This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
This text is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. The reader will find that the text requires them to engage actively with the material, to view topics from multiple perspectives, and to develop deep conceptual understanding of ideas.
Many courses at the high school and college level with titles such as “college algebra”, “precalculus”, and “trigonometry” serve other disciplines and courses other than calculus. As such, these prerequisite classes frequently contain wide-ranging material that, while mathematically interesting and important, isn't necessary for calculus. Perhaps because of these additional topics, certain ideas that are essential in calculus are under-emphasized or ignored.
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
This OER is a list of Discussion Questions for a PreCalculus course using the OpenStax PreCalculus Textbook. There are eight discussion questions included in the Word document which has the equations better formatted.
Attached is an .imscc file that can be used to build a Jenzabar eLearning course shell for MATH 2412 PreCalculus using OpenStax's Precalculus textbook.This project was provided by Larry Whittington of North American University (www.na.edu)Email: email@example.comYouTube Channel: www.youtube.com/@FortBendTutoring
This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.
Mathematics, as we all know, is the language of science, and fluency in algebraic skills has always been necessary for anyone aspiring to disciplines based on calculus. But in the information age, increasingly sophisticated mathematical methods are used in all fields of knowledge, from archaeology to zoology. Consequently, there is a new focus on the courses before calculus. The availability of calculators and computers allows students to tackle complex problems involving real data, but requires more attention to analysis and interpretation of results. All students, not just those headed for science and engineering, should develop a mathematical viewpoint, including critical thinking, problem-solving strategies, and estimation, in addition to computational skills. Modeling, Functions and Graphs employs a variety of applications to motivate mathematical thinking.
This collection of worksheets, homework assignments, and study skills exercises was created through a Round 14 Textbook Transformation Grant. The worksheets supplement the following topics as covered in OpenStax Precalculus: Functions, domain and range, rates of change, inverse functions, exponential functions, logarithmic functions, exponential growth modeling, angles, sine and cosine, right triangles, sum identities, and difference identities. Study skills exercises include growth mindset and metacognition activities.
Unit 1: Composite and inverse functions
Unit 2: Trigonometry
Unit 3: Complex numbers
Unit 4: Rational functions
Unit 5: Conic sections
Unit 6: Vectors
Unit 7: Matrices
Unit 8: Probability and combinatorics
Unit 9: Series
Unit 10: Limits and continuity
Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is 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.
There are key differences between the way teaching and learning takes place in high schools and universities. Our goal is much more than just getting you to reproduce what was done in the classroom. Here are some key points to keep in mind:
• The pace of this course will be faster than a high school class in precalculus. Above that, we aim for greater command of the material, especially the ability to extend what we have learned to new situations.
• This course aims to help you build the stamina required to solve challenging and lengthy multi-step problems.
• As a rule of thumb, this course should on average take 15 hours of effort per week. That means that in addition to the 5 classroom hours per week, you would spend 10 hours extra on the class. This is only an average and my experience has shown that 12–15 hours of study per week (outside class) is a more typical estimate. In other words, for many students, this course is the equivalent of a halftime job!
• Because the course material is developed in a highly cumulative manner, we recommend that your study time be spread out evenly over the week, rather than in huge isolated blocks. An analogy with athletics is useful: If you are preparing to run a marathon, you must train daily; if you want to improve your time, you must continually push your comfort zone.
From the preface, "These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems."
Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.
This is a focused collection of notes for a course in precalculus math taught at San Jacinto College (Houston, Texas). In less than 260 pages, the course offers a compact delivery of the core concepts that students ought to understand prior to taking calculus. In addition to learning algebraic and computational skills, the course is designed for learning how to think mathematically. The chapters on mathematical language and problem-solving highlight this latter objective.
These open-source mathematics assignments are created to be used through the WeBWorK open-source online homework system. The assignments correspond to selected sections in the OpenStax Precalculus textbook. They were created with the help of a 2020-2022 Open Educational Resources (OER) Course Development and Implementation Grant Program through the Texas Higher Education Coordinating Board.
This is an example of a redesigned course that uses the OpenStax PreCaculus Textbook. Emphasis is placed on the structure of course (which is not conics centric) and how homework is implemented. To avoid the financial responsiblity of the student or higher education institution purchasing publisher online homework services like Pearson's MyMathLab, ConnectMath or Aleks; students are assigned exercises from the textbook that have answers available. The strategy is to give access to the answers of the problems so that the students have to prove how the answer was obtained. This allows the students some immediate feedback if their written process does not obtain the solution given in the back of the textbook.This allows the student to recognize that a process, operation or strategy was carried out incorrectly which can be used to draw attention that a question needs to be raised during the next lecture or additional assistance may be required on their journey to mastery of the content.
This is a list of video lectures that can be used in conjunction with OpenStax's PreCalculus Textbook that gives faculty and students addtional resources to utilize throughout the semester of a PreCalculus course. MATH 2412 and MATH 1313 PreCalculus courses among others may benefit from this resource.