Kassandra's Post

Quadratic Equations

Song By: Lillian

X is negative b

Plus or minus squared root

b square minus 4 ac

all over two a (2a)

----------------------------------------------------------

X^2 - 5X - 7

Y- Intercept (0, -7)

Axis of Symmetry X= 5/2

-b +/- squareroot b^2 - 4ac / 2

5+7.3 /2

5 - 7.3 /2

Zeroes (6.15,0) (-1.15,0)

Vertex Y=(5/2)^2 - 25/2 -7

(2.5, -13.25)

(-1.15,0) (6.15,0) (0,-7)

X=2.5 (2.5, -13.25)

Graph should have a positive curve

Homework : P. 262 # 4

Question: Did I do a good job on this blog thing?????lol

Axis of Symmetry

Bellringer: Find the axis of symmetry

A. y=x²+4x+1
-4/2=-2 x=-2

B. 2x²-6x+3
6/4=3/2

C.-2x²+5x+1
x=-5/4

REMEMBER: What you learn in September will haunt you in May!!!

Practice Question 2:

x²-5x+8

1. Axis of Symmetry
x=5/2 or x=2.5

2. Y-intercept
The y-int. is C so in this equation it is 8

3. Vertex
(2.5) ²-5(2.5) +8=1.75

When this is graphed it should look like a “U” above the x-axis. Since the parabola is above the x-axis no real zeros exist.

Question: (To see if you were paying attention to Mrs. Sullivan)

*Do you have to reduce radicals on the IB test?

Leilani's Post

Bellringer: Find the axis of Symmetry

*Remember: Ax2+Bx+C

Formula to find the axis is:

x= -b/2(a)

a) y= x2+4x+1

If we apply the formula our equation would be:
x= -4/2(1) = -2

So.... x= -2

b) y= 2x2-6x+3

Equation: x= 6/2(2) =3/2

So... x= 3/2

c) y= -2x2+5x+1

Equation: x= -5/2(-2) =-5/-4

So...x= 5/4

_____________________________________________________
Practice Question 1:

y= 1x2+4x+1

1) Axis of symmetry

Equation: x= -4/2(1) =-4/2 =-2
So....x=-2

2) Y-intercept
The y-intercept is always C.

So our y-intercept is 1.

3)Vertex
Replace the x in the equation with your axis of symmetry, in our case it would be -2.

-2^2+4(-2)+1 =
4-8+1 = 4-8 = -4...........-4+1 = -3

So our vertex is (-2,-3)

4)Find the Zeroes of the equation
Solution of a quadtratic equation formula= -b+-{b2--4ac/2a

{ = square root

Type it into your calculator like so:
-4+({4^2-4*1*1))/2*1 2 = -4+({12))/2= -.27

Do it again for the negatively:
-4-({4^2-4*1*1))/2*1 2 = -4-({12))/2= -3.7

So our zeroes are: (-.27 , 0) and (-3.7 , 0)



Find the axis of:
a) 6x^2+2x+9

b) -5x^2-7x+3

Yay!

Walter's Post

Graphing Parabola

Direction of the parabola

Ax(square)+Bx+C

A-determines the direction

-A is an upside down U

+A is a rightside up U

y intercept is always C

Vertex of the parabola------>substitute -B/2A into the equation

Axis of symmetry x=-B/2A

zeroes of the equation is where you cross the x-axis

Homework: pg. 306 Problem #1

Math Studies II Factoring and Simplifying (November 1, 2010)

First to post this month! Ha!!!!!

On to the blog.....

Math Studies II (11/1/10)

Bellringer:

• Simplify:

1. -3(4x)

2. (x-5)(x+2)

3. (x-5)(x2+4x+14)

• Solutions:

1. -3*4x = 12x

2. x2+2x-5x-10 = x2-3x-20

3. x3+4x2+14x-5x2-20x+70 = x3-1x2-6x+70

• Factor:

1. (x2-9)

2. x2+8x+16

3. x2-5x+14

• Solutions:

1. (x-3)(x+3)

2. (x+4)(x+4)

3. (x-7)(x+2)

Explanation of Solutions:

Example 1: (x2-9) First, what two numbers will equal -9 when multiplied?.... hmmm? Hey, How about 3 and -3. That works. So next we check to see if (x+3) multiplied by (x-3) equal (x2-9) by using the foil method......and (x+3)(x-3)= x2-9

Example 2: x2-5x+14. First, find two numbers that multiply to make -14 and can be added to make -5. The only two numbers that can do that are -7 and 2. So our solution will be (x-7)(x+2) the answer can be checked to determine if it is correct by using the foil method.

AGENDA

I. Bell ringer

II. Review Factoring and Properties of Parabolas

OBJECTIVE

Students will find zeros and vertex of a parabola and accurately factor it.

BIG PICTURE

Parabolas model objects in motion.

MORE EXAMPLES OF CLASS WORK, ETC

Example 3: (x2-16) this is an example of the Difference of 2 Squares. Why? Because (x-4)(x+4) make (x2-16). 4 and -4 are the squares of 16.

Example 4: (x-5)(x2+4x+4). To solve use distributed property. Meaning; multiply the 1st term in the 1st set by the 1st term in the second set. the end of this part should result in x3+4x2+4x then multiply it by the second term in the 1st set. Then by the third.. Then multiple 2nd term in 1st set by the 1st term in the second set followed by the second term and lastly the third. The result of this should be -5x2-20x-20 Finally you add both your results. your combined result should be. x3-x2-16x-20.

Example 5: x2+4x+4 = Perfect Square. Why? because (x+2)(x+2) results in that answer and 2 is the square of 4.

Example 6: Another Perfect Square: 4x2+20x+25. Why because of 5 duh! (3x+5)(2x+5)

Confused so far? An Explanation of Perfect Squares is

Coming your way......

Is It A Perfect Square?????

To determine if it is indeed a perfect square take the square root of the 1st number and multiply it by the square root of the last number then double the result. If the doubled result gives you the number in the middle then *drumroll* IT IS A PERFECT SQUARE.

WARNING/DISCLAIMER: Do not attempt in problems that do not have 3 numbers.

Anyway.... Example:

16x2+48x+36

ARE YOU SERIOUS THE KEYBOARD DOES NOT HAVE A SQUARE ROOT KEY. THE CALCULATOR HAS ONE. AAAAARRRGHH!!!

Anyway... let's continue. We know that the square root of 16 is 4 and the square root of 36 is 6. Next we multiply 6 and 4 and get 24. Then we double and get 48. 48 is the number in the middle therefor it is a Perfect Square.

NOT PERFECT SQUARES:

Quadratic formula: -b +/- square root of (b2-4ac/2)

Example: 9x2+8x+4 (a is in orange, b is in blue c is in red

Plug in the example and your answer should be.......

AN IMPOSSIBLE ONE! IF YOU GOT AN ANSWER YOU ARE INCORRECT!!!!!

Get the Calculator You'll need it for this one!

(we are graphing now. OH! the joy)

Go to y=

Plug In y= 9x2+8x+4

Click Graph

You'll see a Parabola. Not touching the zero

WOW!!! How Fancy

HOMEWORK

Page 251 #1.

Questions of the day (My Favorite Part of the Segment)

1. List a Perfect Square. That was NOT used as an example on this blog post.

2. Factorize: (x+5)(x-5+25)

Well Now this was fun! Wont be doing this again anytime soon. YAY!!!!!

-Lisette Garcia

IB Math Studies II

BELL RINGER:

Enter data from problem 6 in your calculator.

• Write the Null and Alternative Hypothesis.
• Would you reject or accept the Null hypothesis? Why?

AGENDA:

1. Bell Ringer
2. Review Set 18A in pairs (pg. 597)

OBJECTIVE:

Students will use statistics to Evaluate the data of two Variables.

BIG PICTURE:

Statistics helps quantily the relationship between Data.

HOMEWORK:

Introduction for Internal Assessment is due tomorrow!!

• MUST be Emailed berfore 11:59 tomorrow.
• Atleast 2-3 Pages.
• Include ALL surveys if you are doing some.

Math Studies II 10/18/10

Bellringer: Enter data on page 599 problem number 3.
Low Average High Very high
No success 35 30 41 25
Low Success 28 41 26 29
Success 35 24 41 56
High Success 52 38 63 72

What is the expected value for Average Intelligence Success?
How is it found?

Agenda:
I. Bellringer
II. Writing a formal hypothesis
III. Introduction Questions

Objective:
Students will write and analyze a formal hypothesis.

Bellringer answer/Notes:

32.62 is the expected value for Average Intelligence Success.

[35 30 41 25 ]
[28 41 26 29 ]
[35 24 41 56] =156
[52 38 63 72]
Sum of column 2= 133 Total: 636
ΣR3 ● C2 = ΣC2 ● ΣR3 divded by Σ All students

[Expected value=32.62]

Chi-squared= 25.56
P= 0
Degrees of Freedom= 9
P value= Similar to standard deviation
Look on Page 596 in Math Studies book to learn how to calculate P value.
Page 594 shows you how to write your hypothesis.
Null Hypothesis (H0)= Intelligence level and business success are independent.
Alternative Hypothesis (H1)= Intelligence level and business success are NOT independent.

Cannot say dependent!

Example: Not guilty in a court of law is not the same as innocent because not guilty just means they weren’t found guilty (no evidence found) not that they’re innocent.

Because Chi-squared is less than 21.679 I can say with 99.9% confidence I can reject H0 in favor H1 and say that Intelligence level and business success are not independent.

Question of the Day: When finding the expected value of a data set in my TI-83 calculator where do I insert the data points?

Math Studies II 10-13-10

NO BELLRINGER!!
DUE WEDNESDAY 10/20/10

• INTRODUCTION of the IA

Should include:

1. Title
2. Clear statement of the task:
3. Hypothesis
4. A plan ( in steps)
5. If you have a survey or experiment make sure you attach a sample of it to your introduction.

Also DONT USE WORDS SUCH AS

1. Causation
2. Random

Linear Correlation

• Used for quantitative data > get it through R-Value

We worked on pg. 581 of our text book problem number 3

• Diagnostics on (calculator)
• L1 = Judge A L2= Judge B
• Enter Data in calculator
• Then go to stat, calc, and choose nr. 4=lin.reg
• Your results should look like this:
• y=ax+b
• a=1.297979798
• b=-2.411616162
• r2=.8883643358
• r=.9425308142

Plug everything in the equation of a line formula given = y= 1.30x+-2.41

Then press Stat, plot 1 (on), Fix windows, and Graph it.... Now you have your graph :)

NO HOMEWORK FOR TONIGHT BUT YOU CAN START ON YOUR INTRODUCTION!!!

Question of the day: What is the difference between r2 and r?

Math Studies II

Bellringer: Consider the question; Students' math grades and science grades are an indicator of college success, what data could i collect to pursue an evaluation of my hypothesis?

Agenda: I: Bell Ringer
II: Discussion of student topics

By 10.8.10 3:00pm !
Hw- In an e-mail to susysullivan@gmail.com

1. A topic for your project
2. A hypothesis to be explored
3. A minimum of 5 Data points to be collected

BIG PICTURE: Mathematics provides the tools to analyze data relationships

OBJECTIVE: students will find a project of interest to pursue for their internal assessment.


QUESTION OF THE DAY:
If i wanted to find data points on the effect of music on teenagers and their study habbits what could they be?

Math studies II 10-4-10

Agenda

• Bellringer
• Math Studies paper

Bellringer: Name 5 different Data points you could collect if your math Studies project was " The Relationship of Gross Domestic Product and Infant Health"

Possible answer

death rate per 1000 live births

Objective:Students will indentify a valid project that can be completed in 7 weeks.

Big picture: Math and statistics help und understanding the world around us.

Notes

• $4.3 trillion is Japan's Gross Domestic Income
• Based on population
• Infant mortality per every 1000 births
• Deaths per Day
• By gender/race/ethnicity
• Family income
• Goverment support of medicine

Amount of Data

• About 100 Data Points
• 4-5 data points

Types of Projects you can do

• execute an Experiment
• Execute a Survey
• Written by yourself or data that has be published and is valid.
• Liekert Scale
• from 1-5

Question of the Day: Name 3 data points that can be used to if my project question is "the relationship between obesity and health probelms"??

IB Math 2 10/1/10

Agenda

· Reminders

· Homework Review

· Internal Assessment

!!For All Students that were not at school today (10-1-10) all make up points from the test are due Monday!!

Home Work (We went over EX 18B.2 Questions 1&2)

1. The scatter plot alongside shows the association between the number of cars crashes in which a casually occurred and total number of car crashes in each year from 1972 to 1994. Given that r value is 0.49:

A) Find r^2

R=0.49

So what you do is this .49x.49= r^2=0.240

B) Describe the association between these variables.

Its Weak

2. In an investigation to examine the association between the Tread depth (y mm) and the number of kilometers travelled (x thousand) a sample of 8 tyres of the same brand was taken and the result are given below.

Kilometers (x thousand)	14	17	24	34	35	37	38	39	L1
Tread depth (y mm)	5.7	6.5	4.0	.30	1.9	2.7	1.9	2.3	L2

A) Draw A Scatter plot of the data

To make a scatter plot

Use your calculator and press stat and enter in edit

Place the following numbers in the appropriate Colum as shown by the red marking on top

After you done that go to

2^nd Y= and have the first plot on and the rest off

Then go to window and type in

Xmin=10

Xmax=40

Xscl=2

Ymin=0

Ymax=7

Yscl=5

X res remains as is (1)

Then plot

B) R= .951

R^2= .+904

Internal Assessment

!!Due Monday!! 10/04/10

Everyone must bring in a plan for what you will want to do for your math internal assessment. Use the big packet that ms.s gave you! For an idea. You can Google math internal assessment for ideas.

!!Due Thursday!! 10/7/10

Using your plans that you brought on Monday. You must bring in how you are planning to do your internal assessment.

Math Studies Dos

Sorry it took me so long to post this. I don't have a problem for guys but if I think of one if i can actually understand what I'm doing I'll post it up. So for now, here are the notes for today.

Agenda:
I. Find Correlation Coefficient
II. Mastering Calculator
III. Your Math Project

Objective: Students will be able to find the correlation coefficient using calculators.

On your calculator go to STAT. Click on No.1: Edit. Type in the numbers below.

L1: 2, 7, 12, 4, 9, 20, 8, 3, 32
L2: 7, 20, 32, 16, 27, 58, 5, 10, 104

Once done exit out pressing 2nd then Mode. Click on STAT then go right for CALC. Click on No. 1: 1-Var Stats, press ENTER again.

X Bar should equal and rounded to 10.78.

Next hit 2nd and ENTER. Now click 2nd and 2 for L2. Press ENTER.

X Bar should equal 31.

Next press STAT then EDIT. Highlight L3. Type in L1(2nd and 1) minus 10.78. L3(1) should now equal -8.78.

Next highlight L4. Type in L2(2nd and 2) minus 31. L4(1) should now equal -24.

Next highlight L5. Type in L3(2nd and 3) times L4(2nd and 4). L5(1) should now equal 210.72.

Clear Screen(2nd and Mode) then click clear.

Now press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L5(2nd and 5)). You should get 2396. Divide that by 9 for the number of data. Press ENTER. You should now get 266.2.

Once again press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L4(2nd and 4) squared). Press ENTER. You should get 8114.

Again press 2nd then STAT. Go to the right to MATH. Press No. 5 for sum. Sum(L3(2nd and 3) squared). Press ENTER. You should get 745.6 round to 746.

Now square root 8114 divided by 9. You should get 30.
Again square root 746 divided by 9. You should get 9.1.

Now multiply 30 and 9.1. The answer should be 273.

R= 266.2 divided by 273. Which equals .975. Square that to get .95 as your answer.

I really don't get this part here so yeah.

Press 2nd and 0. Go down to DiagnosticOn Press ENTER and ENTER again. It should say done.

Go to STAT then go to the right for CALC. Go down to No.4 for LinReg(a+b). Press ENTER and ENTER again.
y=a+b
a=3.213710879
b=-3.636661699
r2=.948983395
r=.9741577875


HOMEWORK IS ON PAGE 582. THE PROBLEMS ARE 1-4.

Math Studies 2

Septmeber 27, 2010

Bell Ringer
John has a 10% chance of solving a math problem.
Kate has a 20% chance of solving a math problem.
Joan has a 30% chance of solving a math problem.

If these chances are independent what is the probability that the problem will be solves if they work together?

Agenda
1. Bell Ringer
2. Correlation of 2 variables.
3. using variables in analysis.

Objective: students will be able to construct and evaluate a 2 variable scatter plot.

Big Picture: Two variable analysis allows a person to see patterns in data that may indicate a relationship.

Question

Shawnelle has a 13% chance of solving an art problem.

Rosanna has a 26% chance of solving an art problem.

Jack has a 90% chance of solving an art problem.

If these chances are independent what is the probability that the problem will be solves if they work together?

Review Set 14A

1. Donald keeps record of the number of clients he telephones over a consecutive period of days.
a. for how many days did the survey last?
b.estimate Donald's chances of telephoning:
i) no clients in a day
ii) four or more clients on a day
iii). less than three clients on a day

a. 1+6+12+9+6+3+2=39 total number of days
b. i). 1/39
ii). 6+3+2=11/39
iii). 1+6+12=19/39
2. David conducted a survey to determine the ages of people walking through a shopping mall. the results are shown in your book. find , correct to 3 decimal places the estimated probability that the next person David meets in the shopping mall is:
a. between 20 and 39 years of age
b. less than 40 years of age
c. at least 20 years of age

a. 45/112=0.4017~0.402
b. 45+19=64/112=0.5714~0.571
c. 45+37+11/112 or 112-19/112=93/112=0.8303~0.830
3. A farmer fences his rectangular property into 9 rectangular paddocks:
If a paddock is selected at random,what is the probability that:
a. it has no fences on the boundary of the property
b. it has one fence on the boundary of the property
c. it has two fences on the boundary of the property?

a. 1/9 because all but one is on a boundary
b. 4/9
c. 4/9
4. When a box of drawing pins dropped on to the floor it was observed that 47 landed on their backs and31 landed on their sides.Find correct to 2 decimal places,the estimated probability of a drawing pin landing:
a. on its back
b. on its side

47-Back, 31-Side
78 total number of pins
a. 47/78=0.602~0.60
b. 31/78=0.397~0.40
5. A saw mill receives logs of various lengths from a plantation. the length of a log is important in being able to produce timber of the length required.the following data indicates the lengths of at least100 logs received.
a. what is the probability of a log being less than 11 metres long arriving at the saw mill?
b. What is the probability of a log being longer than 15 metres arriving at the saw mill?
c. in the next batch of 50 logs how many would be expected to be between 11 m and 15 m long?

a. L < 11=3+4+14/100=21/100
b. L > 15=7+8/100=15/100
c. 11< L < 15=12+18+20+14=64/2=32 per 50 logs
6.At peak hour railway crossings are closed 30% of the time. If you have to drive through three railway crossings during peak hour, what are the chances you will have to stop at least once?

o-open=.7, c-closed=.3
Possible combination's
ooo-.7*.7*.7=.343
ooc
occ
coo
coc
cco
ccc

1-P(ooo)
1-.343=0.657
7.In a golf match, Annette has a 70% chance of hitting the green when using a nine iron and Kari has a 90% chance when using the same club. If, at a particular hole,they both elect to use a nine iron to play to the green, determine the probability that:
a. both hit the green
b. neither hits the green
c. at least one hits the green
d. only Anette hits the green

a..7*.9=.63
b. .3*.1=.03
c. 1-P(of no one)
1-.03=.97
d. .7*.1=.07
8. Jar A contains 3 white and 2 red marbles. Jar B contains 6 white and 4 red marbles. A jar is selected at random and then two marbles are selected WITHOUT replacement. Determine the probability that:
a. both marbles are white
b. two red marbles are picked from Jar A

Jar A: 3 whites, 2 red
Jar B: 6 whites, 4 red
a. Jar A- 1/2*3/5*2/4=6/40
Jar B- 1/2*6/10*5/9=30/180
6/40+30/180=19/60 (add because they're independent)
b. 1/2*2/5*1/4=2/40

QUESTION OF THE DAY

If P(C)= .10 P(D)= .3 and P(C U D)= .11 are C and D independent events?

BELL RINGER

A{Q, R, S, T, U, V} B{T, U, V, W, X, Y, Z}

1. How many elements are in {A}? n{A} = 6
2. How many elements are in {B}? n{B} = 7
3. how many elements are in {AuB}? n{AuB} = 10 because T, U, V are in both sets, so they are only counted once
4. How many elements are in {AnB}? n{AuB} = 3 because T, U, V are in both sets
5. Are these two sets independent or dependent? These sets are dependent because they overlap over elements T, U, V

AGENDA
1. Bellringer
2. Homework Review
3. Independent probabilities

OBJECTIVE
Students will learn to identify independent probabilities

HOMEWORK
Begin review set A on pg. 490. Remember to ask questions tomorrow for the test on Thursday.

QUESTION
P(G)=0.3, P(D)=0.7 and P(GuD)= 1, are G and D dependent or independent?


I know, horrible question... Sorry this was so late. My computer has a virus or something so i would get half done and it would crash, leaving me to start over... Hooray for attempt number 11! Yay!

hey

guys I just got my username

September 20, 2010

Bell Ringer

1: If the probability of an Event E is 40%, what is the probability of not E? (E')

2: If the same event E takes place 3 times, what is the probability of the result being

E E' E' ??

1. Probability of E is 40% = 4/10 ....which leaves the probability of E' to be 6/10.

6+4= 10

2. k so its really hard to do a tree diagram, but that would be the best step so, time to go to plan B which iiissss...just explaining it.... ok so

• first we have to calculate the probability of E which is 4/10
• then, we know that the probability of E' is 6/10
• again, we know that the probability of E' is 6/10
• So now we can MULTIPLYYYYY

4/10 * 6/10 * 6/10 = 8/125

So the answer for the probability of E E' E' is 18/125

Agenda

I. Bell Ringer

II. Theoretical vs. Experimental Probability

III. Independent Events (in other words... h.w..we got tricked! =] )

Homework!!

pg. 490 #1-5

OBJECTIVE

Students will be able to differentiate the difference between experimental and theoretical Probability.

Question of the day....drum roll please!!!!

1.The probability that Blazer will spend the day with a Princess is 80%. What is the probability that Blazer won't spend the day with the Princess?

2. Over three days, what is the probability that Blazer will spend the first two days with the princess and not on the third day? (P P P' )

September 16, 2010

Agenda

1) Bell Ringer
2) Homework review
3) Independent Events
4) Review for Quiz

Objective: Students should be able to identify dependent and independent events and calculate probability accordingly.

Bell ringer( we went over it in class)

	Biology	Physics	Chemistry	Total
Male	40	16	35	91
Female	15	24	20	59
Total	55	40	55	150

1) P(M)= 91/150
2) P(M) ∪ P(C)= 91+20/150 = 111/150
3) P(P) ∩ P(M)= 16/91

Homework Review
During class, we went over question 6 from page 483.

You are supposed to draw a venn diagram to solve the problem. (I'm so sorry- I tried many different ways to copy my venn diagram from microsoft word but it won't work.)

The venn diagram has two circles
1st circle is labeled Mu for mumps and the 2nd circle is labeled as Me for Measles.
The part where the two circles overlap(in the middle) is labeled as Me and Me because it contains both
So, here are the values
Mu= 2
Me=12
Mu and Me(middle)= 12
Outside the circle but inside the box (neither mu or me)= 4
All these values add upto 30.

a) P(Mu)= 14/30
b) P(Mu) - P(Mu ∩ Me)
24/30 -14/30 = 2/30
(you don't have to reduce it because IB doesn't expect you to reduce it on the exams)
c) P(Mu' ∪ Me')= 4/30
d) P(Mu ∩ Me)/ P(Mu)= 12/14

Tomorrow's Quiz
- probability question including chart, tree diagram, and venn diagram.

September 23, 2010: Chapter test for Chap. 14.

Practice question:

Out of 30 kids, 20 love strawberry and chocolate, 24 love chocolate and 23 love strawberry.

a) How many kids love neither of the flavors mentioned above?
b) What is the probability that a kid loves chocolate ONLY?
c) What is the probability that a kid loves chocolate given he loves strawberry?
d) What would you pick? Strawberry or Chocolate? :)

Hey everyone :)
I'm so sorry for not posting the venn diagram :\ I really tried to for the past hour but it didn't work. If you have any questions about today's blog, please let me know. I will be more than glad to help you out! I hope the practice question was easy. Do not forget- we have a quiz tomorrow!!!
Have a blessed day guys.

Lillian Sangha