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Algebra Ch3.4 Set I #9 Solutions Manual Error

Angela’s son brought this error in the Earth cover Algebra I Solutions Manual to our attention. Thank you!

The problem (Ch3.4 #9) wording changed completely from the salamander cover to the Earth cover. However, the solution in the old and new solutions manuals is the same.  In other words, both manuals have the solution to the salamander wording of the problem. The Earth solutions manual has the wrong solution to the Earth Ch3.4 #9 problem.

Angela’s son worked it perfectly and here is his correct solution to the Earth cover Algebra I Chapter 3.4 Set 1 #9 problem.

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Algebra Ch1.Review Set I #14b Error

A question brought to us by Marybeth. Thank you!

In Jacob’s Elementary Algebra Chapter 1 Review Set I Question 14b page 51.

“What is the total number of atoms in x propane molecules as a sum?”

The Solutions Manual for Elementary Algebra on page 14 lists the answer as:

b) 3x + 5x

The “5” is a typo. The answer should be 3x + 8x.

3x carbon atoms plus 8x hydrogen atoms

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Algebra Ch2.4 Set IV

Question from Cynthia:
Answer from Dr. Callahan:
You are correct. I assume you have a blue textbook and this is on page 72. It appears the problem got updated between versions and the solutions manual did not.
The y-axis is the weight of the contestant in pounds after he (she) eats each hot dog.
Then I can see in #2 that each hot dog eaten increases their weight in a direct variation.
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Algebra Test 4 #9d

Colleen wrote:

I believe I found an error in the answer key in the 5th Ed. Algebra 1 Teachers Guide.  On Test 4, #9.d., the answer in the key (p. 88) should be (x – y squared)squared, shouldn’t it, rather than (x + y squared) squared?   

Dr. Callahan answered:

You are correct. Thanks for pointing it out. The final answer should be

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Algebra Course Description for Transcript

AskDrCallahan Jacobs Algebra

If you are looking for details for a transcript for Elementary Algebra by Jacobs course, here is the description you need.

Elementary Algebra (this course is the equivalent of an Algebra I course) provides a formal development of the algebraic skills and concepts necessary for students to succeed in advanced courses such as Geometry, Algebra II, Trigonometry, and then Calculus. Students who complete Algebra 1 should take Geometry next. Concepts from this course show up on the ACT and the SAT.

Topics Covered in this Course:

  • Fundamental Operations
  • Functions and Graphs
  • Integers
  • Rational Numbers
  • Equations in One Variable
  • Equations in Two Variables
  • Simultaneous Equations
  • Exponents
  • Polynomials
  • Factoring
  • Fractions
  • Square Roots
  • Quadratic Equations
  • Real Numbers
  • Fractional Equations
  • Inequalities
  • Number Sentences
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Do your students need Algebra or Prealgebra? Algebra Readiness Exams

Something to consider when looking at a PreAlgebra course is that most students can head straight into Algebra I without a problem. Arithmetic and algebraic expressions are the same except algebra uses variables. For instance, in arithmetic you are taught that 1 + 1 = 2. It is a simple relationship between two numbers.

In algebra, while this relationship stays the same, you may be told that 1 + x =2, and be asked to identify that x has to equal 1, since the rules you learned back in arithmetic are still true.

The idea of using the more abstract “x” is the biggest hurdle for students. So if your student is strong in the idea of “x” already, I would consider just going ahead with Algebra I.

The biggest differences between PreAlgebra and Algebra are the pace and the length. Prealgebra introduces algebra concepts and takes each one slower and therefore does not cover as much material as does a standard Algebra I course. Some parents find it just as easy to take a regular Algebra I course and do it in two years.

Our algebra course based on Harold Jacob’s textbook Elementary Algebra. It is quite easy to split the book in half, take one half of the book in one year and complete the second half in the second year. In this way students are given the slower pace of a prealgebra course, allowed the opportunity to be introduced to the idea of algebra, without running headlong into a complete course in one single year. Plus parents only have to buy one curriculum and it lasts them through two years of math. The Harold Jacob’s text is particularly a good choice for this option because it starts out with some review, so students are eased into Algebra I without being overwhelmed.

We offer this textbook in our Algebra course along with video instruction and a free year of support to our customers so that taking this slower pace is easier on the parents and the student.

It is sometimes hard to assess whether your student needs the slower pace of PreAlgebra or if going straight into Algebra 1 would be better. To help you with this step of assessment, we recommend an algebra readiness exam. We do not have one on out site, but we have given you links to some good readiness exams.

Algebra Readiness Exams

These are three versions of a readiness test. One is not better than the other – but wanted to give you options in case links were down or you might want to have your student retake a test.

Evaluating the Algebra Readiness Test

You are not grading the raw score, but each section. The tests are broken into 5 groups. You need your student to get 80% correct in each section to be ready for algebra.

For example, using the Algebra Class link, each section has 5 questions, so your student should only miss one question at max in each section to pass the exam.

What if they do not pass?

Before I would jump into a whole year of prealgebra, look at where your student is weak. Was there only one section they needed to work on? Or were they close in all sections? If either is the case, work on the problem area with math sheets or videos. See the Algebra Class exam for information on review content.


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Algebra Ch13.6 #9h – Completing the Square

Question from Cynthia:

Algebra I Chapter 13 Lesson 6 Problem 9 h. If we follow the books example on page 632 we get the correct answer. If we try to use your DVD’s formula for this lesson we can not get it to work out at all.

Answer from Dr. Callahan

Yes, this is confusing. 

The reason it does not work, is the for the normal method to work the first term MUST BE = 1.

Method #1:

So to do this you can divide everything through by 16. This can make the math a little messier – but works. 


Method #2:

Another method would be to setup squares like he does on page 632. 

         4x            5
4x |  16x^2  |  20x   |
     |             |           |
5   |  20x     |   25    |
     |             |           |

I prefer method # 1, but Jacobs did the squares in his. 

Remember this – when trying to solved quadratics, completing the square is just one method (tool) to do it. When it gets messy like this one, the quadratic formula is easier. (NEXT LESSON) Also, just doing by hand would work for this one. 

Hope this helps. 
See also


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Algebra 1 Ch2.3#6


We just started Elementary Algebra a couple weeks ago after frustration with Saxon. We are struggling with Chapter 2, Less 3, #6. How do I teach my son to determine if these graphed coordinates are a function? He understands the tables and graphing formulas…but we are getting tripped up on #6. Please help! 🙂

Answer from Dr. Callahan:

The key here is pretty simple.

A function can only have ONE Y value for every X value. To see this on the chart, look for any place where you can draw a straight vertical line and cross TWO or more of the points in the function.

For instance – in a) you cannot. Any vertical line will only cross one point. So x = 1 will get y = 1 (assuming each block is 1)

But, for c) you can see that this is NOT the case. When x=2, you have y = 0, or y=2 or y=4. One x with more that one Y is NOT a function. Same applies to g and h.

Does that help?