Learning Objectives

Each chapter is divided into multiple sections (or modules), each of which is organized around a set of learning objectives. The learning objectives are listed explicitly at the beginning of each section and are the focal point of every instructional element

Narrative text

Narrative text is used to introduce key concepts, terms, and definitions, to provide real-world context, and to provide transitions between topics and examples. Throughout this book, we rely on a few basic conventions to highlight the most important ideas:

• Key terms are boldfaced, typically when first introduced and/or when formally defined.
• Key concepts and definitions are called out in a blue box for easy reference.

Examples

Each learning objective is supported by one or more worked examples that demonstrate the problem-solving approaches that students must master. The multiple Examples model different approaches to the same type of problem, or introduce similar problems of increasing complexity.  Embedded videos and knowledge checks are built into the text to make it an interactive experience for the student.

Supporting Features

Three unobtrusive but important features contribute to and check understanding.

• A “How To” is a list of steps necessary to solve a certain type of problem. A How To typically precedes an Example that proceeds to demonstrate the steps in action.
•  A “Try It” exercise immediately follows an Example or a set of related Examples, providing the student with an immediate opportunity to solve a similar problem. In the Web View version of the text, students can click an Answer link directly below the question to check their understanding. In the PDF, answers to the Try-It exercises are located in the Answer Key.
•  A Q&A may appear at any point in the narrative, but most often follows an Example. This feature pre-empts misconceptions by posing a commonly asked yes/no question, followed by a detailed answer and explanation.

Section Features

Each section of every chapter concludes with a review of most import take-aways as well as a set of exercises.

• Key Terms provides a formal definition for each bold-faced term in the chapter.
• Key Equations presents a compilation of formulas, theorems, and standard-form equations.
• Key Concepts summarizes the most important ideas introduced in each section, linking back to the relevant Example(s) in case students need to review.

Sections Exercises

Each section of every chapter concludes with a well-rounded set of exercises that can be assigned as homework or used selectively for guided practice. Section Exercises are organized by question type, and generally appear in the following order:

• Verbal questions assess conceptual understanding of key terms and concepts.
• Algebraic problems require students to apply algebraic manipulations demonstrated in the section.
• Graphical problems assess students’ ability to interpret or produce a graph.
• Numeric problems require the student to perform calculations or computations.
• Technology problems encourage exploration through use of a graphing utility, either to visualize or verify algebraic results or to solve problems via an alternative to the methods demonstrated in the section.
• Extensions pose problems more challenging than the Examples demonstrated in the section. They require students to synthesize multiple learning objectives or apply critical thinking to solve complex problems.
• Real-World Applications present realistic problem scenarios from fields such as physics, geology, biology, finance, and the social sciences.

Chapter Review Features

Each chapter concludes with additional practice problems that students can use to prepare for exams.

• Chapter Review Exercises include 40-80 practice problems that recall the most important concepts from each section.
• Practice Test includes 25-50 problems assessing the most important learning objectives from the chapter. Note that the practice test is not organized by section, and may be more heavily weighted toward cumulative objectives as opposed to the foundational objectives covered in the opening sections.

This Introduction section was adapted from: “Preface.” Algebra and Trigonometry, 2nd ed., OpenStax, https://openstax.org/books/algebra-and-trigonometry-2e/pages/preface. Accessed 16 Dec. 2024.

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