This Chapter covered exponent rules and rules of polynomials. First we talked about negative and zero exponents. A negative exponent means to turn it into a fraction by flipping the fraction. An exponent of zero means and answer will be turned into a 1 except zero to the zero power that would be undefined. We also reviewed scientific notation in the beginnings of this chapter. Here is a video reviewing negative exponents:
Review of negative exponents click here
Here is a review of powers of 10 and scientific notation with some sample problems: Powers of 10 and Scientific Notation
We also talked about multiplying and dividing properties of exponents. The quick reminder is to add exponents when they have the same base being multiplied and subtract exponents when the same base is being divided. You also need to remember that an exponent raised to another exponent (one inside parenthesis and one outside) means the outside exponent is applied to everything inside including numbers if there is already an exponent inside then that exponent needs to be multiplied by the exponent outside for further examples see this video:
Multiplying and Dividing properties of exponents video
The last thing we talked about in Chapter 7 was multiplying polynomials and special products of binomials. We also talked about special names for polynomials such as quadratic trinomial etc. you will need to review those. Here is a video of multiplying using the generic rectangle he does it slightly different than how we do it in class but you will still arrive at the same answer:
In this Chapter you learned several ways to solve systems of equations. Remember a solution to a system of equations is where the two lines on the graph intersect. You can solve them by graphing, by eliminating or by substitution. You can also be given a solution and asked if it is a true solution of the equations, to do this you plug the x and y values from the ordered pair ‘solution’ and if it makes the statement true then it is a solution if it doesn’t make BOTH equations true then it is not a solution this rule also applies with inequalities. Check out the below video for a reminder on solving systems of equations:
Solving Solutions through graphing, substitution and elimination
We also found solutions for systems of linear inequalities. You will need to remember that an inequality is when a number is less than, greater than, less than or equal to or greater than or equal to. You will not simply have one ordered pair as a solution if your equation is x < 2 then your solution is ANY number less than 2 can be x. In these equations we dash the line if it is < or > we draw a solid line if it can also be equal to. We plot the points the same when graphing but we shade above the line if it is > or > or equal to. We shade below the line if it is < or < or equal to. Anywhere where two shading regions over lap are our solutions to two inequalities. Here is a video review:
Solving systems of linear inequalities
This Chapter focused a lot on direct variation and slope. Do not forget to use your rise/over run aid to help you when reading slope from a graph just don’t forget to look at the graph and make sure you are counting in the units the graph is actually graphed in. Also do not forget you can find the slope from any two points on the graph it does not have to be the x intercept and y intercept but those are very useful to find! (To find the slope use m = y2 – y1/x2-x1) Here are a couple of videos to help review these topics. Below is a video on Direct Variation and a fun song to help you remember how to find slopes!
Click this link to watch a video about direct variation!
This week we learned all about functions! How to write an equation as a rule and to apply it in function notation. (Remember y=2x is a rule f(x) = 2x) is that rule written in function notation. We talked about discrete and continuous graphs (discrete being where you have to plot each point and continuous being where the graph flows through where you did not have to plot points). The most challenging portion of this weeks lessons for most of you were determining if an equation/graph was even a function to begin with so below I have attached a few pictures to help you review.
Last week we reviewed for some and introduced inequalities for others. Most of you
took right to it in fact I saw more independence on this section than I have seen
so far this school year! Many of you did superb on classwork and homework with
very few questions but there were some issues on the quiz…luckily for us it was
just a quiz so I am attaching a video here to help you review…just remember
it is just like an equation with an inequality symbol in the middle and if you are
unsure if you picked the right inequality (<, >, <, >) then plug in a number and see
if it 1. Makes sense in the question (If the question says she has to sell at least
50 fundraiser books then 10 won’t suffice) and 2. It makes sense in your inequality!
For a refresher check out the video below!
For a refresher of chapter 2 part of it was equations and the other part percents.
Here is a video to help you through Chapter 2 on multi-step equations with variables
on both sides. Click the video below.
We are in the middle of the holiday season so there is lots going on at school and at home for everyone! I hope you all have enjoyed the time off with your families and are having a happy new year. So far so good in Algebra we are now halfway through Chapter 2 and 1/9th through the course!
Just a reminder to everyone we will be having a quiz on Wednesday 9/25/13 covering equations (solving equations through adding, subtracting, multiplying and dividing within equations and two step equations as well as multi-step equations and solving for variables.) The key to solving equations no matter what actions are being done in the problem or if you have 20 terms or all variable terms you always do the opposite action to both sides to undo what has been done and keep on doing that until your variable is alone. As always you can e-mail me anytime you are stuck on a problem. We are off to a great year! 🙂
I am very proud of all my Algebra students this week! You guys have really stepped up to the challenge, you all have come ready to learn and have worked hard this week. We have covered all of Chapter Zero the first week and started on Chapter 1-1 Friday. This week we will continue to dig further into Chapter 1 with a mid-chapter quiz on Friday (8/30/13).
Make sure your notebooks are organized each day at the end of class. You all should have 4 dividers the first one is warm-ups, the second notes, the third assignments and the last is Quizzes/Tests. At the end of class each day make sure to put your notes in your notes section and your classwork in your assignments section.
See you Monday! 🙂