As you move deeper into each textbook (Algebra, Geometry, Calculus, etc), the problems will contain several concepts you’ve learned earlier – all in one problem. This complexity can make it difficult to find the “how-to” or examples in the book to help us understand how to work it.
Recently, we received this question from our student support page: There doesn’t seem to be any examples or teaching that I can find that helps me solve this problem.
This is a common question – not this particular problem, but in general, as the problems develop into including several simple concepts stacked into compound calculations. However, the explanations are there, they just may be back a few, or several, chapters.
For example, Jacobs Algebra Chapter 12 Summary and Review Problem 14h.
Concepts include but are not limited to:
Chapter 12: Square Roots. Simplify radical as much as possible. Example of this step page 480-481
Chapter 5: Equations in One Variable. Specifically for this review problem, Equivalent Equations (Lesson 3) page 162-163.
Chapter 12: Square Roots: Radical Equations. Page 505 has examples of squaring both sides to eliminate the radical.
Math builds on itself. As you learn more and more concepts, the problems reach back and build on calculating and analyzing skills learned earlier in the book or even in an earlier course. These complex problems can be hard to find “how-to” when we just can’t see it! The solutions manual is a good resource to help with steps, but sometimes even with those steps, we need to see where it was explained or taught.
We are here to help! Send us your homework questions and let us help. Filling out this form makes it easy to be sure you’ve told us what we need to know to help you, but you can also send an email to email@example.com.
Look for the following material or heading in the contents.
Limits and Derivatives
· Limit of a function
· Calculating limits
· Limit laws
· Rates of change
· Derivative rules (polynomials and exponentials)
· Product rule
· Quotient rule
· Derivatives of trigonometric functions
· The chain rule
· Implicit differentiation
· Derivatives of logarithmic functions
Applications of Differentiation (subtitles may differ widely here)
Notes for use: This course should be equivalent to a Calculus One course at a local university. If you know what school your child plans to attend, find out which textbook they use and go with it. In fact, ask for a syllabus and sample tests. A good deal of information can be gleaned from the UAB website on the screening test and the UAB test bank. (See the resources at the end of the chapter.)
Also, note that these books are often written for Calculus I, II, and III. So your text will be a lot bigger than what you will teach in high school. Also, if you do go with a college textbook you will pay a hefty price. An alternative is to find the previous edition on eBay – much cheaper with probably little change in material.
#3 – on the test copy I have says to use three equal subintervals. But in the handwritten solution, it appears that they used 6. If the student uses 3 subintervals wouldn’t the ∆X be 2 and the right endpoint sum be 0.2, left end point be 39.8, and midpoint be 15.8?
Answer from Dr Callahan – That is correct – in the solution we used an interval of 1 and it should have been 2.
#8b – The handwritten solution has dV= √t and V = t^1.5. Shouldn’t V = 2/3*t^1.5? With that, our final solution came out to be 3.39.
Answer from Dr Callahan – That is also correct – we have an error in our solution.
#9a – Instead of factoring the cos^5x into (cos^2x)(cos^2x)cosx, my student used the Form 74 from the Table of Integrals followed by Form 68. But he didn’t get the same answer as he would have solving it as we learned in 5.7 (p. 403) like the written solution did. Why don’t the two methods yield the same answer? I’m thinking it has to do with the limits of the integral, but it’s been 25 years since I had calculus, and I’m struggling with explaining the why on this one.
Answer from Dr Callahan – Yes you should get the same answer – but I noticed an error in our solution!!!! When you integrate we added a 4. Should be as below
#9b – In the handwritten solution it looks like it evaluates 3*ln 3 as 9.89, but isn’t it 3.3? I believe the answer would be -0.17 if 3.3 is correct.
Answer from Dr Callahan – Yes it should be 3.3
Extra Credit – The solution just substituted into the Form #95. Did you not expect them to continue to solve the remaining integral or just stop with that first substitution?
Answer from Dr Callahan – Yes we just stopped there because that was the challenging part!
Hello, I am looking for a math course for my daughter who just finished her sophomore year of high school. She received a 97 in Algebra 2 Pre-AP and was planning on taking Pre-Calculus Pre-AP next year. However we have decided to home school next year because of our travel schedule, so I’m looking for a course for her. I noticed that you don’t have a separate Pre-Calculus class. In your opinion would it be ok for her to go straight to the Calculus class? She’s a very strong student, but I wouldn’t want her to take something that she is not prepared for. Any input would be appreciated.
Answer from Dr. Callahan:
My guess is she would be OK as long as she has had some trig. I would first have her go to out online textbookhttp://www.mhhe.com/math/precalc/barnettcat7/student_index.mhtml and take the chapter quizzes of each chapter, 1-8. This will show any weak spots. If she has any, a quick study of those sections should help her get ready.
But I’m wondering if calculus will be too difficult for me to teach. Trig was a bit of a challenge for me, just wondering what your ideas were. Thanks
Answer from Cassidy Cash:
Calculus is designed to be mostly self-taught on the part of the student. The parent might come in and assist in grading, or provide accountability for homework, etc, but students at this level should be able to not only teach themselves using the dvds and the textbook, but they are more than capable of finding the answers to problems they don’t understand.
Also, not only do they have Homework Help as a resource, but we are actually expecting Calculus 1 students to be proactive at this level about asking questions and seeking help when they need it. (some students even do internet and library searches to find answers–which is great. Considering the next step for most students after this course is to take a college course, this is definitely the time to be learning how to be proactive about their own education. Being able to find answers outside the textbook is an excellent place to be)
To sum up, I would say not to worry about it. If your student ever arrives at a problem or concept that they cannot figure out from the materials they have available to them, we are here to help them. And we are here to help you as well. If you have questions about anything related to teaching this course, we will assist you as well. 🙂 I think you will do just fine 🙂
And we are here to help whenever you need.
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