Getting Ready for the Diploma

There is a lot of time between the last class and the diploma exam - so here are some ways to get ready.

• work with a friend from class
• study a little bit each day - at least 1 hour but no more than 3
• study a variety of topics and questions every day instead of all from 1 section on one day, and then all of a different section on another
• do 3 questions from each unit each day instead of 30 questions from 1 unit on one day
• use your resources
• you have all of your old quizzes and assignments
• use them for practice by covering over the answers, doing the question and then checking it
• each chapter has mid-unit review and end of unit review - use these questions for more practice
• purchase a Key Booklet 
• check out Quest A+ Online Practice exams
• Check the blog for notes and reminders
• Make a summary sheet (not a cheat sheet)
• list the most important things to remember from each unit on the sheet such as 
• difference between perms and combs
• remember to subtract the overlap in Venn diagrams 
• don't write formulae they give you, write the ones they don't such as the finance formula from exponentials or max/min from sinusoidal

Exam day tips

• arrive early!!  return your text book after the exam
• eat breakfast!!  you will be smarter for longer on a good breakfast
• get ready the night before - put these items in your shoes by the door!!!
• calculator
• pencils
• erasers
• ID
• study your summary sheet , put it away and do a memory dump when you get your test
• TURN YOUR DIAGNOSTIC ON!!!!  (2nd 0 -> Catalog, scroll to Diagnostic On)

Good luck!!  Let me know how it goes by email swmoses@cbe.ab.ca or twitter @swmoses

Rational Expressions - Simplifying, Multiplying and Dividing

Today we worked on

• Simplifying Rational expressions - similar to reducing fractions by dividing by the same value into all terms of BOTH the numerator and denominator
• Creating equivalent expressions - either multiplying or dividing numerator AND denominator by the same value
• Multiplying rational expressions - similar to multiplying fractions 
• (num x num over denom x denom)
• Dividing rational expressions - similar to dividing fractions
• division becomes multiplication
• invert 2nd fraction (or rational expression)
• NPV's - Non permissable values - values such that when used produce a denominator of 0
• check all denominators from the ORIGINAL expressions
• Check denominators of second fraction after division (numerator of 2nd fraction becomes denominator after inverting it)

Class notes below

Equivalent rational expressions

Simplifying Rational Expressions

Meaning of NPV's

Multiplying Rational Expressions

Dividing Rational Expressions

Getting Ready for Rational Expressions

To get ready you will need to know all of these skills and concepts.  Furthermore, you may need to draw upon these skills or concepts at any given time and often multiple skills in a random order to solve problems

• Fraction Skills
• Common denominators
• reducing
• multiplying and dividing
• Order of Operations
• Solving Linear Equations
• Expanding Polynomials
• Factoring trinomials
• Solving trinomial equations
• Using the Quadratic Formula

Here is the answer key to the review pages

Re-writes

Any student wishing to re-write a unit test can under the following guidelines

• Choose only 1 test to re-write
• check HomeLogic to see which one you did worst on or which one would benefit you the most by re-writing by its relative weighting
• Inform Mr. Moses by Monday at the end of class (don't inform = don't re-write) as I need time to copy tests)
• complete ALL (each and every) HW question for the ENTIRE unit of the test you wish to re-write
• Each question has to be fully completed with ALL work, steps and diagrams shown
• Each question has to have had the answer checked.
• submit your HW on Tuesday morning
• re-writes will be held on Tuesday July 28 from 12:15 - 3:00 only.  
• Due to very limited time left Tuesday is the only day that works to copy, mark and update your marks in time for the end of the course
• You will get to keep your better of the 2 marks
• did better 2nd time?  get the new mark
• did worse 2nd time?  keep your first test mark.

Sinusoidal Functions

We started using a new type of function today
Sinusoidal Functions are functions that resemble repeating wave patterns
There are Periodic functions (ones that repeat in a regular pattern but cannot be drawn using a sine function.  Examples might be heartbeats, tangent functions)

We saw for the general sin equation y= a sin (bx + c) +d
a is the amplitude
b is the number of waves that fit in the space of 2pi (and is used in the formula Period = 2pi/b)
d is the median or middle value

We can use these to find other values as well
Max height = d + a
Minimum height = d - a

Or if we know the Max and min then (max + min)/2 = middle or median value

You can manipulate the formula to determine other values as well.

(Pictures of class notes to come soon)

Polynomial Functions - Quadratics

We looked at applications of polynomials.
We saw that we can

• Enter a table of data into our Calculators L1 and L2
• Perform Regressions (Stat> Calc #4 Linear, #5 Quadratic or #6 Cubic)
• Decide which is best (Look at the r or r^2 values - closer to 1 or -1 is better)
• Copy and Paste the best function into y= to graph (y=   VARS   #5Statistics > > Enter)
• Set your windows in the context of the question 
• Solve problems using either the 2nd> Calc #1 Value if you know X and are looking for Y, OR graph y2 = known value and find the intersection

Here are some notes:

# of Turning Points = Number of Local Max or Min Points

Log Functions and Applications

Today we used the CHANGE OF BASE LAWS to solve problems and make life a lot easier when dealing with Logs.
  See class notes below

We can use Log functions and regression to solve problems when given data to create a function

HW See Homework chart

Logs Unit Test Wednesday

Logarithmic Functions - Answer Key

Today we did a few examples from the class booklet on Log Functions

Example 1: a) v = 3      b) w = 4     c)  x = -4       d) y = 0.83     e)  z = -3
Example 2:  a)  v = 4    b)  w = 2    c)  x = -3       d)  y = 7.39      e)  z = 3
Example 3:  a)  6         b)   3      c)   -2    d)    2      e) 2              f)   12
Example 4: B (Dividing entire logs is not the same as dividing the arguments)
Example 5:  NR x = 32
Example 6:  D
Example 7:  NR x = 1.29
Example 8:  NR x = 4.46

Example 9:  C Logarithmic because the independent variable and dependent variable are interchanged
Enter L1 and L2, Stat Calc 9 (Ln Regression)
y = 32434.05 + -6974.1 lnx

y=  VARS    #5 Statistics > > EQ Enter

Graph with x:{0, 120, 10} & Y: {0, 16000, 1000} for window settings

Example 10
Graph y = 8848 and find intersection at X = 90
Graph y = 1049 and find intersection at X = 30
Subtract to find the difference = 60

Evaluating Logs using Exponents and Using Log Laws to Evaluate Values

Today we looked at the similarities between exponent forms and Logarithmic fomrs of values of numbers.

We saw that for y = b^x we can rearrange this exponential form to a Logarithmic form such that

y = b^x < -> logbx = y

We can use this to evaluate expontial values

It is easy to see that 10^x = 1000 because 10^3 = 1000, so 10^x = 10^3, and dropping bases x = 3

But what if 10^x = 81?  This means: 10 to the power of what will result in 81?

We can see that 

10^1 = 10 and 10^2 = 100

81 lies between 10 and 100 (closer to 100) therefore the exponent of 10 must be between 1 & 2 (and closer to 2)

81 = 10^x -> changing exponents to log form x = log 1081,  x = 1.908.

This means 10^1.908  = 81

We summarized the steps to be:

• REARRANGE Log form to Exponential form
• re-write exponential forms to have the SAME BASE
• Use EXPONENT LAWS if necessary
• DROP BASES due to equivalent forms of exponents
• SOLVE

We also discovered the laws that apply to log functions are similar to exponent laws.

See the notes below.

• Apply LOG LAWS where you can to create a single Log function
• REARRANGE Log form to Exponential form
• re-write exponential forms to have the SAME BASE
• Use EXPONENT LAWS if necessary
• DROP BASES due to equivalent forms of exponents
• SOLVE

HW - see calendar from the first Post for today's HW.

Intro to Logarithmic Functions

Logarithmic functions are the inverse (reverse the positions of x and y) of exponential functions.

Using the Log of a exponent allows us to solve exponential equations algebraically instead of graphically (more on this to come later).

We

• investigated how Logarithmic functions compared to Exponential functions
• compared the Domain and Range
• compared the x and y intercepts
• compared what the a value represents in each situation
• exponential functions: a is the initial value
• logarithmic functions: a is the value of the function when x = 10 ( or when x= the value of the base of the log - more to come on this later)

Homework

Lots of homework - check the HW section for July 17 on the first blog post in June

Exponential Equations Notes

We did a lot of work on Exponential Functions
We applied the General y = a x b ^x function to a number of different situations

Recall that in all of these the common ideas of

a = the initial value:

• maybe for bacteria it is the initial number of bacteria, 
• for financial situations the Principal (or initial) investment

b = the rate of growth or change:

• doubling b = 2
• growth by % in financial situations b = 1 + i, where i is the interest rate/100
• growth by % in financial situations where there are compounding periods 
• divide the annual interest rate by the number of compounds per year

x = the number of times the event occurs 

• bacterial growth hours or 
• total number of compounds  = years x # compounds per year

There is a lot of homework

Check the HW chart on the first Blog post from June

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