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 is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This task provides a simple but interesting and realistic context in which students are led to set up a rational equation (and a rational inequality) in one variable, and then solve that equation/inequality for an unknown variable.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

An interactive applet and associated web page that shows how triangles that have two angles and their included side the same must be congruent. The applet shows two triangles, one of which can be reshaped by dragging any vertex. The other changes to remain congruent to it and the two angles and the included side are outlined in bold to show they are the same measure and are the elements being used to prove congruence. The web page describes all this and has links to other related pages. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

ASLCORE is a Deaf-centric project which honors and celebrates Deaf culture and American Sign Language. The suggested signs you see in each ASLCORE branch are developed according to ASL linguistic principles by fluent Deaf ASL signers. Our goal is to provide descriptive signs which may serve to complement other initialized or English-influenced sign choices. These signs are presented for your consideration, modification, and adoption if they function well in your work as students, professionals, teachers, or interpreters! Copyrighted -link out or conduct a Fair Use Analysis.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The profit, $P$ (in thousands of dollars), that a company makes selling an item is a quadratic function of the price, $x$ (in dollars), that they charg...

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"The transcription factor ATF5 plays a vital role in the formation of several cancers, including breast, lung, ovarian, pancreatic, rectal, and liver cancer. But ATF5’s function in esophageal cancer—one of the most common forms of cancer worldwide—remains unclear. To find out, researchers monitored the activity of ATF5 in esophageal cancer tissues. Much like in other cancers, ATF5 was upregulated in esophageal cancer tissues cultured in the lab, and ATF5 overexpression promoted the proliferation, migration, and invasiveness of esophageal cancer cells. Silencing ATF5, however, inhibited these abilities. In fact, in mice, silencing ATF5 hampered tumor growth. ATF5’s role as a lever that triggers tumor growth is believed to occur through an interaction with HIF1, a protein complex also known to promote the growth and spread of tumors. These findings suggest that the known anti-cancer effects of silencing ATF5 might also be powerful against esophageal cancer..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

In this seminar you will read closely and analyze the structure of ATP- Adenosine Triphosphate. You will curate your own  information about the importance of ATP in a cell by listening and reading text as to what the experts have to say.  By modeling the function of ATP in an inquiry lab you can accurately identify the  various levels of cellular work done by Adenosine Triphosphate.StandardsBIO.A.3.1.1 Describe the fundamental roles of plastids (e.g., chloroplasts) and mitochondria in energy transformations.BIO.A.3.2.1 Compare and contrast the basic transformation of energy during photosynthesis and cellular respiration.BIO.A.3.2.2 Describe the role of ATP in biochemical reactions

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"The non-receptor tyrosine kinase Abelson (Abl) is a key player in oncogenesis, causing diseases including chronic myelogenous and acute lymphoblastic leukemia. Drugs targeting Abl kinase activity serve as paradigms of targeted therapy. Drosophila is an ideal model for studying Abl’s function because there is only a single fly Abl family member. In flies, Abl is essential for embryonic morphogenesis, playing diverse roles in embryonic and adult viability. To examine the role of the intrinsically disordered region (IDR) of Abl, researchers deleted the IDR in Drosophila. They found that Abl lacking the IDR was not able to rescue the roles of Abl in viability and embryonic morphogenesis. The IDR was also essential for cell shape changes and cytoskeletal regulation during embryonic morphogenesis and, surprisingly, for modulating protein stability..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

The abomasum is the fourth chamber in the ruminant. It functions similarly to the carnivore stomach as it is glandular and digests food chemically, rather than mechanically or by fermentation like the other 3 chambers of the ruminant stomach.

Aboriginal Hand Print
(art + history; art + social studies)
"One old man in Arnhem Land remembered being carried as a child on his father's shoulders as his father climbed up a log leaning against a rock wall. His father then sprayed his hand with red ochre against the rock, leaving a stencil he could still recognize many years later. The main function of the stencils was to record people's presence and association with a site." — Aboriginal Art Online

The stenciled hand print and aboriginal style drawings help children to relate to the man from the Australian Aboriginal Culture stated above, while helping them to understand the use of line in art. A black paper with white splattered paint was used, but white paper with red (ochre) splattered paint would make a nice impression also. Construction paper crayons make bright, bold, linear designs around the hand stencil.

Grade Levels K-4

Understanding accessible formats requires some background knowledge of the barriers many learners with disabilities experience when reading or accessing information in print-based and certain digital-based materials.

"Text-based" refers to materials with static or fixed text and images, such as textbooks and supplemental text materials. Both print and digital materials can be text-based. For example, an electronic textbook that replicates a standard print textbook is considered a text-based material.

Books in standard print are common examples of text-based materials. To successfully use print, learners need functional skills related to sensory, physical, and cognitive abilities. Some learners may have visual disabilities that make it difficult to see the text and images on the page. Other learners may be unable to hold printed materials because of a physical disability. Still others may be unable to read or derive meaning from the printed text because of a learning disability.

Certain digital materials also have text and images. Specifically, text-based digital materials are not consistently designed for use with assistive technology (AT). Some learners use AT to read and navigate text and images in digital materials. Screen readers, text to speech, and switches are a few examples of AT devices and software that learners with a wide range of disabilities use. To prevent barriers for learners who use AT, see Vetting for Accessibility.

Because of the frequent barriers presented by text-based materials, some learners with disabilities need alternative forms, known as accessible formats. Examples of accessible formats include audio, braille, large print, tactile graphics, and digital text conforming with accessibility standards.

The term accessible format is defined in section 121 of the Copyright Act, known as the Chafee Amendment: