Weekly Math Problem! #13

Integration. Are you familiar with CLEP exams? I've heard the acronym before but didn't know what it stood for or what kind of exams they were. Now, I know. I got to find out a little more about CLEP by working with a student who will be taking a CLEP Calculus exam. CLEP stands for College-Level Examination Program. CLEP exams allow students to "demonstrate their mastery of introductory college-level material and earn college credit". There are 34 CLEP exams one can take. To get more information about CLEP exams, click here.

In helping a student prepare for the CLEP Calculus exam, the question below showed up in some practice questions.

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  How to solve a definite integral

    ✔️  Substitution method in integration

    

I present to you WMP! #13...

Happy solving! 

Check back on Friday, July 31st for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

⬇️

⬇️

⬇️

⬇️

⬇️

Here is plot of the function on the domain:

**This plot was created using Geogebra's Graphing Gaclulator.

As you can see, it's a semicircle. I can find the area of this via geometry with a straightforward calculation.

Then, there is the calculus way to do this problem. In the world of calculus, trigonometric substitution is the method to use. I decided to use the cosine substitution, because I already used the sine substitution.

As you can see, I arrived at the same answer. For me, this trig sub problem wasn't so bad to complete. However, I feel like the ones that involve tangent/cotangent, won't be so easy. 🤷🏿‍♀️ I'll present one in a future WMP.

◾️ Do you understand how to use trigonometric substitution?? 

◾️ If you've taken calculus before, what is your favorite topic from calculus?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Tired yet? No? GREAT! 😉

Up next...WMP! #14 😁

Cheers!

The Younge Lady

Weekly Math Problem! #12

Solving A STATISTICS Word Problem. One of my favorite sections of math is stats! 😍 I really like it because it was the first time I really noticed math that I learned in school all around me--in advertisements, commercials, in education, in finance, in the medical field, pharmaceuticals, etc. This is one area in mathematics that I want to be so much more comfortable with and better at. I have a few books that I've purchased over the years from the time I first started learning and understanding stats in undergrad until now. Two of those titles include The Humongous Book of Statistics Problems by W. M. Kelley and R. A. Donnelly Jr., and Statistics in a Nutshell, Second Edition by Sarah Boslaugh. Of course there are also electronic textbooks and stats PDF files in my possession. **Does anyone else scour the internet for PDF files? 👀 Asking for a friend. 😅** Also, because I tutor statistics, I make sure to have resources on hand to refer to, so that the people I work with get the best help they can get from me. I have also purchased and read Numbers Rule Your World by Kaiser Fung. I need to read this book again. I enjoyed it the first time I read it and definitely wouldn't mind reading it again.

Even though I really like statistics, word problems can definitely be annoying. If you're like me, you need to read word problems at least three times before feeling comfortable enough to start solving. 

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Working with normally distributed data

    ✔️  Working with "small" sample sizes

    ✔️  How to conduct a t-test

    ✔️  Hypothesis testing 

    

Here is WMP! #12...

Happy solving! 

Check back on Friday, July 24th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

⬇️

⬇️

⬇️

⬇️

⬇️

I'm working with some students this summer and after their review of pertinent information concerning methods to solve specific types of word problems, they freely expressed how much word problems gave them a problem. I totally get it. Word problems definitely make me sigh quite a few times while reading them. So, I decided to color-code this week's word problem with the information and formula used to come to the appropriate conclusion.

**The critical value above came from this t-table.

GeoGebra Classic  has a cool probability tool that shows you the graph of some discrete and continuous probability distributions. It also generates some statistical results of a few different types of statistical tests that are typical when learning statistics. (I encourage you to check it out.) Here are the graph and results of the t-distribution with information from the word problem:

◾️ How do you feel about statistics?? 

◾️ Were there any differences between how you solved the word problem and what I presented above?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

See you next week for...WMP! #13 👩🏿‍🏫

Cheers!

The Younge Lady

Weekly Math Problem! #11

Conic Sections. Graphing is cool. I like pictures a lot; I'm very visual. Conic sections are cool. I just thought I'd throw this problem in the mix, so I could do some more graphing.  

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Completing the square method

    ✔️  Factoring polynomials

    ✔️  Other algebra techniques 🤷🏿

    

I present to you WMP! #11...

Happy solving! 

Check back on Friday, July 17th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

⬇️

⬇️

⬇️

⬇️

⬇️

I previously used the completing the square method in WMP! #7 which required me to solve a quadratic equation. Here's how the completing the square method looks for the curve from this week's problem:

L👀ks like we have a...🥁drum roll please🥁...HYPERBOLA! 🎉 Now that we know we have a HYPERBOLA, we can find the center, vertices, and asymptotes. I color coordinated the important information from the standard form with the components associated with a HYPERBOLA.

Here is the graph of the HYPERBOLA with the center, vertices, and asymptotes identified:

*This graph was generated on Geogebra.org.*

😄 I had fun with this one. 😄

◾️ Have you ever studied conic sections?? 

◾️ If so, what was your experience like?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

See you next week for...WMP! #12 📚

Cheers!

The Younge Lady

Weekly Math Problem! #10

Solving An Exponential Equation. Exponential equations are very different from polynomial equations (linear, quadratic, etc.) not just in the way they look, but also in behavior and methods needed to solve them. Exponential equations sometimes require a different type of "manipulation" via logarithmic properties, as opposed to what is needed to solve polynomial equation types, which do not require that. 

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Logarithmic properties

    ✔️  How to solve polynomial equations

    

I present to you WMP! #10...

Happy solving! 

Check back on Friday, July 10th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

⬇️

⬇️

⬇️

⬇️

⬇️

Listen here...I looked at this problem an automatically assumed that all I needed to do was, somehow, get the exponential term in one spot--factoring it out--then I'll be good. Nah fam, not at all. 😕 When I tell you that wasn't it....that was not it. I needed another technique and wasn't quite seeing it. I was stumped for a bit. What I needed wasn't apparent to me because I was not used to using this technique to solve a logarithmic equation of this form. Factoring is what I needed to do...just not in the way I originally thought. Here's what I did:

I had to solve this thing by factoring a trinomial. It took me too long to see it. Once I saw it, it was solved in minutes. Even though, I didn't post it this week, I did check both solutions. None of them are to be rejected. 

◾️ Have you ever solved a logarithmic equation like the one above??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

On to WMP! #11 ▶️

Cheers!

The Younge Lady