Precalculus is intended for college-level Precalculus students. Since Precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing a College Algebra and Trigonometry title tailored to the particular scope, sequence, and pedagogy of those courses.

Precalculus is intended for college-level Precalculus students. Since Precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing a College Algebra and Trigonometry title tailored to the particular scope, sequence, and pedagogy of those courses.

This short video and interactive assessment activity is designed to teach fourth graders about estimating measure by image: centimeters or meters?.

Students learn that buoyancy is responsible for making boats, hot air balloons and weather balloons float. They calculate whether or not a boat or balloon will float, and calculate the volume needed to make a balloon or boat of a certain mass float. Conduct the first day of the associated activity before conducting this lesson.

This short video and interactive assessment activity is designed to teach fourth graders about estimating measure by description - multiple choice.

This math problem determines the areas of simple and complex planar figures using measurement of mass and proportional constructs. Materials are inexpensive or easily found (poster board, scissors, ruler, sharp pencil, right angle), but also requires use of an analytical balance (suggestions are provided for working with less precise weighing tools). This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases. Random sampling (like mixing names in a hat and drawing out a sample) is not a new idea to most students, although the terminology is likely to be new.

An interactive applet and associated web page that describe the Euler line. It shows a triangle whose vertices can be dragged. As you drag them, the centroid, circumcenter and orthocenter move appropriately, showing that they are always collinear, always lying on the Euler line. There are controls to individually turn on the construction lines for each center. This helps visualize the concept since if they are all drawn at once, the diagram would be hopelessly confused. The web page has a full description the Euler line and has links to separate pages which go into each center in depth. Applet can be enlarged to full screen size for use with a classroom projector. Diagram can be printed. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

We express the exponential function of an imaginary variable in terms of sine and cosine. The "complex exponentials" that result trace out a circle in the complex plane. Pointing to one of the positions in the complex plane, we obtain the identity exp(i pi) = -1.

In the first video segment, we introduce Euler's number by considering the problem of interest compounded continuously. After we obtain the power-series representation for exp(x), we explore its properties, in the next four video segments, to convince ourselves that exp(x) is literally an exponential function, meaning a number, approximately 2.71828, taken to the power x. In the final two segments, we present the natural logarithm and demonstrate that it is the anti-derivative of 1/x.

In the first video segment, we analyze the population dynamics for a test-tube of cells that affect each others' likelihoods of replication when they collide. The particular example we use is a prisoner's dilemma, which has the almost paradoxical property that survival of the relatively most fit leads overall fitness to decrease. In the second video segment, we suggest that the population dynamics from the first segment can be related to an analysis that uses payoff matrices found in traditional game theory.

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.

Using the 5E instructional model, students discover the value of using color maps to visualize data. The activity requires students to create a color map of the ozone hole from Dobson data values derived from the Aura satellite. Students then interpret that map and compare and evaluate different color scales. Note that this is the Spanish version of Exploring Color Maps: Using Stratospheric Ozone Data.

Through the use of the 5E instructional model, students discover the value of using color maps to visualize data. The activity requires students to create a color map of the ozone hole from Dobson data values derived from the Aura satellite. Students then interpret that map and compare and evaluate different color scales.

This is a collection of mathematics problems relating to the moons of the solar system. Learners will use simple proportional relationships and work with fractions to study the relative sizes of the larger moons in our solar system, and explore how temperatures change from place to place using the Celsius and Kelvin scales.

In this activity, student teams explore connections between parts of the Earth system, by examining a time series of environmental data maps. By examining scientific visualizations of a data pair in two time slices, they will see that the environment is the result of the interplay among many processes that take place on varying time and spatial scales. This is one of six interrelated learning activities associated with the GLOBE Earth System Poster, Exploring Connections in Year 2007, which also includes a series of assessment and extension activities. GLOBE (Global Learning and Observation to Benefit the Environment) is a worldwide, hands-on, K-12 school-based science education program.

In this activity, student teams explore connections between parts of the Earth system, by examining a time series of environmental data maps. Each team examines a single variable displayed on a global data map, and identify the unit of measure, the range of values, and patterns they observe in the data. Variables include: insolation, surface temperature, precipitation, cloud fraction, aerosols, biopshere. This is one of six interrelated learning activities associated with the GLOBE Earth System Poster, "Exploring Connections in Year 2007," and includes a series of assessment and extension activities. GLOBE (Global Learning and Observation to Benefit the Environment) is a worldwide, hands-on, K-12 school-based science education program.

This book introduces students to some of the most unusual places in our galaxy outside of our solar system. Answering the question, "How many stars are in the sky?" introduces students to basic counting, tallying, and grouping techniques, as well as allowing for the use of simple proportions.

Students will explore time series plots and raw data to understand the role of sea surface temperature increases on arctic ice melt. This is part three of a four-part activity on polar science. The activity builds on the knowledge gained in Using Data and Images to Understand Albedo (part 2). Extension activities examining air and sea surface temperature in relation to changing Earth albedo are included. Information is provided on data access using the NOAA Earth System Research Laboratory Web site. This activity is one of several learning activities connected with the 2007 GLOBE Earth system poster.