4 Dividing Polynomials

5.5 Zeros of Polynomial Functions

5.6 Rational Functions

5.7 Inverses and Radical Functions

5.8 Modeling Using Variation

Unit 6: Exponential and Logarithmic Functions

6.1 Exponential Functions

6.2 Graphs of Exponential Functions

6.3 Logarithmic Functions

6.4 Graphs of Logarithmic Functions

6.5 Logarithmic Properties

6.6 Exponential and Logarithmic Equations

6.7 Exponential and Logarithmic Models

6.8 Fitting Exponential Models to Data

Unit 7: The Unit Circle: Sine and Cosine Functions

7.1 Angles

7.2 Right Angle Trigonometry

7.3 Unit Circle

7.4 The Other Trigonometric Functions

Unit 8: Periodic Functions

8.1 Graphs of the Sine and Cosine Functions

8.2 Graphs of the Other Trigonometric Functions

8.3 Inverse Trigonometric Functions

Unit 9: Trigonometric Identities and Equations

9.1 Solving Trigonometric Equations with Identities

9.2 Sum and Difference Identities

9.3 Double-Angle, Half-Angle, and Reduction Formulas

9.4 Sum-to-Product and Product-to-Sum Formulas

9.5 Solving Trigonometric Equations

Unit 10: Further Applications of Trigonometry

10.1 Non-right Triangles: Law of Sines

10.2 Non-right Triangles: Law of Cosines

10.3 Polar Coordinates

10.4 Polar Coordinates: Graphs

10.5 Polar Form of Complex Numbers

10.6 Parametric Equations

10.7 Parametric Equations: Graphs

10.8 Vectors

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