Category: Algebra II with Trig

Question: 

My daughter has taken Saxon Algebra 1 and Algebra 2 and Jacobs Geometry. I am looking for a precalculus course, but I see that yours is Algebra II with Trig. I’m wondering does that sound is that something that would make sense for someone who is taken Saxon Algebra 1 & 2 or would that be an overlap.

Answer from Dr. Callahan:

Algebra 2 with Trig and Precalculus are just repacked content of basically the same material. See Algebra 2 with Trig vs Precalc for more information on this.

What your daughter is likely missing is the trig part, and maybe some of the more advanced Algebra 2. Since you likely are trying to make sure she is prepared for college and not missing anything, here is what I would do:

1. Go to the publishers online Student Center (You can always find the link here at our course on the Algebra 2 with Trig Everything You Need page.)
2. Pick chapter 1, and have her take the Practice Quiz. (They are all pretty short and are graded online). If she does 80% or better, have her move on to the next chapter.
3. Do this through chapter 8 until she finds the place where she is missing a lot or is totally lost. I would expect this might be in chapter 6-8.
4. Now develop a plan to cover the content from those chapters.

Here are some options for developing a plan:

• Use the textbook we have (you can use the online version) and have her study the content and do the online quizzes as her tests. You can use our syllabus as a guide.
• You can do the above and mix in some free online videos such as Khan Academy. Here is their Algebra 2 and their Trig.
• You could buy the course and cover the content you need. (If she is weak in a lot of the chapters this might be the best option.)

Caution: If she is heading for any STEM (Science, Technology, Engineering, or Math) study in college or career, she needs to be very strong – so be careful not to skimp here. The biggest reason for kids to bail out of these career paths is weak math skills.

Question from Amelia:

Dear Dr. Callahan, I found a place where the answer key for even-numbered problems in Algebra II with Trig is incomplete.  In Ch 5 Section 5, problem 90 explains what a photic zone is in lakes or the ocean, and gives the formula I = Io e ^ -kd where k is the constant called the coefficient of extinction and d is the depth.  It then gives the depth where, in a certain lake, half of the surface light remains, and asks you to find both k and the depth of the photic zone.  However, the answer key only has the answer for the value of k.  It says nothing at all about the depth of the photic zone.

Answer from Dr. Callahan:

Thanks for pointing this out. Actually there are TWO errors in this problem – so let me resolve it

Starting from 

and solving by taking the natural log (ln) of both sides we get

-0.693 = -k * 14.3

k = 0.0485 (In the Solutions to Selected Problems this is 0.485. If you tried with the other number 0.485, your answer would not make since because you get 1% of the light at about 9 feet which is more shallow than when you get half the light at 14 feet)

Now, to complete this you would need to take the k value and insert it in the equation where you are at 1% of surface light remaining. 

This gives you

now take the natural log (ln) to get

-4.605 = -0.0485d

d = 94.95 feet

and rounding to 3 significant digits (See page A-3 in back of book)

d = 95.0 feet

CHECK OUR WORK

Now we can check the work!

I = Io e^(-0.0485*95)
I/Io = 0.00997 or 0.01 or 1%

Hope this clears it up. 

dwc

PS – Sorry for the delay – I just thought you were telling us we were missing something and did not look at it close till today!
dwc

Here is a solution for Algebra II with Trig Chapter 2.8 #18.

A2T-Ch2.8#18.pdf

How do we work Algebra II with Trig Chapter 1.3 #73?

Solution

a) Area after purple section cut out

A = (20 times 20) – 4(x^2) = -4x^2 + 400 = -4(x^2 – 100)  = -4(x + 10)(x – 10)

b) V = Area of bottom times height = (20-2x)(20-2x) x = (400-80x+4x^2)x = 4x^3 – 80x^2 + 400x = 4x(x^2 – 20x + 100)