Probability..

Tipsandtricks.

4 big ideas(question types)

1........ pathway problem.
- pascals triangle(be able to create it)

2.......... fundamental counting principle.
-nPr ------------------------------ math over 1 prb
(big #) order matters,
ex: books on a shelf in a different orders
: licence plates
: phone #
: locker combo
= n! / (n-r)!

-nCr
(small #) order doesnt matter,
n!/(n-r)!*r!
ex:
:pizza toppings
:committees

SHOW ALL WORK (sample space ... )

3..............INDEPENDENT / DEPENDENT
* denominator changes through the question chronologically

dependant >> without replacement
independent>> replacement

**consider tree diagram

4.............MUTUALLY INCLUSIVE vs MUTUALLY EXCLUSIVE

inclusive >> P(A or B) = P(A) + P(B) - P(A and B)
exlusive(they cant happen at the same time)>> P(A or B)=P(A)+P(B)




****COMPLEMEMTARY.. FORMULA.
P(not exactly 1 head)= 1-P(exactly one head)

vector exam review.

one or both of these type of problems

1. parellelogram, simple resultant.
used in these circumstances :
- two forces acting on a stationary something
-simultaneous vectors
(same time)
-magnitudes of vectors and only angle between them

2.... OR questions... "open response"
- means that there is no specific correct answer to the problem but rather many possible correct answers that satisfy the requirements of the problem.
** look for 4 or more marks.

3..... conversion/speed

ex. diver on the ocean floor
14 m/s for 3 mins = 2520m

Make origins.... when using triangle methods.

exam review

matrix modelling

What will i be expected to do?

** do not do anything WITHOUT a calculator.
depend on your calc. **

Questions to expect.
1...... maybe 1 to 2 multiple choice and one longer answer.
(MATRIX OPERATIONS) -> add, subtract, multiply(scalar * multiplying it by one number ) , multiply (matrix multiplication -> one matrix times another one)

2.... TRANSITION MATRIX question
(switching behaviour over time)
** are always n by n (SQUARE)
** rows add up to 1.0 (use decimals)
Also - "initial condition matrices must be row matrices in the form 1 by n.
- set the one up by 1 by 3; then the changes in a 3 by 3.
to show stability.... times matrix a * b ... times them by 99(ex) to the power... then add one and if its the same number... then stability is reached.

3.... MATRIX MULTIPLICATION as a word problem
-> probably something like inventory problem.
-> remember to avoid nonsense calculations (answer has no meaning.)

4.....NETWORK/MATRIX question
-> (# of routes to plan, for instance, transportation)


Show the matrix operations to calculate the number of trails from one town to another passing through at most two other towns. Do not solve.

A + A squared + A cubed
direct + through one town + through 2 towns

Test Review

skills i need to have--

1. Measures of central tendancy (mean, mode, median)
   - measures of spread/variability(range, standard deviation of a population)
   
   GROUPED(Frequency table..L1etc.) VS UNGROUPED DATA.(single list)
2. Normal Distributions / Z-Scores
   -ronblond, normalcdf..... etc.
   
   *Is it normal or not?
   68-95-99.7 rule... 3 sets of tallies.. look in notes.
   
   Areas under the curve vs scores based on areas under the curve..
   
   Standardized tests
   - z-score..
3. Bionomial Distributions
   -mean=n times p
   standard deviation = sq root n times p times q
   p = prob success
   q = prob not success
   
   - binompdf(# of trials, prob success, no of success)
   - binomcdf ' ' ' '
   
   pdf - " exactly "
   cdf - " at most "
4. Confidence Intervals
   Stat - tests - A : 1 propZInt
   
   x=mean
   n=n
   c-level = either 0.9, 0.95, 0.99
   
   *read the question, or it'll lose me marks.
   - either precentages
   - real numbers of .. "3 ice cream cones.. "
   (... times the decimal.. with the number of ice cream cones)

*What does it (the interval) mean?

Sequences and Series.

one way -> mode - seq.

BIG IDEA.
*solve problems using technology ( at least 4 methods),
to predict population, exponential, fractal geometry trends.

ex.

The moose population near hudson bay seems to be increasing. The mortality rate is 12% per year, but generally, 30 new calves are born every year. If the herd size is known to be 800 animals in 2008, answer the following:

a) SHOW POPULATION numbers for the next 5 years, starting with 2008 As year 0.

STRATEGY NUMBER ONE.
"home - screen calculator"
200 moose - (.12%*200)= whatever, + 30 moose.

STRATEGY NUMBER TWO.
"sequence mode"
u, v and w all are different sequences.

STRATEGY NUMBER THREE
excel

STRATEGY NUMBER FOUR
SHODO
www.shodor.org/interactivate/activites/sequencer/
fair game
n=200
x 0.88
+30
steps (my choose)


b) HUNTERS want to hunt moose.
Design a plan to hunt moose and maintain the population at between 200 - 225 moose....
* you may bring more moose from outlying areas every year.

things to pay attention to....

1. EXAM (2 parts)
A) part 1 - longer answer
MONDAY, JAN 28TH. @ 1030 ROOM 204
*** noon hour extension to a maximum of 1230pm
* constructive response
SHOW ALL YOUR WORK.

B)PArt 2 - selected response(multiple choice)
THURSDAY, JAN 31 @ 1250 ROOM 204
no extension *3:40pm maximum(50-60 multiple choice)


2.Blog Rubric
- fill it out, if he agrees i get the marks.
out of 15 points.


3.Accelerated Math
- FRIDAY, JAN 18- first deadline (50 objectives)
- FRIDAY, FEB 1 - last possible day to scan (53+ objectives@12noon)


4. Circle geometry quiz
(one on one with him, prior to end of course)


FINAL EXAM
30% of grade in the course

Simple and Compound Interest

Simple- interest that gets calculated a grand total of one time

compound- interest is calculated continuely at the end of every compounding period

Interest:
(think 2 perspectives)
* lend .......... * borrow.
(invest) .......
*to bank ..... *from bank
give ......... get

An amount of money generated through the use of 3 variables:
PRINCIPAL AMOUNT(P)$
INTEREST RATE (r)%
TIME (t)years

SIMPLE
I=(P)(r)(t)

COMPOUND
A=1(P+r/n)n(t)

P=principal
r=rate
t=time
n=number of compoundings per year
I=interest (by itself)
A=amount(principal plus interest)




Example

Bob invests money. He starts with $1000.00. He invests it at 5% interest. He invests only 1 year at a time, but every year he decides to reinvest his interest. Calculate the value of his investment at the endof 5 years.

^^ simple interest(5 times).
I=Prt

I=?
P=1000
r=0.05
t=1

1.....I=Prt
=(1000)(0.05)(1)
=$50
at end of 1st year, he earns $50.

2.....
I=Prt
=(1050)(0.05)(1)
=$52.50

3.....
I=Prt
=(1102.50)(0.05)(1)
$=55.13

4.....
I=Prt
=(1157.63)(0.05)(1)
=$57.88

5.....
I=Prt
=(1215.51)(0.05)(1)
=$60.78

Total value of his investment:
$1276.29
^^ this is the compounded amount
(interest was added.. (compounded)
to the principal each time).

OR ..
once through this formula.

A=P(1+r/n)n(t)
A=1000(1+0.05/1)(1)(5)
A=1000(1.05)^5
A=1276.28

Hmmmm.... remember this ..
y=a*b^x