Intro to Exponential Functions

There are a number of different functions
Linear - y= mx+b create a straight function, where m is the slope and (0,b) is the y-intercept

Quadratic - y = ax^2 + bx + c creates a U shaped function, were a represents whether or not the function opens up (+a) or opens down (-a) with a y-intercept at (0,c)

The Exponential functions are those where x is the exponent of the function y = a b^x

We saw that with positive exponents

• a is the y-intercept 
• when a is positive the function behaves as normal
• when a is negative, the function is the reflection of the function when a is positive
• the b value determines the behaviour of the functions - either going up or going down
• when b > 0, the function increases from left to right
• when 0 < b < 1, (proper fractions or decimals) the function decreases from left to right

See the examples below

HW

P337 # 1-3

P346 # 1-7, 11, 15, 18

QUICK CHECK UP ON THIS TOPIC ON THURSDAY!!!

Today we worked on problems where we have to decide either Permutations or Combinations to solve the problem.
Good examples were
P122 Example #1 and P152 Example #1
Here is a flowchart to help you to decide when to use Perms and when to use combs.

HW 

P126 # 1,2,5,6,7,10

and

P159 #2-10, 12

Combinations - when order does NOT matter

Combinations are ways of arranging elements in a manner that the order does not matter

HW P110 #1,2 & P 118 Any 8 of 1-12

Permutations with Repeats 2.4

Up to now each element has been unique.
For example there are 6! different arrangements of the word PENCIL because each letter is different.
We found there were only 12 different arrangements of the word TOOL because the O is repeated.
It cannot be 4! to give us 24 different arrangements but we can divide 24/2 because of the 2 O's

To find the number of arrangements with repeats is n!/(a!b!) where a and b are the number of elements that are repeated.

How many different arrangements are there of the city TORONTO?
7!/(3!2!) = 420

We can use this principal for finding the number of ways to follow a pathway.

HW: 

• P 105 # 1,2,5,6,7,9, 12, 15, 16
• Name arrangements (see below)
• Quiz NR3 & MC 6,7,8

Name Arrangements Assignment

How many different ways can you arrange the letters in your name using...

• only your first name?
• only your last name?
• both your first and last name as one "all-together" name?
• both your first and last name as separate names?

Intro to Permuations

Today we looked at Permutations - the number of ways items can be arranged in a specific order.
That is to say for elements A and B the permutation A then B is different from B then A such as ways of entering or exiting a room, positions on a team or drawing items from a selection.

Class Notes:

HOME LOGIC - Check your marks online

Hey everyone

Check your marks here at Home Logic

If you are a CBE student and have logged onto a CBE computer at school AND have an updated password - use your usual username (ID #) and Password

If you are new to the CBE (from Calgary Catholic, returning to Chinook, Rocky View etc) - go to the Viscount Bennett School library, log on with your CBE ID# and your first password is your birthday YYYYMMDD.  You will receive a prompt to change your password - it should be at least 8 characters long with capitals, lower case and numbers  ie Mathi5C00l would be a great password!!

Probability Notes

July 8 - Today we did a bit more with Independent events.

We saw that:
IF - 2 events are independent THEN   P(A) X P(B) = P(A and B)
But the corollary to this is
IF P(A) X P(B) = P(A and B) THEN events A and B are independent

We can use this idea to test if 2 events A and B are independent.

See the class notes below:

HW - P198 1,2,3,5,6,9,12,13

July 7 - Today we covered a good deal in Probability sections 3.2, 3.4 & 3.5 that covered Odds & Probabilities, Mutually Exclusive Events, and Independent Events.

Language:

• Odds - expressed For: Against
• Probability - fraction or division of For/ (For + Against) or For/ Total
• Mutually exclusive - no overlap or P(A and B) = 0
• Not Mutually Exclusive - Overlap exists - Remember to subtract the double counted elements or probabilities!!

Click on the Pictures to Enlarge them..

3.2 Odds 1

3.2 Odds Part 2

3.4 Mutually Exclusive Events 1

3.4 Mutually Exclusive Events 2