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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 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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Algebra Readiness Test | Do your students need Algebra or Prealgebra?

algebra readiness test

Do you need an Algebra Readiness Test?

Many students and parents come to algebra with a bit of fear and apprehension. As parents, we are just not sure they are ready to jump into higher math like algebra and geometry. As students, they have often heard horror stories.

But the truth is, algebra is not really that bad. Many students who are bored to tears with basic math find algebra a welcome relief and, as a result, do better in math than they have done in years.

But still, the decision must be made. Do you jump into algebra or start with a prealgebra class? To help you make that decision, you can take our Algebra Readiness Test.  

What is Prealgebra

We have been taught that prealgebra must come before algebra. After all, that is how the school systems usually do it. But as homeschoolers, we have the luxury of deciding what is best for our children and not just following the system’s way.

Prealgebra is usually taught in the 6th or 7th grade as a preparation stage to get to algebra.

Concepts covered in prealgebra are

  • negative numbers,
  • integers,
  • properties of operations,
  • exponents,
  • factorization
  • basic equations.

Generally, students ready for prealgebra have a good grasp of basic concepts like addition, subtraction, multiplication, division, fractions, decimals, exponents, variables, and inequalities. This does not mean they are perfect in any of these areas – but just that they get the concepts and can do the work.

Can I Just Start with Algebra and Skip PreAlgebra?

Something to think about when considering pre-algebra is that most students can head straight into algebra. Arithmetic and algebraic expressions are the same except that algebra uses variables.

For instance, in arithmetic we 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 length. Prealgebra introduces algebra concepts and takes each one slower and therefore does not cover as much material as a standard Algebra I course. Some parents find it is just as easy to take a regular Algebra I course and do it in two years, especially if the student is in the 6th or 7th grade. Most older students can dive straight into Algebra without pre-algebra and finish in one school year. Jacobs Algebra starts out slow and starts with the math basics and gently moves the student into the abstract critical thinking of algebra.

Jacobs Algebra Contains Prealgebra

Our algebra course is based on Harold Jacobs’s textbook Elementary Algebra. This course is really a prealgebra and algebra combined. It starts with basic concepts you would find in a prealgebra course and then slowly moves into algebraic methods. If your student needs more time, 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. Harold Jacobs’s text is particularly a good choice for this option because it starts with some review, so students are eased into Algebra I without being overwhelmed. Again, don’t underestimate your student either, they may easily move through the Algebra book in one year as well.

We offer this textbook in our Algebra course along with video instruction and a free year of support (or two years if you choose that route) 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 would be better. To help you with this step of the assessment, we recommend an algebra readiness exam.

AskDrCallahan Algebra Readiness Test

We are always getting questions about readiness. So to help, we have developed our own simple, straightforward algebra readiness test. Unlike some of the others below, this test is simple and directed to what you will need to jump into almost any algebra program, including Jacobs. Also, we have provided a grading guide (unlike most others) that tells you as the parent what to do with the results.

Get the AskDrCallahan Algebra Readiness Test Here

Finished Geometry? Here are some Algebra 2 with Trigonometry (PreCalculus) readiness tests.

“College Algebra” is the university language for Algebra II with Trigonometry or Precalculus.  The readiness tests below are not necessary if you have finished well in Algebra 1 and Geometry.  You are ready for Algebra II with Trig. However, if you aren’t sure where you are in your high school math sequence, these tests can help.

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. In other words, just do a few weeks in a unit study on that problem area rather than a whole year covering what they already know. A whole year of mostly review can be a devastating blow to math confidence and interest.

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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?