Graphs and Quadratic Functions

Today in our math class we reviewed how to sketch the graph of a funtion. When given a function the a part of the equation is the x squared part, the b part is the x part of it and the c is the y intercept. You can use the c to find your y intercept when graphing. you can also use a table of values to find where numbers repeat. Where they repeat will get you close to the max or min value. If the function opens up there will be a min value and if it opens down there will be a max value. The axis of symmetry is the line that goes through the point of the function, the max or min value. We then ended off the class by doing an assignment on pg. 368-372 questions 1,3,4,6,7,9,11 part i and ii and 13.

Next person to go will be Koralyn

Project Hand-in

Please, have your files prepared for your presentation. You should either bring your files on a memory stick or email them to me at mrbanow at gmail.com. 


Please, do not plan to sign in to your email account or school account.

Project Info Re-Posted

Here is the Project Assignment if you have misplaced it: http://dl.dropbox.com/u/39411274/Math%20Foundations%2020%20Project.docx

I have decided that giving you the Holiday Break to finish your projects may be better than having them due before the break. Presentations will be on Wednesday, January 4 and Thursday, January 5. If you would prefer to present before the break, speak to me and we will arrange that.

The presentations will be as follows:

Wednesday, January 4
Michelle
Aaron
Alex
Kelsey
Jeff
Nina
Brydon
Emily
Colby
Joel

Thursday, January 5
Sarah
Amy
Koralyn
Allysa
Tanner
Cody
Taryn
Miranda

You should email your presentation and other files to be displayed on the SmartBoard ahead of time. Email my mrbanow at gmail.com account. If you have any materials that are not digital, please bring them the day of your presentation and hand them in to me.

If you have questions now or over the break, email me and I will get back to you fairly quickly.

Good luck and have some fun! I hope your topic interests you!

Next Stages in the Project: Data and Controversy

In chapter 5, we studied measures of central tendency and Normal Distributions. Depending on your topic, this may relate to your project. If you have done a survey or have collected data (even from online), then you will want to consider how to analyze your data:

• will you discuss mean, median, or mode?
• is your data Normally distributed?
• do you know that sample size and margin of error/confidence level for the data you found online?
• see pages 284-286 for more suggestions

Now that you have completed some research, you will want to scrutinize your data for any controversial issues. 

• have you found two sources that provide contradictory information or data?
• does the contradictory data represent different viewpoints? (eg. is the data being provided by a group that would want a certain outcome?)
• see pages 352-353 for more ideas

Everyone needs to follow this link and complete the short survey regarding your controversial issue(s). 

CLICK HERE ----> Complete this once you have done a significant amount of research

If applicable, discuss the controversial data in your presentation.

Chapter 6 Review Answer Key

Click here: http://dl.dropbox.com/u/39411274/Review%20Answers%20Ch%206.pdf

6.6 Optimazation Problems: Linear Programming

On Tuesday we started 6.6 Linear Programming. Linear Programming is a mathematical technique used to determine which solutions in the feasible region result in the optimal solutions of the objective function.

To solve this, first you find the linear inequalities and put them on a graph. After that you fine the maximum and minimum values of the objective function. You can do this by using a vertex/value chart. Then using the information from this chart make a statement showing your results.

We were given five steps in using Linear Programming to solve an optimization problem which includes the information we have learnt in 6.4 , 6.5, and 6.6.

The steps are as followed:

1. Define: - Variable

- Domain/Range

- Inequalities (Constraints)

- Objective Function

2. Graph

3. Evaluate the objective function at the vertices's

4. Analyse and Interpret - choose desired solution

5. Verify

After we went through EX.1 on the handout Mr.Banow gave us. Question found below in picture.

For practise we got assigned Page 341-345 # 1,2,4,6,11,13

:)

6.4 and 6. 5 Optimization Problems

:)

In 6.3, we learned that what kind of numbers were dealing with contribute to our answer. This still applies to 6.4.



In 6.4, we learned about optimization problems. In an optimization problem, it asks you for the maximum and minimum possible solution.

Optimization problem
a problem where a quantity must be maximized or minimized following a set of guidlines or conditions.

Constraint
A limiting condition of the optimization problem being modelled, represented by a linear inequality.



Objective function
in an optimization problem, the equation that represents the relationship between the two variables in the system of linear inequalities and the quantity to be optimized.

Feasible region
The solution for a system of linear inequalities that is modelling an optimization problem.

The area in yellow represents the feasible region.



When graphins linear inequalities we must remember which part of the inequality goes on certain areas of the graph.



We then went over the last page of our 6.4 booklet.
We found out that you can tell you're dealing with an optimization problem if you have to find the minimum or maximum.
We found that the constraints are the linear inequalities in the problem.

We did practice on pages 330-331 # 2,3,5,6.

In 6.5 we looked at the race car and suv problem again.
We realised that the maximum and minimum was on the vertices of the feasible region, but we had to find out which two vertices.

The objective function to optiimize was: C = 8r + 12s
C = cost
r = race cars
s = suvs

We found that (60, 40) was the maximum.
C = 12(60) + 8(40)
C= $1040

We found that (30, 40) was the minimum.
C = 12(30) + 8(40)
C = $680

But does the minimum cost satisfy all the constraints?
Constraints:
r<40 (less than or equal to)
s<60 (less than or equal to)
s+r>70 (greater than or equal to)
YES IT SATISFIES ALL CONSTRAINTS!

We then did practice questions on pages 334-335 #1-3

here is a math video to brighten your day! lolol
http://www.youtube.com/watch?v=cgEuUzHYvOY">


Next will be Aaron :D

Extra Assistance for Graphing Linear Inequalities

Graphing an Inequality Video

Writing an Inequality for a Given Graph Video

Solving a System of Linear Inequalities Video - note: @ 3:50 he accidentally says 6/4 equals 6. The b-values and y-intercept should be 3/2 or 1.5, not 6.  Also, in this video he has three inequalities. For 6.2 and 6.3 we only had two in a question.

Online Quiz - Choose Check Answer to verify if you have done it correctly

6.3 Graphing to Solve Systems of Linear Inequalities

Today, we started off the class by reviewing some examples from the 6.2 unit, Exploring Graphs of Systems of Linear Inequalities. A quick summary of that that is, a set of two or more linear inequalities that are graphed on the same coordinate plane; the intersection of their solution regions represent the solution set for the system.

Next, we moved on the 6.3 Graphing to Solving Systems of Linear Inequalities. Systems of inequalities are similar to systems of equations. A solution is still an ordered pair that is true in both statements. The video below shows Graphing and Solving Systems of Linear Inequalities, therefore I'm not putting pictures up because that seems to explain everything I need to say.

http://www.schooltube.com/video/5b3ebaca5377c2d10e59/Solving-Systems-of-Linear-Inequalities-by-Graphing

Mr. Banow assigned Practice pp. 317-319. It wasn't due, we just heard about it briefly at the end of class.

The next person to go is whoever has not gone their second time.

6.0 Systems of Linear Inequations

Today in class we looked at graphing inequalities. An inequality says that two values are not equal.

We also did a work sheet about Amir buying nuts and raisins with $200, no more. We worked out the inequality of 25x+8y=200 to a y=mx+b formation so that we could graph it. (the picture is just an example) The line that was created was to be dashed to signify that we can only use information under the line, or Amir would be going over budget. We than did a test point to make sure all the information was correct. To do a test point, choose two points, under or over the line and substitute them for x and y and figure out the equation. The results should come out correct if the line is right.

ex.Inequality: x-3y>6

graphing formula: Y=1/3x-2

Test Point: (below) (2,2): 2-3(-2)>6 =8>6 <-yes, this is correct, 8 is greater than 6.

We than did three more examples of graphing inequalities before we were assigned the pages 303-305 #1-3,4,6,a,c,e,7,10

This lovely post was done by Amy,

I don't know who else has to go so Mr banow can choose.

:)

Review of Terms and Connections

On Friday we reviewed what we need to know in order to start chapter 6 on Monday. We went over terms and definitions of words which was a helpful hand for people who completely forgot what any of those terms meant.We briefly went over the real numbers classification system, which looks like the rings of a tree. It has natural numbers in the centre, whole numbers around that, integers around that, real numbers on the outside, then rational and irrational numbers in the very outside. We also reviewed applying number concepts, number classifications, working with linear equations ans linear inequalities, rearranging equations, rearranging inequalities, verifying solutions to equations, solving systems of linear equalities on a Cartesian coordinate plane. The Cartesian plane's quadrants go counter-clockwise with the 1st quadrant in the upper right hand corner.

This was a good review for the upcoming chapter 6, so hopefully everyone got a good weekend because today is crack down time!

Next up: Whoever Mr. Banow picks from that list of names that I completely forgot who's on! Yaaay.

5.6 p. 275 #7 Form

For the Confidence Intervals assignment you need to find an article online and answer two questions about it.

Complete the question by filling out this form:
https://docs.google.com/spreadsheet/viewform?hl=en_US&formkey=dDdkVkVvTXRCSlJfTnAzMDhUbGlhdUE6MQ#gid=0

This must be complete by Friday, December 2.

Thanks.

Project

Here is the Project Assignment if you have misplaced it: http://dl.dropbox.com/u/39411274/Math%20Foundations%2020%20Project.docx

I have decided that giving you the Holiday Break to finish your projects may be better than having them due before the break. Presentations will be on Wednesday, January 4 and Thursday, January 5. If you would prefer to present before the break, speak to me and we will arrange that.

The presentations will be as follows:

Wednesday, January 4
Michelle
Aaron
Alex
Kelsey
Jeff
Nina
Brydon
Emily
Colby
Joel

Thursday, January 5
Sarah
Amy
Koralyn
Allysa
Tanner
Cody
Taryn
Miranda

You should email your presentation and other files to be displayed on the SmartBoard ahead of time. Email my mrbanow at gmail.com account. If you have any materials that are not digital, please bring them the day of your presentation and hand them in to me.

If you have questions now or over the break, email me and I will get back to you fairly quickly.

Good luck and have some fun! I hope your topic interests you!

Statistical Analysis Exam

On Monday, November 21 there is an Open Book exam on sections 5.1-5.4.

The key concepts are:

• mean
• standard deviation
• frequency distribution tables
• histograms
• frequency polygons
• Normal distribution

Standard Deviation Calculator

Here are a couple of online tools to calculate standard deviation (among other things)!

http://www.numberempire.com/statisticscalculator.php   On this one, check off Mean and Standard Deviation

http://www.miniwebtool.com/standard-deviation-calculator/  Works like a charm!

Good luck with your assignment!

5.4 NORMAL DISTRBUTION CURVE

To day we did 5.4 the normal distribution we looked at 4 different kinds of histograms

The first one is called a single point histogram or NORMAL DISTRBUTION CURVE the pink one is skewed
The blue one is a bi- modal and the orange one is uniform
Than we did a thing that involved rolling a dice 50 times and recording the sum of the numbers
Than we combined the whole class’ results and made the histogram
It was like the purple one with the top ones being 7 and 8
Than we looked at this graph

And this gave the standard deviation purpose. Telling us a lot about one set of data
Next is joel

Standard Deviation

We started section 5.3 today. We got a hand out and did the following question together:

"The coach of a girls' basketball team keeps stats on all of the players. Near the end of one game, the score is tied and the starting point guard gets fouled out. He needs to make a substitution. There are five girls on the bench who can sub in for the point guard."
The stats for the players were stated next.

Then we were asked which player was most consistent. We found that Paige was most consistent because her percentages were all between 33-35. They were not scattered, therefore they were consistent.

After that it said that the coach found that Paige and Patrice's values were close in value. He compared them more closely using standard deviation (a measure of the dispersion or scatter of data values in relation to the mean.)

We followed these steps to calculate the standard deviation for Paige:
-Determine the mean of Paige's shooting percentage.
(add all of Paige's percentages then divide by the amount of percentages there is. In this case there is ten.) We found that Paige's mean was 33.9.

-Calculate the deviation of each field goal percentage.
(Take one percentage and subtract it from the mean. Continue doing this with all the percentages.)
EX. 34-33.9=.1

-Calculate the squares of the deviations.
EX. The square root of .1 is .01. (Square root all deviations.)

-Fill in the values into the chart on the second page of the handout.

-Determine the standard deviation by:
-determining the mean of the squares of deviations.
(add all the squares of deviations and divide by 10)
Our answer was .69

-determining the square root of the mean from the step above^:
The square root of .69 is .8307.

Then we did the steps above for Patrice.
Next, we were asked who was more consistent between the two players. Our answer was Paige because .8307 is a smaller standard deviation than 1.4976(Patrice's standard deviation) and a smaller number means that here is more consistency.

We then calculated the mean and standard deviation using a graphing calculator. To do this, you must follow these steps:
-Stat
-Edit
-Enter the numbers
-Stat
-Calc
-1-var stats
-Enter.
(I probably forgot a step.)

We didn't finish the whole sheet but we will be finishing the rest in class tomorrow.
Next up is Colby.

5.1 Exploring Data

On Friday we started a new unit called Statistical Reasoning. This is about collecting data from a set of numbers or statistics. We learned new terms like: outliers, range, mean, median, and mode and how to draw a line plot. Alex did a pretty good job of summarizing those in the last post which makes it unnecessary for me.

Today we were supposed to hand in our diagnostic tests which the majority of people didn't do, so remember to hand those in asap. We then worked on a sheet given to us on section 5.1 Exploring Data, and we had to find the mean, median, mode and range for the life of a car battery. We discussed the results and found that based on our data neither brand x nor brand y were a better choice, but it depended on whether or not the consumer was willing to take a risk on purchasing a battery that could either last longer or shorter than the average time. We learned one new term which was dispersion.
Dispersion is a measure that varies by the spread among the data in a set; dispersion has a value of zero if all the data in a set is identical, and it increases in value as the data becomes more spread out.
After that we were assigned Pg. 212 #2 and 3.
The next person to write the blog will be Brydon. :)

Chapter 5: Statistical Reasoning

On Friday we began our next chapter: Statistical Reasoning. This chapter is to help us understand and apply standard deviations, confidence intervals, confidence levels, margin of error, z-scores, and more.

We looked at page 207 and discussed on how statistics help monitor the polar bear population, and how it can determine whether the population is stabilizing or taking a decline. We figured that by using inductive reasoning, one could predict the future outcome of the population.


Math.

Next, we looked at page 208 and 209 to apply our potentially new-found knowledge of mean, median, and mode values. The definitions for these terms are as follows:

Mean: A measure of central tendency determined by dividing the sum of all the values in a data set by the number of values in the set.

Median: A measure of central tendency represented by the middle value of an ordered data set.

Mode: A measure of central tendency represented by the value that occurs most often in a data set.

An example in which we can apply these terms is:

Let's say that this represents the size in cm of the diameter of school spheres. The mean is 47.857 cm (add the numbers up, 335, and divide by the amount of numbers, 7). The median is 50 cm (the middle column holds the 50 cm), and the mode is 20 (the only number repeated twice).

We also went over questions A-E on page 209. From doing so we learned about ranges (the difference between the maximum and the minimum value), outliers (a value in a data set that is very different from the others), utilized our knowledge about central tendencies to determine values for the 3 companies' salaries on page 208, and learned about line plots.

At the end of class, we were given our marks for our Oblique Triangle Trigonometry test, and were assigned the Chapter 5 diagnostic test, which was expected to be done by Monday.

The next person to make a blog will be Nina.

How to Rewrite Your Sine and Cosine Laws Exam

Many of you struggled with this exam.  I know that most of you can calculate sides and angles using Sine and Cosine Laws.  That is part of our goal for this unit, but we also need to be able to:

• understand and apply the Ambiguous Case
• solve written problems involving oblique triangles

I encourage you to attempt to improve your mark on this outcome.  To do this, you must:

• talk to Mr. Banow about coming in at a lunch hour to practice
• hand in all assignments from Chapters 3 and 4
• complete p. 200 #3, 5, 6, 7, 8 and p. 195 # 11 (I used to have 8 on this list - skip it) - You need to show all diagrams and calculations.  You may work on this during the lunch hour you come to work
• schedule a second lunch hour to write the exam

Good luck!