Don't Forget the Properties!

Distributive Property- a (b+c) = ab+bc
Inverse Property- a+ (-a) = 0 and -a + a = 0
Identity Property-a+ 0=0 + a = a
Commutative Property- a + b = b + a and ab = ba
Associative Property- a + (b+c) = (a+b) + c and a(bc) = (ab)c
Multiplication Property of 0- a * 0 = 0 and 0*a=0

Old Vocab Review

Here is some vocab from chapter 2 that you probably need to know for the final :

Type of Linear Equation           Number of Solutions               Indication When Solving
Conditional                                   one                                             final line is x= a number

Contradicition                               none                                          final line is false


Identity                                          infinite solution set                      final line is true, 0=0

Form for joint variation

Some people had trouble with this on the test:
Y varies jointly as x and z:
Y/xz=k if finding the constant is required.

Solving for b in slope intercept form.

It's been a while since we've done this so here is a refresher:

• Find the equation of the straight line that has slope m = 4
  and passes through the point (–1, –6).

Okay, they've given me the value of the slope; in this case, m = 4. Also, in giving me a point on the line, they have given me an x-value and a y-value for this line: x = –1 and y = –6.

In the slope-intercept form of a straight line, I have y, m, x, and b. So the only thing I don't have so far is a value for is b (which gives me the y-intercept). Then all I need to do is plug in what they gave me for the slope and the x and y from this particular point, and then solve for b:

y = mx + b
(–6) = (4)(–1) + b
–6 = –4 + b
–2 = b

Then the line equation must be "y = 4x – 2"




Taken from here: http://www.purplemath.com/modules/strtlneq.htm

Dividing inequalities by negative numbers

When dividing an inequality by a negative number always flip the sign. A more in depth explanation is linked.

http://mathforum.org/library/drmath/view/53287.html

Switching the sign for Inequalities

Whenever x is not on the ride side after you solve an equation, you always flip the sign so that the number will be on the right side and the variable on the left side

Switching the sign for Inequalities

Whenever x is not on the ride side after you solve an equation, you always flip the sign so that the number will be on the right side and the variable on the left side

Percentage Problems

Some people in my class were having trouble with percentage problems. Here is what you need to remember the proportion x/100 = is/of. x = the percentage.

In vs. Exlusive

Don't forget that in notations etc. to check to see id it is inclusive or exlusive. Like for Interval notation if the number line went from -3 (included) to infinty (to the right (positive)) you would want to remember that WHENEVER you see an infinity it is EXlusive. ALWAYS.
So it would end up being [-3,infinty)
Brigid

Set interval and such

Hey guys, so I remembered that there was a little confusion about set and interval notation.
Set: -3Interval: (-3,5)
Brigid

Helpful website

This website has some walkthroughs of some of the mixture problems on the selected problems from chapter 2 google doc. Check the comments, windows won't let me paste it.

2.3 !!!!

I have the same question as christine about rate problems can someone please show me how to do one step by step? Please!

Another Question!

Also, I am a bit confused about the mixture, rate/time, and interest/principle problems.

If someone could go over it, that would be really helpful! :)

Help Please!

Hey everyone!

So looking over my previous test, I was a bit confused about some things! If someone could help me that would be great! :)

I don't understand how to graph

f(x)=3x! or g(x)=1-x^2

I was also confused on how to graph a relation!

remember chapter 3

We only did section 3.1-3.3

DO NOT DO ANY EXTRA SECTIONS TO THROW YOU OFF!!!!

 GOOD LUCK EVERYONE!

Solving compound inequalities with and

Step 1. Solve each inequality in the compound individually.

Step 2.  Since the inequalities are joined with and, the solution set of the compound inequality will include all numbers that satisfy both inequalities in step 1 (the intersection of the solution sets).

Chapter three info

A linear inequality in one variable can be written as Ax + B < C.  This is true when A, B, and C are not equal to 0.

Addition property of inequality
A<B and A+C< B+ C are equivalent.   Adding the same number to each side of an inequality does not change the solution set.

Multiplication property of inequality
for all real numbers A, B, and C, with C not equal to 0
A<B and AC<BC are equivalent if C>0
Here are the steps to solving a linear inequality.

1. Simplify each side separately. Use the distributive property to clear parentheses and combine like terms as needed.

2. Isolate the variable terms on one side.  Use the addition property of inequality to get all terms with variables on one side of the inequality and all numbers on the other side.

3.  Isolate the variable.  Use the multiplication property of inequality to change the inequality to the form of x<k or x> k

Khan academy

On youtube there is a man whose channel is called khanacademy.  He has really helpful videos for math that would benefit everybody in the class.  Here is the link to a video about solving inequalities.

http://www.youtube.com/user/khanacademy#p/c/7AF1C14AF1B05894/4/VgDe_D8ojxw

Remember

When a number is included on a number line, use a closed circle and you have a solid line.  When a number is not included, you use an open circle, and have a dashed line.

The questions we went over in class today

Today in class we went over some of the questions that were asked during class today. We did talk about them but maybe this way you can use Noa's method (putting the equation on one side...) I will put the questions in the comment section of this post and make another with the answers so you can also quiz yourself.
Good luck tomorrow!

Extra Help chapter 1

Natural numbers (counting numbers) = {1,2,3,4,5,6.....}
Whole numbers = {0,1,2,3,4,5,6...} They are counting numbers but they include 0.
Integers = {..., -3, -2, -1, 0 , 1,2,3...}
Rational numbers = {p/q, p and q are integers not equal to 0} 4/1, 1.3, -9/2, 16/8
Irrational numbers = {real number that is not rational.  Square root of 3, negative square root of 2, Pi
Real numbers = a point on a number line.

Study Problems for Chapter 2

Here are some study problems I am using for chapter 2
Reply and comment

Study Problems for chapter 3

Here are some Problems from chapter 3 that I am using to study
I will post the problems and then we can all post the answers to the different problems as comments and that way we are colabrating!

Study Problems from chapter 4

Here are some problems I am doing to study for the book
They cover all the concepts that we went over in class
I hope that they are helpful for you!
They are problems from the book but they are the most important ones for me to consentrate on and study.
The answers can be found in the back of the book.
You can reply on the blog as a comment to answer the questions
that way we are colabarating and helping each other to study and learn! :)
Amelia

Scribe post 12/14 Patrick

Today in class we went over the google document that is meant to help us prepare for finals. Jojo answered questions that people had about it and went over problems. I will do a few of them now:

Rational numbers are numbers that terminate. Irrational numbers do not terminate or repeat. An example of a rational number is 2/3 or 1/3. In decimal form 1/3 is .3333(repeating). An example of an irrational number is pi or 3.1415... pi goes on forever and does not stop.

Absolute value equations:

|2x-1|=7

2x-1=7 -(2x-1)=7

+1 +1 -2x+1=7

2x=8 -1 -1

x=4 -2x=6

x=-3

x=4 or x=-3

A number (v) plus 15% is 287.5

(1)v+.15(v)=287.5

1.15v=287.5

___ ____

287.5 287.5

v=250

250x.15=37.5

37.5+250=287.5

I guess this is the last scribe post of the term.

Important thing to remember for finals! 2.1

When solving an equation, if both sides have the same thing.
Example: x+1=x+1 then the answer is all real numbers
but if both sides are totally different
Example; 2=5 Then the answer is no solution.
Amelia

4.4 and 4.5 Key Terms!

List of key terms you should know before our test!

4.4

1) Linear Inequality in two variables

2) Boundary Line

4.5

1) Dependent Variable

2) Independent Variable

3) Relation

4) Function

5) Domain

6) Range

7) Function Notation

8) Linear Function

9) Constant Function

4.1, 4.2

4.1

1)Ordered Pair

2)Origin

3)X-axis

4)Y-axis

5)Plot

6)Components

7)Coordinate

8)Quadrant

9)Graph of an equation

10)First-degree equation

11)Linear equation in 2 variables

12)X-intercept

13)Y-intercept

4.2

14)Rise

15)Run

16)Slope

Helpful website for "Percent of" word problems.

I was having some trouble with percent problems earlier and this website really helped me. A few of the examples that helped were:

• What percent of 20 is 30?

We have the original number (20) and the comparative number (30). The unknown in this problem is the rate or percentage. Since the statement is "(thirty) is (some percentage) of (twenty)", then the variable stands for the percentage, and the equation is:

30 = (x)(20)

30 ÷ 20 = x = 1.5

And:

If you need to find 16% of 1400, you first convert the percentage "16%" to its decimal form; namely, the number "0.16". (When you are doing actual math, you need to use actual numbers. Always convert the percentages to decimals!) Then, since "sixteen percent OF fourteen hundred" tells you to multiply the 0.16 and the 1400, you get: (0.16)(1400) = 224. This says that 224 is sixteen percent of 1400.

And:

• What is 35% of 80?

Here we have the rate (35%) and the original number (80); the unknown is the comparative number which constitutes 35% of 80. Since the exercise statement is "(some number) is (thirty-five percent) of (eighty)", then the variable stands for a number and the equation is:

x = (0.35)(80)

x = 28

Twenty-eight is 35% of 80.

Here's the link: http://www.purplemath.com/modules/percntof.htm

Info from sections 3.1, 4.1, and 4.4

Here is some other info from :

3.1

( ) are for less than or greater than problems.

[ ] are for less than or equal too, or greater than or equal too problems.

4.1

Vertical line has an undefined slope.

Horizontal line has a slope of 0

Lines that start from the bottom left corner and go up on the graph have a positive slope.

Lines that start form the top left corner and go down have a negative slope.

4.4

Shading above or below the line on inequalities:

A good way to check to make sure you shaded in the right area is by plugging in a point from the shaded area and if it makes the inequality true than the area is correctly shaded.

Something to remember is if the inequality is less than or greater than then the line is dotted. And if the inequality is less than or equal too or greater than or equal too, then the line is solid.

Good Ways to Study

1. Google Docs

2. Test Aftermath

3. Blog

4. Youtube Videos!

5. Cumulative Review in Book!

4.4 Linear Inequalities Notes

Here is the google doc for 4.4.
It has some really good examples and answers some questions you might have.

How To Study For Finals!

http://www.teencollegeeducation.org/2010/01/crunch-time-study-tips-how-to-study-for.html

This is a great site if you need any tips on how to study for Finals!

Good Luck!

Some helpful google documents

Because its sometimes really difficult to remember terms (especially when its from the first couple of chapters we went over,) I will put the links to some helpful links in the comments. Hope it helps!

Chapter 1 notes

The link to the chapter 1 tutorial are in the comments section of this post!

Chapter 2 Tutorial

So even though we only made tutorials for the first few chapters I still think they would be really helpful to look over, they have key terms, example problems and so on. It won't let me paste the link for some strage reason but if you just go to your google docs it will be right there. I will aslo try to attach it in the comments section. Good luck studying!

Good things to do while taking the final

Here are some helpful things to do while taking the final to make sure you do your best!

1. Always check your work whenever you can to make sure your answer is right!

2. Take your time and don't rush through problems because you may make a careless mistake!

3. Always read every problem carefully, especially word problems, because it is important to find out all the information that is given, and what you are supposed find in the problem. (There are a lot of word problems in chapter 2 that I think are hard, so practicing a lot of those will help)!

4. Read all of the directions given throughout the test because you don't want to skip over something accidentally!

5. Always try each problem, even if you don't know what to do! It is always better to try because you may get some credit, even if the answer is wrong!

How to Study Math!

Another way to study math, that I have found useful, is to write a sample problem, on a flashcard, of the math you are working on,and study / memorize it! I have found this useful for learning how to do word problems. Another way to memorize how to do a word problem, is to write the “equation”, or how to do it on a piece of paper 10 times...This is also a very good way to learn!

Hope this helps!! Good luck on the Final!

Studying For Final Exam

Here are some ways to study for the final exam!
Go through your old tests and mark areas that you did poorly on and practice re doing the problems.
Amelia

Chapter 4 Review Post! Graphs Linear Equations, and Functions

Here is the chapter 4 review post to help for our final test!

Chapter 3 Review Post! Linear Equations and Absolute Value

Here is the Chapter 3 review post for finals!

Chapter 2 Review Post! Linear Equations and Applications

Ok so this post can be a chapter 2 review post for finals! Hope it helps! :)

Chapter 1 Review!

Ok so this post can be a chapter 1 review post! Just comment on it to add things from chapter 1! This will really help everyone study for finals.

Final Review: Chapter 1, Review of the Real Number System

1.1: Basic Concepts

-Natural Numbers

otherwise known as counting numbers {1,2,3,4,5,6,...}

-Whole Numbers

{0,1,2,3,4,5,6,...}

-Integers

{...,-3,-2,-1,0,1,2,3,...}

-Rational Numbers

{p/q⎮p and q are integers, q≠0}

Examples:

-Irrational Numbers

{x⎮x is a real number that is not rational}

Examples: √x, -√2, pi.

-Real Numbers

{x⎮x is represented by a point on a number line}

-Additive inverse

-Number Line

-Set Builder Notation

More Variations

The area of a circle varies directly as the square of the radius= A=kr^2

Pressure varies inversely as volume. P=k/v

For a given principal, intrest varies jointly as rate and time: I=krt

Variation

y=kx^n, then y varies directly as or is proportional to, x^n

y= k/n then y varies inversely as x^n

y=kxz,then y varies jointly as x and z

Function notation practice problem

2x+3y=12 subtract 2x

y=-2/3x +4 divide by 3

f(x)= -2/3x +4

Video Explanation of Function Notation

This lady explains function notation and domain and range pretty clearly. I hope the video in some way helps yall too.

http://www.brightstorm.com/math/algebra/graphs-and-functions/function-notation

Practice Problems - Variation

After looking over the first and some of the second page these practice problems were pretty helpful.
This website covered all the types of variation equations

http://www.purplemath.com/modules/variatn.htm

Differences between Domain and Range and Independent and Dependent Variables

Domain- Set of values for the indepedent variable (x)
Range- Set of values for the independent variable (y)

Indepedent Variable- Experimental variable (what you manipulate)
Dependent Variable- What is affected during the expermiment

Vertical Line Test, and Horizontal Line test

Vertical Line Test- The relation represents a function when every vertical line intersects the graph of a relation in no more than one point


Horizontal Line Test- A graph passes the horizontal line test when its not possible to draw a horizontal line that intersects the graph in two or more places

Jared Scribe Post

Today in class JoJo taught us how to solve a joint variation problem and an inverse variation problem.  When solving an inverse problem the equation to solve is: y= k/x.  Once you find K, the constant, you can solve the problem.  To solve a joint variation problem you have to use the equation y=kxz.  Y varies jointly as x and z if there exists a real number k.  I was confused on how to solve these problems before today, but after the lesson I felt very confident with solving joint and inverse variation problems.  The rest of the class time was used to review for the test!  The next scribe will be done by Cole

 GOOD LUCK EVERYONE!

Test review

Harrison said...
slope intersept form: slope 3/5; y-intercept (0,-8)
y=mx+b y=3/5x+-8
This is helpful to remember while graphing inequalities.
Also remember: y=x - solid line w/ no shadeing
y>x - dashed line, all above shaded
y y>_ - solid line, all above shaded
y<_ - solid line, all under shaded
{(-4,2),(-4,-2),(1,5),(1,-5)}
Domain={-4,1} Range={2,-2,5,-5} this is not a function.

Varies directly y=kx
Varies inversly y=k/x y decreases as x increases
Varies jointly y=kxz - the two variables are x and y
Combined variation y=kw/h
Remember: k is a constant, it will never change

Domain: any value of x variables
Range: any value of y variables
A relation represents a function only if all x values are unique.
while graphing a relation, plot the points, don't connect them.
f(x)= just a formal name for Y

OK - lots of fun stuff to help you on the test, I'm sure most of what I just said has already been posted but this is my summery of things you may want to look at before tomorrow.

Helpful ways to review!

Here are some things that I am doing to review for this test, I hope you find this helpful! One thing is make sure to remember that with you are graphing a line with a '>/<' sign, that the line will be dotted, and when you are graphing a line with a less than or equal to/greater than or equal to sign that the line is solid. Also practicing shading the different sides is very helpful for section 4.4, on pages 206-208 in our books have good practice problems on the right and left sides, and the problems have the answers at the bottom (they have these problems in all of the sections). In section 4.5 make sure to practice using the vertical line test and giving the domain and ranges in functions. Also make sure to remember that f(x) is the same thing as y. In section 4.6 practice all types on variations (direct, inverse, joint, combine) and make sure that you know how to set up all of the different types. On page 242 in our books there is a summary of lessons 4.4-4.6 and it explains the key points that we learned about and gives examples. I found this page super helpful, so make sure to look at it!

Harrison said...
Here's how to solve a inverse variation problem.
If z varies indersely as w, and z = 10 when w = .5 find z when w = 8.

z=k/w
10=k/.5
multiply by .5
k=5

z=5/8 z=.625

Definition of a Relation

Ist variable paired with one or more values of the second variable. (x.y)

(1,3), (1,5)

Ex. The change you recieve for buying a $.65 soda depends on how much you gave the vending machine. x .65 .70 .75 1.00 5.00

y 0 .05 .10 .35 4.35

Domain Restrictions

Values of the variable that will make the function undefined, values not included in the domain.

y=1/x D: All real numbers when x isn't equal to zero. R: All real numbers when y is greater than or equal to zero or when y is greater than 0.

Linear Functions

Multiply by the same umber over and over again.

y=output or dependent variable

x=input or independent variable

Things to remember

In order to have the variation equation you must solve for k.
Amelia

Things to remember

In order to have the variation equation you must solve for k.
Amelia

Scribe Post WITH IKE! AAAHHH YAY 4.6

OK! So, get pumped. Because 4.6 is really just... a great chapter. Really, it is the BEES KNEES.

What we covered today in this chapter of wonder is only the first part of it: direct variations.

According to our trusty book, these types of equations are extremely common in everyday business and physical science life. If those are part of your life, this may mean the world to you.

When Y is said to 'VARY DIRECTLY AS X', it means that Y is dependent on a multiple of X.

This is known as direct variation. An easy way to remember this is to just remember the formula

Y = KX .

Good? What this means is basically what was just said; that Y is dependent to a multiple of X: aka, KX.

(y is proportional to x.)

So, in order to be able to say this, really powerful people who can make laws about math have decided to give the number that you multiply x with (k) a handy dandy name. They call it...

THE CONSTANT OF VARIATION!

Whew.

In a direct variation, (which is what were covering right now,) as long as K is greater than zero...

AS X INCREASES, Y ALSO INCREASES.

So, in a real world situation, K would be the constant in the problem. For instance, if you want to find the cost for buying yummy in my tummy candy bars, (Snickers, of course,) they will always cost the same. I mean, theoretically, and for the sake of the problem, the cost will never change. This means that the cost is CONSTANT, meaning it is THE CONSTANT OF VARIATION, or K! Easy enough. The equation to write this would be:

y = (COST OF SNICKERS) x

Y would equal your final cost, and x would be how many snickers you bought. And, again, since the cost of the snickers is positive (k), the more snickers you buy, the higher the cost will be.

There!

And that is about it for DIRECT VARIATION problems, in simplicity.

JARED is the next scribe.

Direct variation and Joint variation

Direct variation: Y varies directly as x if there exists some constant k such that y=kx

joint variation: Y varies jointly as x and z if there exists a real number k such that y= kxz

Inverse Variation

y varies inversely as x if there exists a real number k such that: y= k/x

also y varies inversely as the nth power of x if there exists a real number k such that y=k/x^

Solving a Variation Problem

Step 1= Write the variation problem
Step 2= Substitute the initial values and solve for k.
Step 3= Rewrite the variation equation with the value of k from step 2.
Step 4= Substitute the remaining values solve for the unknown and find the required answer.
Amelia

Function Machine!!

http://www.amblesideprimary.com/ambleweb/mentalmaths/functionmachines.html

This is the website to the function machine we played with earlier in the week... maybe it will help for our next test?!?

Examples of Function Notation, and Definition of Relation!

Definition:

A relation is a correspondence between two sets (called the domainand the range) such that to each element of the domain, there is assigned one or more elements of the range.

FUNCTION NOTATION

We write f (x) to mean the function whose input is x

Example

If

f(x) = 7

then

f(12) = 7

Here f is called the constant function. Whatever comes in to f, the number 7 comes out.

http://www.ltcconline.net/greenl/courses/152a/functgraph/relfun.htm

This is a great website if you need example problems, or help on the upcoming test!

function notation

y=f(x). This is function notation.

To solve an expression for f(x) step 1: solve the equation for y.  Step 2: replace y with f(x).

Here is an equation
Find F(-2)
F(x) = X squared +1
F(-2) = (-2) squared +1
F(-2)= 4+1
F(-2) = 5

Reminder about Relations

Remember that a relation is not always a function because a relation only represents a function if all x values are different. So a relation can or cannot be a function, it all depends on the x values. When you graph a relation that is not a function, you don't connect the dots on the graph, you just leave them as points rather than a line since it is not a function.

Domain and Range

Domain= all the possible values of x.
Range= all the possible values of y.
Amelia Hess

function

An easy way to tell if a graph is a function or not is to use the vertical and/or horizontal line test.  If the vertical or horizontal line passes through the graph more than once, than it's not a function.

Example of functions

X=0,1,2,1,0
y=3,4,5,6,7
this function doesn't work because the same x has two different x's have the same y.
X=1,2,3,4,5
y=1,2,3,4,5
this works and is a function because none of the x values have the same y.
Amelia

Functions

For every x there is only one y.
Amelia

How you write a function

Y =3x+2 is how you write a linear equation
You write the same thing with an f(x) for it to be a function
F(x)=3x+2
f(1)=3(1)+2
f(-2)=3(-2)+2
Amelia

Function

If any two points on the graph have the same x value, it is not a function. Vertical lines are not a function.
Amelia

Function

Christine, 4.5 introduction to Functions

Today in class, we started learning about functions! At first, we all thought that it would be super confusing! But when looking into the chapter, it makes a lot of sense. We use a lot of information we learned in past chapters. We did a digital scavenger hunt on google docs which helped us understand functions. I feel like I am starting to really understand math and especially functions. I thought that it was really cool that x and y values are also known as domain and range. At first, I really didn't understand the what a function was, but the definition in the book made it very clear to me. A function is a relation in which, for each value of the first component of the ordered pairs, there is exactly one value of the second component.

Sorry the pictures of graphs wouldn't upload but I will post them later!