Highschool Math -- Does this exist?

[Mr. G]

I want a link or a book or anything that concisely shows how/why the standard highschool math formulas relate to one another in a brief guide.

It's important that this not be spread out over the course of a whole book.

I need to know where I can find this information summarized.

 

Does anyone know where I can find such a source?

[regentrude]

What do you mean by "the standard high school math formulas"???

[purplelily]

Are you looking for something like this?

 

https://www.pinterest.com/pin/389209592771498133/

[Mr. G]

What do you mean by "the standard high school math formulas"???

Formulae? :unsure: I mean...hmmm, how to explain...I'm probably not using the correct terminology. "Highschool math" is my  short way of saying Algebra, Geometry, and Trigonometry and Calculus.

You know how the formula for the area of a triangle is related from the formula for the area of a square?

Or how the distance formula is related to/taken from the Pythagorean theorem? Similarly to how we can use a right triangle in a circle to understand the formula for a circle?

 

 

Are you looking for something like this?

 

https://www.pinterest.com/pin/389209592771498133/

No, those types of charts do not come close to talking about the relationship between the various algebraic/geometry formulas/concepts etc...

 

 

[regentrude]

Formulae? :unsure: I mean...hmmm, how to explain...I'm probably not using the correct terminology. "Highschool math" is my  short way of saying Algebra, Geometry, and Trigonometry and Calculus.

You know how the formula for the area of a triangle is related from the formula for the area of a square?

Or how the distance formula is related to/taken from the Pythagorean theorem? Similarly to how we can use a right triangle in a circle to understand the formula for a circle?

 

I do not believe that what you want is even possible. There are so many different equations for different things one could derive that it would be impossible to "list" all the relationships between them.

The trig identities alone can fill a page, and they can be related to one another in various different ways, derived geometrically, some can be easily found from the definitions of sine/cosine, and all easiest from the exponential form.

 

Learning HOW to make the connections is what takes four years of high school math.

 

 

[Mr. G]

I do not believe that what you want is even possible. :( Figures as much. There are so many different equations for different things one could derive that it would be impossible to "list" all the relationships between them.

Do you know of anything that comes close to doing it with at least some of the common HS formulas? What about for just algebra and geometry?

 

The trig identities alone can fill a page, and they can be related to one another in various different ways, derived geometrically, some can be easily found from the definitions of sine/cosine, and all easiest from the exponential form.

Do you know of anything that walks through some of the trig formulas and how they are related?

 

Learning HOW to make the connections is what takes four years of high school math.I wish that there was a nice conceptual refresher type book on the content though. Digging through textbooks is cumbersome when I just want to grab one or two things from Chapters 6 and 11 to give a broader view of the concept in chapter 2.

 

 

[regentrude]

Sorry, I still do not fully understand what it is that you envision.

 

In any trig text, there will be a section that explains how to derive/prove the trig identities, starting from a small subset or just the definitions.

And with the simple tool of the exponential form, they all derive rather quickly from the definition of sine and cosine.

 

And in algebra, I don't know what "formulas" there would even be -a side from the quadratic formula, which can be obtained from factoring.

 

 

Edited September 11, 2016 by regentrude

[Emerald Stoker]

Would this book be any use to you, Mr. G? (In case the link doesn't work: George F. Simmons, Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry, Wipf and Stock, 2003.) It's only 128 pages, so maybe?

http://wipfandstock.com/precalculus-mathematics-in-a-nutshell-geometry-algebra-trigonometry.html 

 

ETA the Amazon link: https://www.amazon.com/Precalculus-Mathematics-Nutshell-Geometry-Trigonometry/dp/1592441300/ref=mt_paperback?_encoding=UTF8&me=

Edited September 11, 2016 by Emerald Stoker

[Mr. G]

Would this book be any use to you, Mr. G? (In case the link doesn't work: George F. Simmons, Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry, Wipf and Stock, 2003.) It's only 128 pages, so maybe?

http://wipfandstock.com/precalculus-mathematics-in-a-nutshell-geometry-algebra-trigonometry.html 

 

Thanks!  I'm not sure but this could be a lead. I'll read over the preview in more depth.

[Emerald Stoker]

You're welcome! I hope it will be useful.

[almondbutterandjelly]

Maybe google "Unit Circle" and see if that gets you what you want.

 

 

[daijobu]

We've just been learning about polar, cylindrical, and spherical coordinates in AoPS PreCalculus.  Take a look at chapter 5.  You'll find algebraic equations that represent curves and lines or 2d surfaces in 3d space.  You'll learn how to express x,y,z coordinates in terms of other parameters (angles and distances) using the pythagorean theorem and trig identities.  Lots of good stuff from many different areas brought together.  

[daijobu]

I just thought of another source of problems that use many different aspects of math.  Look at the solutions to the harder AMC 12s or the AIMEs and Putnams.  

 

Here's an example of a problem that  requires the understanding of:

 

recursively defined functions

logarithms and exponents

modular arithmetic

Fermat's Little Theorem

 

 

 

 

[Pen]

Some appendix and glossary or similar sections from big high school  textbooks cover a lot without having to go through the whole book itself.    Might that help?

 

Or, not brief and concise, but a math encyclopedia might at least have this sort of information in an accessible and organized way.

 

Probably way too brief, but we had a high school planner that had a Mathematics reference section with some of this sort of information.