Precalculus

Open source precalculus textbook.

Material Type: Textbook

Authors: Carl Stitz, Jeff Zeager

Precalculus

Prior to 1990, the performance of a student in precalculus at the University of Washington was not a predictor of success in calculus. For this reason, the mathematics department set out to create a new course with a specific set of goals in mind: A review of the essential mathematics needed to succeed in calculus. An emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical tools. This text was created to achieve these goals and the 2004-05 academic year marks the eleventh year in which it has been used. Several thousand students have successfully passed through the course. This book is full of worked out examples. We use the the notation “Soluion.” to indicate where the reasoning for a problem begins; the symbol ?? is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the final examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with ”answers” to most of the problems in the text. It should be emphasized these are ”answers” as opposed to ”solutions”. Any homework problems you may be asked to turn in will require you include all your work; in other words, a detailed solution. Simply writing down the answer from the back of the text would never be sufficient; the answers are intended to be a guide to help insure you are on the right track.

Material Type: Textbook

Authors: David H. Collingwood, K. David Prince, Matthew M. Conroy

Precalculus

Word Count: 5097 (Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Material Type: Textbook

Authors: Mike Weimerskirch, Stan Pride

Precalculus: An Investigation of Functions

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.

Material Type: Textbook

Authors: David Lippman, Melonie Rasmussen

APEX PreCalculus

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.

Material Type: Textbook

Authors: Amy Givler Chapman, Jessica Libertini, Meagan Herald

Precalculus

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."

Material Type: Textbook

Authors: Holly Carley, Thomas Tradler

Modeling, Functions, and Graphs: Algebra for College Students

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.

Material Type: Textbook

Author: Katherine Yoshiwara

Active Prelude to Calculus

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.

Material Type: Textbook

Author: Matthew Boelkins

Precalculus and Advanced Topics Module 2

Module 2 extends the concept of matrices introduced in Module 1.  Students look at incidence relationships in networks and encode information about them via high-dimensional matrices.  Matrix properties are studied as well as the role of the zero and identity matrices.  Students then use matrices to study and solve higher order systems of equations.  Vectors are introduced, and students study the arithmetic of vectors and vector magnitude.  The module ends as students program video games using matrices and vectors.

Material Type: Module

Precalculus and Advanced Topics Module 3

Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions.  They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots of polynomials and roots of unity. Students compare and create different representations of functions while studying function composition, graphing functions, and finding inverse functions. Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Material Type: Module

Precalculus and Advanced Topics Module 4

This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle.  New tools are introduced for solving geometric and modeling problems through the power of trigonometry.  Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.

Material Type: Module

Precalculus and Advanced Topics Module 5

In this module, students build on their understanding of probability developed in previous grades.  In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent.  Students are also introduced to three techniques for counting outcomes.  Topic B presents information related to random variables and discrete probability distributions.  Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts.

Material Type: Module

Trigonometry Lecture Videos (Open Campus Math 112)

These Trigonometry lecture videos coterminal angles, trig functions, quadrantal angles, special acute angles, co-functions, finding theta, reference angles, trig functions, radian measure, arc length, area of a sector, graphing sine and cosine using t-table, amplitude and frequency, phase shift for sine and consine, vertical shift, tangent curve, cotangent transformations, evaluating trig identities, trig expressions, sum and difference for cosine, double and half angle identities, inverse, principal values, solving difficult trig equations, law of cosines, area of a triangle, and vectors and bearing.

Material Type: Lecture

Author: Stacey Black