June the Third Scribe

First of all we split into groups and Mr.K informed us that we were starting our new unit, sequences. We should be done this unit on Friday or Monday. So be prepared to move really fast!

Okay well apparently today was mostly a review from grade 10 (if you can remember that far back.. good job!)
On the first slide there were four sequences...

4, 7, 10, 13, __, __, __
3, 6, 12, 24, __, __, __
32, 16, 8, 4, __, __, __
1, 1, 2, 3, 5, 8, 13, __, __, __,

Mr. K wanted us to fill in the blanks and explain how we found the missing terms...

4, 7, 10, 13, 16, 19, 22 (Add 3 to the first term to find the second term. This is called an arithmetic sequence. )

3, 6, 12, 24, 48, 96, 192 (multiply the first term by 2 to find the second term. This is called a geometric sequence.)

32, 16, 8, 4, 2, 1, 1/2 (multiply by 1/2.)

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 (this is the Fibonacci sequence! Add the first and second term together to find the third term.)

Now let's take a closer look and try to identify some patterns that can be applied to any other sequence we might encounter in the future.
4, 7, 10, 13, 16, 19, 22

Note: If you are asked to find the 37th term and you plan on adding 3's, you must add 36 threes.How do we get 3n + 1 ?
Well since we found the y-intercept we can graph this.

By looking at this graph we can see that the slope is 3. So for future reference remember that our slope is the constant. So let's make an equation for this sequence.
tn= 3n+1
Where 3 is the slope and 1 is the y-intercept.

Everytime we have an arithmetic sequence it will be a linear function.
This is the graph of our sequence. Here is how you would make that on your calculator! Hit stat, edit. Under L1 enter your rank (1-7) under L2 enter your values (4, 7, 10, 13, 16, 19, 22) Now hit 2nd stat plot (top left corner of the calculator). Hit enter and make sure plot 1 is on, under type make sure the dots are selected. Then hit graph.


Next we covered some definitions:
Recursive: Repeats again and again.
Implicit Definition: This is the teenage way of saying hi, it's an implied hello. Only clear to people who know what they're looking for.
The Common Difference (d): The number that is repeatedly added to successive terms in an arithmetic sequence.
Common Ratio: The number that isrepeatedly multiplied to successive terms in a geometric sequence.

How to find the nth term in an arithmetic sequence.

tn= a + (n-1)d
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
d is the common difference

How to find the nth term in an geometric sequence.
tn= ar^(n-1)
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
r is the common ratio

Here is the next sequence we looked at, 11, 5, -1, -7...
We were asked to find the 51 term.
Look at the difference between the terms.
5-11= -6
-1-5= -6
Therefore we know our constant is -6. Remember we're not subtracting 6 from the first term to get the second term, we are adding -6! :D

Okay so how to find the 51 term. First let's make a formula.

tn= a+ (n-1)-d
Where n is the term. a is the first value and d is the difference. So we have..

t51= 11+ (51-1)(-6)
= -289

Next we looked at the sequence 3, 6, 12, 24, 48, 96, 192
Notice the difference is not constant, so this is not an arithmetic sequence.

To make an equation for this kind of sequence we use the formula, tn= ar^(n-1)
a= the first term r= ratio
The ratio for this sequence is 2 because 6/3=2 and 12/6=2 etc.
So the implicit definition is tn= 3(2)^(n-1)

Next question! 32, 16, 8, 4, 2, 1, 1/2
We multiply by 1/2 to get the next term so 1/2 is our ratio. Now we find the 10 term.
tn= ar^(n-1)
t10= 31(1/2)^10-1)
t10= 1/16

Remember!!
If differences in sequences are different it is NOT arithmetic.
If there are common ratios it is geometric.

And the last slide..

Um next scribe is Mary.

Homework is exercise 44 and 45.

BOB for Conics

Hooray we are done our DEV! :D
Now its time to do the OTHER math homework that I have been procrastinating on...

Well this is my Bob for the conics unit. I found this unit pretty easy, except for the moments where I was just confused... or couldn't remember the equation for a circle... I think the test will be pretty easy as long as I don't do anything stupid like get an ellipse and a hyperbola mixed up.

Hmmm well what is important for this unit?

1. Equations for...
parabola: (x-h)^2 = 4p(y-k) (vertical) and (y-k)^2= 4p (x-h) (horizontal)

Circle: (x-h)^2 + (y-k)^2= r^2 (standard form)

Ellipse: (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1 (horizontal) and (x-h)^2 / b^2 + (y-k)^2 / a^2 = 1 (vertical)

Hyperbola: (x-h)^2 / a^2 - (y-k)^2 / b^2 = 1 (horizontal) and (y-k)^2 / a^2 - (x-h)^2 / b^2 = 1 (vertical)

So for the test i think we just need to make sure to know all the parts of shapes and how everything fits together. Remember how to find the vertices, foci, center, radius and length of major and minor axis! I think that's all I have to say for this unit. Just remember to get lots of sleep, (something I need), DON'T eat a ton of candy and study the formulas! :D

BOB for combinatorics (=

Hey everyone!

Well I started off this unit feeling pretty comfortable with what we were doing and I thought it would be pretty easy. After the third class I started to change my mind.

Here is a brief summary of what I learned during this unit
The Fundamental Principle of Counting: This means if you have M ways of doing one thing and N ways of doing another then you have MN ways of doing both things.

An example for a question where you could apply this is, how many ways can you seat 4 students in 4 desks?

Answer: 4 x 3 x 2 x 1 = 24 ways

The first person has a choice of 4 desks to sit in, the second person has a choice of 3 desks etc..

Another way of writing this is 4! which means 4 x 3 x 2 x 1. You say this as four factorial.

Permutations: A permutation is when then order matters and there is no repition!

An example would be a question like, there are 5 horses in a race, how many ways can they finish first second and third?

You can do this in 2 ways...

Fundamental principle of counting: 5 x 4 x 3= 60

OR

Use the pick formula: nPr= n!/ (n-r)! (do this on your calculator by hitting math, left arrow, 2)
5P3= 5!/ (5-3)!
= 120/ 2!
= 60

Permutations of Non- Distinguishable Objects (here's where i started to get a little confused)
Use this when attempting to arrange non- distinguishable objects among distinguishable ones.

An example is, how many different "words" can be made out of the letters from the word blogger?

Answer: 7!/ 2!= 2520
There are 7 letters in the word blogger and 2 of them are non- distinguishable (the 2 g's).

Circular Permutations (I do not like these they will be my downfall!!!)
This is the number of ways L objects can be arranged in a circle. To figure out these questions when there are no restrictions simply go (n-1)!

An example with restrictions is... How many different ways can 3 couples sit at a circular table if they must sit opposite each other.


BRACELETS/ NECKLACES!! (these are tricky!)

To figure out a question involving a bracelet or necklace use the formula (n-1)! / 2. We have to do this because a bracelet (or any object that can be flipped over) will have half as many combinations. Think about it carefully (:

Combinations: Order does not matter!

An example of this is... How many ways can you select 4 committee members from a group of 10 people?

Use the choose formula: nCr= n!/ (n-r)!r!
10C4= 10!/ (10-4)! 4!
= 10!/ 6! 4!
= 210

The Binomial Theorem: Use this for finding the nth term (: Remember the patterns!!

1: The coefficient of the ith term is nC (i-1)
2. The exponent on a is given by [n- (i-1)]
3. The exponent on b is given by i-1
4. exponent on a + exponent on b = n
5. The number of terms in any binomial expansion is (n+1)

Ummm so I think that mostly covers the basics... wow this turned out pretty long.. Just remember to watch out for those trick questions that seem like a lot of work but are only worth one mark...

B0B

Hey, here is my bob for the exponents and logarithms unit.

I was at the U of W for last week so I missed a lot of stuff, but after reading over the slides and doing the homework I think I have a grasp on what I'm doing.

Some things that I think will be important for the test are:

A logarithm is an exponent!

That means that when you are multiplying 2 logarithms (logMN) it is the same as adding them! (logM + logN) This is known as the product law.

When dividing 2 logarithms (logM/N) it is the same as subtracting them! (logM - logN) This is known as the quotient law.

When you have an exponent (logM^N) it is the same as multiplying (NlogM) This is known as the power law.

It would also be handy to remember the change of base law. This means that when you want to change the base of log all you have to do is divide log the base you have by log the base you want. (If that makes sense? It helps me to think of it that way)

Also know the equations for finding interest A= Pe^rt. (this also works for decaying questions or for finding the half life!)
A is the end amount. P is the amount you start with. r is the rate. t is the time in years.

This equation is handy for word problems, but if it doesn't work there is always A= P(1+r/n)^tn
where n is the number of times the principle is compunded per year.

ln is the natural logarithm, it is the same as log base e, but we never write this! Just write ln! We can use ln the exact same way we use log!

Well those are the things that I discovered from doing the homework. I think that pretty much sums up the unit.

I think the hardest part of this test will be remembering the word problems because I wasn't in class to learn what not to do. Hopefully my day of studying will pay off though because I feel like I really understand this unit! (:

Diabollically Evil Villians Timeline (DEV)

already done: question 1

April 16- make our first question presentable, make question two.
April 23- make question two presentable, make question three.
May 7 - make question three presentable. make question four.
May 17- make question four presentable, make question five.
May 21- make question five presentable.
May 23- upload everything and make sure it's pretty (evil) (:


OUR DUE DATE OF DOOM: MAY 28

Sample Questions

1. For a Saskatchewan town the latest sunrise is on December 21 at 9:15 am. The earliest sunrise is on June 21 at 3:15 am. Sunrise times on other dates can be predicted using a sinusoidal equation.
a) Sketch the graph of the sinusoidal function described above.
b) Write 2 equations for the function; one using sine and the other using cosine.
c) Use one of the equations in (b) to predict the time of sunrise on April 6.
d) What is the average sunrise time throughout the year?
e) On what days will the sunrise at 7:00 am?

Taken from the slides on transformations.

2. Given that a= 7/25, and cosb= 9/41 and neither P(a) nor P(b) are in quadrant 1, find:
a. sin(a+b) b. cos(a+b) c. sec(a+b) d. in what quadrant is the point P(a+b)?
Taken from exercise 16, question 8.

3. A 5 digit pin number can begin with any digit (except zero) and the remaining digits have no restrictions. If repeated digits are allowed, find the probability of the PIN code beginning with a 7 and ending with an 8.
Taken from the math40s website, lesson 3 exercise

4.One plan is 20km from the Winnipeg airport. A larger plane is 17km from the airport. If the angle between the sightings is 110 degrees, how far apart are the planes?
Taken from exercise 6, question 17.

5. If there are 190 handshakes in a room and each person shook every person'shand one time, how many people are in the room ?
Taken from math40s website.

pre-test day!!!

Hi everyone!

Today in math class we covered a lot and did some reviewing for our test on Thursday.

We started off with a pre-test! Here are the questions and answers.

Question 1

Simplify: sin(2x+π)

A) sin 2x B) cos 2x C) -sin 2x d) -cos 2x

Answer: C) -sin 2x
(highlight to see)

Here is the logic behind that idea....

sin(2x+π)= sina cosb + cosa sinb
= sin(2x)cos(π) + cos(2x)sin(π)
= sin(2x)(-1) + cos(2x)(0)
= -2 sinx

Question 2

The terminal arm of angle θ in standard position passes through point (m,n), where m>0, n>0. Determine the value of sin(π+θ).

A)

B)

C)

D)

Answer: A

Question 3


Question 4


Question 5

When we were done the pre-test we had time to do a quick review question.

Now for some final remarks about today's class.

1. thanks to Ingrid for making our awesome mascot!!!
2. check out the websites on the right hand side of the blog, for some extra math help. (www.math40s.com)
3. remember to give Rebecca a million dollars tomorrow!
4. There are some extra review questions on today's slides!
5. TEST ON THURSDAY! STUDY!
6. Don't forget to do your BOB
7. I just wanted to make 7 to finish the rainbow (:

The next scribe is my ANNABANANA!!!!

Gelatinous Blob Post

Hey everyone here is my gelatinous blob post!!

Well to start off I'd like to say that I really liked this unit!! The questions reminded me of puzzles and puzzles > boring old math problems. Also I really understood what was happening in class, which made it easier to not get distracted by shiny objects. So I am going to do really well on this test because I want my mark to go waaaaaay up!

Here are some formulas to understand for the test. (understand them don't just memorize!!)

1. sin² x + cos² x = 1
2. 1+ cot² x = csc² x
3. tan² x + 1 = sec² x
4. sin (a+b)= sina cosb + cosa sinb
5. sin (a-b) = sina cosb - cosa sinb
6. cos (a+b)= cosa cosb - sina sinb
7. cos (a-b)= cosa cosb + sina sinb

When solving trig identities here are some rules of thumb that would be handy to keep in mind (but not necessary to follow)

1. work with the most complicated side first
2. rewrite both sides in terms of sine and cosine
3. use a Pythagorean identity
4. simplify complex fractions, rewrite fractions sums or differences with a single denominator
5. use factoring, deference of squares

I think one of the hardest parts about this unit is deciding how to start. Don't be afraid to make mistakes and try things that don't end up working because that's what an eraser is for. If people stopped making mistakes then all the eraser makers would go out of business and we don't want that, right?

Okay so remember to draw in your great wall of china! When you have proven that both sides are the same write Q.E.D so we know that's your final answer.

Well that's all the advice I have for now. Good luck on the pretest tomorrow!!

B0B for transformations

Hey, this is Rebecca and this is my BOB.

So I think it's safe to say that I didn't really like this unit because it confused me. We learned how to graph reciprocal functions, absolute values, and inverse functions. We also learned how to check if a function is odd or even. I think the hardest part of this unit was understanding reciprocal functions. Luckily the light bulb in my brain went off yesterday and now I understand what I'm doing! :D

For anyone who needs a little bit of help... here is the unit in a nut shell.

Odd Vs. Even Functions

Even Functions: Symmetrical about the y-axis. If f(-x)=f(x) it is even.

Odd Functions: Symmetrical about the x-axis, if you rotate the graph 180 degrees it will appear the same. If f(-x)= -f(x) it is odd.

REMEMBER: You can turn your paper if that helps you visualize things! :D

Graphing Reciprocal Functions

1. Find the invariant points where f(x)=1 or f(x)= -1.
2. Find the asymptotes.
3. Use the "biggering, smallering" method to sketch the graph.

Graphing Inverse Functions
-For these types of questions all you really have to do is switch the X and Y values.


f(x)= A(Bx-C)+D

A: Stretches the graph vertically
B: Stretches the graph horizontally
C: Shifts the graph right and left, watch the sign!!
D: Shifts the graph vertically.

REMEMBER: STRETCHES BEFORE TRANSLATIONS!!!!!

Well I can't think of anything else important to say.. so good luck to everyone!! Don't forget to be on the lookout for graphs in the real world! (:

Reflection

Hey this is Rebecca and this is my reflection for this unit.

I found it pretty confusing when we began this unit, I didn't really understand the radians to degrees thing. After a few days and some help from my friends the light bulb went off! I also have had some troubles with the sin graph, that might be because I missed the class where we learned about it.

I found the unit circle pretty easy because we learned about it last year. I kept my pie plate from last year and that helped to refresh my memory!! Well that's all I have to say about this unit, hopefully the test wont be too hard. Good luck everyone!

The Life of π

Hii bloggers, this is Rebecca your scribe for the evening.

In today's class we talked about solving trigonometric equations larger than 2π.
We began the class by reviewing some of the algebraic questions from yesterdays class.

I believe we were then called down to the MPR for our biannually assembly. At the assembly we were told how wonderful we were and how to become even more wonderful! If you are confused about school rules and missed this assembly speak to a teacher and I'm sure they will help you. :p

So back to math class...
We were then asked to solve the following questions. Mr. K took a few minutes telling us how our calculators were stupid and only told us one answer to a question and how since were smarter than the average bear we need to find the other angles. He then told us that later we will learn our calculators weren't actually lying to us, but we wont worry about that in this unit.

One question we had while answering this question was "Couldn't you also have -π/6?" The answer was no because it does not fall in the interval.

Next we did some fun mental math. (sorry for my poorly drawn paint pictures but the equation writer was not cooperating!)

When doing these types of questions think about where in the unit circle you are. For example for cos 13π /3 you are in quadrant 1. This means your answer will be positive because x is positive in quadrant 1.

Some side notes:

• 
  Mr. K told us that if you have something that is tedious to rewrite you can use substitution. Always show what you are substituting at the top of your page. You can use a letter (NEVER USE X) from any alphabet or a symbol.
  
• Always go to 4 decimal places for this class!!

Homework for today was exercise 5, questions 11-20. Good luck!

Last but not least tomorrows scribe will be Annabanana!! :D