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Algebra 1 Test 4 #13

Question from Valerie:

Algebra I; Test 4; Problem 13.

I have the answer, but can you explain how you got the answer and give the pages in the textbook that talk about this problem? Thank you!

Answer from Dr. Callahan:

The question is asking is the equation is true.

It is NOT true is there are values where it does not work, or at least not true for those value.

So for instance, if you get x= 6 and y =1 — it does NOT work.

Also true for other values. In fact, the only times it DOES work is when x=y.

You will find this kind of thing in chapter 11.


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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 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.

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Algebra Test 3

Algebra Test 3 #13


Question: Test 3, Number 13: Answer book says number gets smaller by 7. Yes, the number gets 7 digits smaller but the question is asking about what happens to the exponent – doesn’t the exponent get larger by 7? That’s what we were thinking but we are no experts so here we are asking! Thanks!

Answer: When you are moving to the left with the decimal, the exponent is getting smaller. Let’s work through an example to show you what I mean:

If we start with the number 6,000

That’s 6 x 10^3 in scientific notation.

If I take the decimal in 6,000 and move it 7 places to the left I end up with

.0006000 = .0006 = 6 x 10^ -4

Notice that the exponent goes from 3, to –4, which is a difference of 7 digits in the negative direction. So we say the exponent gets 7 digits smaller.

I hope this helps!