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The school year is back in full swing, and many students have received their first progress reports. Whether you are doing well, or not so well with your studies it is important that you well, study! But that is sometimes the tricky part. Those text books are big! Especially math books. Today I hope to offer you some tips on how to best use your time and math text. Here are the 6 most important parts of a math text book:

1. The Contents - its in the beginning and tells you what the book is about. This section is great for finding old information, especially if your class doesn’t approach the book from front to back. This is also good for taking a sneak peak of what is yet to come. Finally, you can learn where the tests, quizzes, extra practice problems, and additional resources are hiding.




2. The Boxes (formulas, rules, theorems, properties, etc) - When it comes to math books, if it is in a box then it is important. If it is in a shaded box, then it is really important. Here you will find your formulas, rules, theorems, postulates, properties, equations, etc. This boxed info should automatically be copied on your “cheat-sheet” if you are allowed one. Perhaps more importantly than the boxed information itself, however is understanding what it means. Consider copying it down word for word, but then do so in your own words as well. If you own your text book, mark these pages for easy reference.




3. Examples/Solutions - Most math texts I have seen always begin each section with examples. Later, the practice problems are often the same examples just with different numbers. Try working through each example along with your text and then try a practice problem that relates. If (when) you get stuck on your homework or studying flip back to the beginning of the section to find the example which applies. Remember that math builds upon what you learned before, so you may have to go back a few sections (or chapters) to find the info you are looking for.




4. Tests/Quizzes - I am absolutely amazed at how many teachers copy their own tests and quizzes directly from the text book which their students are using! Sometimes they will assign the even numbered problems for a review and then the odd numbered problems will show up on a test. Other than a sneak peak at tests, this is the best way for you to determine if you really know the material or if you need extra work. Text books will often refer you to the section a particular problem came from if you need to go back for a refresher.




5. Index - This is like the contents, except it is in the back of the book. Indices (plural for index) are great if you are looking up a specific topic which may be in several different sections. They are also good if your book does not have a glossary and you just need a simple definition or formula. Instead of endlessly flipping through your book for the Quadratic Formula (which I can never remember), just look it up in your index and you will know exactly where to go.




6. The Answers - Every lazy student’s favorite part. But don’t abuse it; there is a right way and a wrong way to use this important part of the book. Answers to extra, unassigned homework problems because you really want to understand = good. Answers so that you can get back to the Playstation sooner = bad.

Did I miss any important parts of the math text book? Use the comments feature to weigh in. It’s nice to be back for the 2009-2010 school year.

You may notice the blog looks abit different today. I just updated WordPress here, and ran into some difficulties.

Bear with me and I hope to have things back to normal by weeks end.

This videos looks at problems involving solutions. Example: You have a 15mL solution which is 10% salt, how much water do you have to add to make it 8%?

There seems to be a problem with the video hosting service I use for the tutoring videos. I am switch everything over to YouTube and hope to have all of the videos back up and running on the site by the end of the day.

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update: I finished moving all the videos over to YouTube. All the videos should be working now.

This video explains how to factor a quadratic equation with a leading coefficient. (an equation that looks like ax^2 + bx + c).

This lesson is the first of a four part series about systems of linear equations. Here, I define what a system of equations is, and the three types of solutions. Future lessons will cover graphing, elimination, and substitution.

Also in this series:

• Lesson 1: Introduction (current page)
• Lesson 2: Graphing
• Lesson 3: Elimination
• Lesson 4: Substitution

Welcome to Your Tutor Online video lessons. This is the first of a four part series on solving systems of linear equations. This first lesson will serve as an introduction.

A system means a group, or more than one. And the word linear here, refers to a line, and also means we will be dealing with two equations which each have two variables in them. Normally they will be x and y. We need to work with both equations at the same time to get a solution. Here’s an example of what a system of equations problem looks like. 3x minus 4y is equal to 2 and 7x plus 3y is equal to 4. Now, using the ways I’ll show you in future lessons you will be able to work with these two equations and get a solution for x and y.

There are three types of solutions to this kind of problem. You can have one solution, no solutions, or infinite solutions.

You have one solution when the two lines intersect. The point where the lines intersect is your solution. You can give the answer as an ordered pair, in this case “(4,2)” or you can split up the coordinates and say that x is equal to its coordinate which is 4 and y is equal to its coordinate which is 2.

A system has no solutions if the lines are parallel or never intersect. This can be seen clearly with graphing. Or, prior to graphing if the two lines have the same slope but not the same y intercept then they are parallel and have no solution. You can simply write “no solution” or this symbol, a zero with a slash through it, which means the same thing.

There are infinite solutions if the two lines you are dealing with are actually the same line. Here is an example. I have a blue line and a green line right on top of each other. This can happen if the first equation you are given is a multiple of the second or vice versa. We’ll take a closer look at that in upcoming lessons. These two are the same line, so they’ll intersect at every single point. So, we say there’s an infinite number of solutions.

There are three ways to solve systems of linear equations: By graphing, elimination, and substitution. Each of these will be the focus of the next three lessons. Be sure to visit www.YourTutorOnline.com to see them when they become available. And, as always, if you have any questions leave a comment underneath any of the lessons. Thanks for watching, class dismissed.

I will be putting up 4 new video lessons. They will all look at how to solve systems of linear equations. Click on a link below to jump to that lesson.

• Lesson 1 will serve as an introduction
• Lesson 2 will look at solving by graphing
• Lesson 3 will cover elimination
• Lesson 4 will wrap it up with substitution

Lesson 1 will be posted tomorrow morning, bright and early.

This lessons looks at how to simplify radical expressions which are not perfect squares or cubes. I include an example of square root, cube root, and 4th root. I show a technique to simplify n-root expressions. Also I look at how to simplify variables in radical expressions.

Welcome to Your Tutor Video lessons. Today we’ll look at how to simplify radicals.

A radical is anything with a radical symbol which looks like this. It can be square root, cube root, fourth root, or any numbered root. If there is no number in the symbol then its a square root, otherwise there will be a tiny number here to show you what root it is. In this example it is cube root. These expressions need to be simplified like anything else in math.

Lets look at this example: radical 54 or square root of 54. The easiest way I have found to simplify radicals is to do a factor tree for the terms inside the radical. Now this only works if everything inside the radical is multiplied together or you only have one term.

First draw two lines out from the number or term inside the radical. And on this line we are going to write any two numbers that multiply together to give us our originial. I’m going to choose 9 and 6. We are going to repeat the process until we have nothing left except for prime numbers. 3 times 3 is equal to 9 and 3 times 2 is equal to 6. Now we are left with only prime numbers here at the bottom, 2s and 3s.

Now we want to look and see which root we are dealing with. Here it is the square root or 2nd root because there is no number in the symbol itself. Since its the second root, we are looking for groups of two of the same numbers. Here I see two-3s. When you get a group, you can write the group number outside of the radical, in this case its 3. Then we’ll go ahead and write our radical and write everything thats left over inside, multiplied together: 3 times 2. Go ahead and multiply those together: 3 radical 6, and thats our simplified expression.

You can look for shortcuts as you do your factor tree. As you get more practice with this type of problem, you will know that 9 is a perfect square and so it’s square root can automatically come out of the radical. For cube roots you are looking for perfect cubes and so on according to whatever radical you happen to be dealing with. Now its going to get harder as you get into higher radicals and you probably won’t have high powers memorized, but thats okay you can just do your factor tree when in doubt.

Lets look at how this works for a cube root. We’ll use the example cube root 135. We are still going to go the factor tree just like we did in the previous example. 5 times 27 is equal to 135. 5 is a prime number so we will just leave that alone. 27 is 3 times 9 and 9 is 3 times 3. Notice we could of had a shortcut there if you knew that 27 was a perfect cube.

This time we are going to look for groups of three because we are dealing with the cube root. Here you can see three-3s. So that means a 3 is allowed to come out of the radical. So I write 3, the radical symbol with its cube root and whatever is left over that didn’t find a group of three, which is 5. So this radical simplified is 3 cube roots of 5.

Lets look at how to do radicals with variables in them. For a coefficient we are still going to do a factor tree. 48 is 12 times 4. 12 is 3 times 4. 3 is a prime number. 4 is 2 times 2. And this 4 is 2 times 2. This time we are going to be looking for groups of four because we are dealing with the fourth root. So here, I found four-2s. So the two is going to come out and a 3 will stay inside.

Now lets look at our variables. This part is a little tricky. We are going to look at each of our exponents for our variables. We are going to take our root number and divide it into each of the exponents. The number of times that the root goes into the exponent, will be our new exponent on the outside of the radical and the remainder will be the new exponent that stays behind inside the radical.

Now we can get started on our answer. We know a 2 comes out so I’m going to write that. I’ll leave some space, draw my radical symbol with is the fourth root. I know a 3 is stuck inside. Now I can start dealing with the variables.

4 goes into 6 one time so x to the first power is on the outside. 4 goes into 6 once and there are 2 left over, so its x squared left on the inside. 4 does not go into 2 any so a y does not come out of the radical. 4 goes into 2 zero times with 2 left over so we have a y squared left on the inside. 4 goes into 8 two times so we have z squared on the outside. 4 goes into 8 twice with no remaineder so there is no z left on the inside. And this is our final answer: 2 x z squared times the fourth root of 3 x squared y squared.

Thanks for watching Your Tutor video lessons, now I know today was a little bit of a tricky topic so if you have any questions head over to the blog and leave a question at www.YourTutorOnline.com And also, if you haven’t been there yet be sure to check out the quizzes I’m going to put up after each lesson and see how much you understand. Thanks for watching, class dismissed.

This lesson shows how to solve equations involving absolute value.

Welcome to Your Tutor Online video lessons. Today we will learn how to solve equations that have an absolute value in them.

As a review, absolute value refers to how far away a number is from zero. To put it simply, the absolute value makes a number positive no matter what. Three is three units away from zero. Negative four is four units away from zero. So the absolute value of three is three, and the absolute value of negative four is four. Three stays positive, number four becomes positive.

What if there is a variable inside the absolute value sign? Well, in our order of operations, we want to treat the absolute value sign just like we would parentheses. So simplify everything inside them first, and move everything you can to the other side. In this example, 3 times the absolute value of x plus 2 is equal to 9, we can divide both sides by 3 and we are left with the absolute value of x plus 2 is equal to 3. When you get the absolute value all by itself on one side, you are done with the simplification.

Now we need to split this equation into two separate equations. For the first one, simply drop the absolute value signs. We have x plus 2 is equal to 3. For the other equation drop the absolute value signs and this time make the other side of the equation negative. Or if its already negative make it positive, just flip the sign of the other side of the equation.

Solve each equation that you came up with. On the left x is equal to 1 and on the right x is equal to negative 5. So for absolute value equations we will have two solutions, In this case x is equal to 1 or x is negative 5.

I hope you found this lesson useful. If you have any questions leave a comment on the blog at www.YourTutorOnline.com If you have any lessons suggestions send an email to podcast[at]yourtutoronline.com Thanks for watching, class dismissed.