# Resources for precalculus applications

Do you know any good sources of free/open application-style problems for the precalculus level?

I would like to use an OER precalculus book, but the few I am most happy with seem to lack (what we would call) application problems. There might be a few here and there in a text, but skill questions dominate the homework section.

So, I am not looking for recommendations for OER precalculus texts, but rather just sources of good problems. Do these exist without the standard expository content found in textbooks? Do feel free to suggest a book if it contains lots of good application/concept problems and less "factor these trinomials" kind of skill problems.

• Just a comment because I don't have specific references, but I recommend looking for good applications problems from calculus and then, whenever possible, stripping away the calculus aspects to get a precalculus problem. For example, take the famous optimization problem of running along the shore then swimming in the water while minimizing total time. Ask the precalculus students to find the function yielding the total time and then use a graphing calculator to approximate the optimum (instead of taking a derivative to find the optimum exactly). Feb 26 '18 at 22:54
• @BrendanW.Sullivan You should certainly write that as an answer, as it is a reasonable source of problems. Feb 27 '18 at 8:37
• @TommiBrander It would be an alright answer if it included a link to a good OER calculus book including such problems. Ultimately, though, I would find it less than ideal because of the amount of work required to completely rewrite every problem to suit a precalculus audience. Feb 27 '18 at 13:31

I don't know of a good problem book but I found D.H. Collingwood, K.D. Prince and M. M. Conroy's OER precalculus book to be a quite good source of well thought out word problems.

NASA has some interesting problems. They're maybe more like projects rather than short homework problems, but maybe you'd find them interesting. You can see them here.

Also, the North Carolina School for Science and Mathematics has various links to various problems they use in their courses on modeling.

A number of proponents of problem based learning (PBL) have mapped interesting problems on to various common core standards. Maybe you'll find some interesting problems here.

Don't have a good answer but consider the following:

1. Free physics textbooks (non calc based, use the problems, not the book). Here is one, but are others on the web:

https://cnx.org/contents/Ax2o07Ul@9.99:HR_VN3f7@3/Introduction-to-Science-and-th (You will have to skip through to the problem pages)

Linear kinematics is useful for basic algebra. 2-d kinematics (shooting the cannonball) is useful for vectors and trig. Simple AC circuits (reactance, resistance, impedance) is useful for vectors and trig and complex numbers.

1. For exponents, I think the key application is investment economics. Uses the concepts, easy to understand without a lot of other physical concepts to understand and one sees the application to something that people care about, . William Hart College Algebra has a nice chapter on them but it is either still in copyright (c. 1940s) or no one has put up a pdf yet even if rights lapsed. There are some sites on the web (including Khan) with similar problems but I didn't find any with large amounts.

2. Would be helpful if you can describe a little more the nature of your precalc class. I have seen that term used loosely to mean everything from "Algebra 2" (logs and partial fractions) to trig to analytic geometry to "functions" (inequalities and functions) to "baby calculus" itself. The applications for different areas will be different and it is not clear to me how advanced your precalc class is (closer to algebra 2 or closer to "baby calculus").

P.s. In general, you don't want problems that assume the person has studied the physics or the like but that explain the law or such in the problem statement (or are clearly intuitive). But I would not hold back from problems that state something technical in the problem statement (e.g. "Scientists have modeled the effect of carbon dioxide as a logarithmic proportionality. If 200 ppm of CO2 gives 0 change in world temperature and 400 ppm of CO2 gives 2 degrees increase in temperature, what will 600 ppm give?" [You don't need to understand the chem-physics-earth science to just solve this as a word problem given the model was given to you in problem but is reasonable and applied.]

• To your 3rd consideration: The class is closer to Algebra 2 than baby calculus. Mar 2 '18 at 1:13