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Geometry Material Skipped in Chapters 12,13, 15, and 16

In Harold Jacobs Geometry we skipped over material is chapters 12, 13, 15, and 16 because
1. It is not needed for ACT/SAT nor future math classes, and
2. it is a overly complex for the course at this level.
Our recommendation is that the student look over this material and get the idea – but move on. You will find a test problem that points back to some of this material in a trivial way, but we decided to leave it in as a learning tool since often in life we find ourselves having to dig a little to get to an answer – even when being tested.  Since we recommend open book tests, this usually works well. And, just in case, it is only one problem and the teacher can decide to skip it if they like.
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Geometry 6.1 #18-20

For 19 you can get a line of symmetry between each one that is hand to hand (wing to wing) and each one that is nose to nose. Those total 7. In other words, you can make a fold in many places if you take two at a time (or individuals which is what the problem asks).

For 20 assume you cut two penguins at once (those wing-to-wing) So the folds to get what w have on this page is 2, once in the middle, then fold that one more time to get four patterns of two penguins each.
To get 16, double that.
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A2T Ch 5, Lesson 5 #37

Start by taking log of both sides to get

Log ( x^Logx) = Log (100x)

now using rules from page 380

bring down the exponent in front and separate the multiplication into addition to get

Logx (Logx) = Log 100 + Log x

and Log100 = 2

now we have

(Logx)^2 – Log x – 2 = 0

factor to get

(Logx -2) (Logx +1) =0

now you have two equations to solve for 0.

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Algebra Midterm


The Algebra I Teacher’s Guide does not have a midterm exam nor a final. Do you suggest using the “Midterm Review” and the “Final Review” sections in the book? Thanks


Our course does not require a formal midterm exam, nor a final exam. For parents that choose to include those, you have a couple of options.

You can, as you suggest, use the midterm and final review sections that are in the textbook.

Or some parents take whichever test naturally falls during the middle or final portion of the year, and count those exams as the midterm and final, respectively.

I hope this helps!



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Algebra Chapter 2 Lesson 4 – Direct Variation


Hello. I am a homeschooling mom using your DVDs and the Jacobs text. I also happen to have a bachelors in math and taught Algebra in VA for 5 years. (But that was 14 years ago now.) In the Set I questions we are sometimes asked review type questions about functions. Sometimes we are asked “What type of function is this?” How do we know when to answer “direct variation” and when to answer “linear function.” I do know the difference between them, but not sure when a linear function IS a direct variation, which answer is correct. Hope my question is not too confusing…Thanks so much!


Direct Variation equations are also linear equations, so understandably they get overlapped. The distinction is the y-intercept. Direct Variation lines will always go through the origin Their y-intercept will always be 0, that’s why their equations always fit the form of y = ax. It is the same as a line which you have y = mx + b, but the b term is 0 for direct variation, so it shortens to y = mx (or y = ax, which is the same thing).

When you are answering the questions in the book, a lot depends on what you are studying in the text, or that section as to whether the book is looking for direct variation or linear. The distinction, though, is whether or not it goes through the origin. If you have an equation that is both a linear function, but also a direct variation equation, I would allow both answers as correct. If you want to be technical about what’s correct, then the answer to “what kind of function is this” would probably be “linear function with a direct variation equation” since direct variation is a special case of linear function. But take into context what the student is learning. If they have already learned what linear equations are, and are now in a lesson specifically designed to teach them about direct variation, then when they come across a problem that graphs as a line through the origin, then the likely answer is “direct variation”.

Does that help?

God Bless,

Cassidy Cash


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Algebra Chapter 2 Graphing


Hi, I am going through the Algebra one course and am struggling through Chapter 2 (all of it!)and especiallythe graphs. My mom is super picky and it has to be PERFECT. Is there a short way to do it without a ruler or graph paper? Also, how exactly do you do decimals on graphs? Thanks.



Here is a video that goes over some tips about how to graph accurately without using graph paper. They should help!



However, if you are struggling with the whole chapter, I would be happy to help you with some particular problems. Take a look at the latest lesson you’ve been working in, and pick one or two problems that are particularly difficult. Then email me the lesson and problem numbers, and I can go over graphing as it applies to those problems specifically. I hope this helps!

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Algebra Test Taking


My daughter just tried to take the test for chapters 7-8.  She does fine with the lessons but has trouble transferring the information for a test. We read over the review lessons before the test but did not work any of the problems.  She said that she remembered everything at the time .  Then, she says that she never saw a certain kind of problem when I vividly remember the it.  Can you give me any tips to help her prepare for the test?  We decided that she should do the review problems but there are 40 for chapter 8 alone.    I appreciate any advice you can give us.



Here are a few pointers:

When you are studying a course all year, you spend a lot of time with the material, so the concepts and the problems will sound familiar to you. It is easy to think you “remember everything” when in fact you still need some practice. I work math problems every single day, I am in these courses all the time, and I still have to go back and practice, so I can assure you that once through the lesson and homework, and you are not going to have everything memorized—nor should you be able to memorize that much material. You are trying to learn, trying to grow, and that takes practice. So when studying for any kind of math test, consider working through problems a must.

When you are choosing which problems to work, though, it is ok to be selective. I would encourage you to approach the test in this way:

Go back through the lessons themselves and pick out problems based on “Which ones of these problems do I absolutely hate to work?” The ones that you dislike the most are usually the ones that you are most likely to get wrong on a test. So that’s a good clue that the despicable ones are where you should practice. You can also work through example problems, or select homework problems. As you are going through the lessons you should have been grading your homework and re-working missed ones. So you should be able to go back over your homework and see “Where did I seem to have trouble the first time I worked these problems?” There is another way to locate which concepts are most difficult, and therefore in need of the most attention when preparing for a test.

Another thing I am noticing from your email is that your daughter seems to focus on problems being exactly as they are presented in homework, and that makes sense if Algebra 1 is her first high school math course right out of elementary math, because elementary math is typically taught with a “here’s a problem, here’s exactly how you work it step by step, now come over here to homework and work one that is exactly the same.”  However, in college math, that approach really is not going to last as something you can rely on to get you through. The idea of examples and homework at this stage of mathematics is to teach your daughter how to learn the concepts overall, then she will be able to work any kind of problem where that concept appears instead of having to rely on it being a “certain kind of problem”.


The last thing I will tell you is that every single problem on our tests come from the Chapter Review section. So a fantastic way to get ready for the test is to work through the Chapter Review. PLEASE UNDERSTAND: DO NOT work every problem available there. There are simply too many. Your daughter will need to go through the lessons, compare the homework to the chapter review, and choose problems to practice based on what she needs practice with. If she thinks she understands everything and does not need practice, then a good way to start would be by going back to the homework and simply re-working anything she missed the first time around. Even if she has already done re-works on the homework. Have her make herself a mock worksheet made up entirely of copied over homework problems she writes onto notebook paper. Then have her work them (Using the textbook if she needs) and just not looking back at her original work on that problem. You’ll be surprised how this approach will bring to light things you might have missed the first time.


Then don’t forget that after she takes the test, she should be allowed to go back to the exam itself and re-work anything she misses for credit back on her test. She will not get everything right, she will need to go back, and the going back and being able to answer “I missed this problem because___and this is how you work it correctly__” is where the real learning happens. If she can answer these questions for her missed work, then you can feel comfortable that she understands what she is doing.

I hope this helps you as you approach studying and test taking, but feel free to call me as well if I can help further.