BOB likes to eat icecream [cones]

I feel pretty confident for the test tomorrow, I might not get 100% but I believe I'll do better than what I have been doing so far. I liked this unit because it was pretty straight forward and I had no real trouble understanding any concepts.

I think that for this unit I just need to make sure I know the formulas really REALLY well. Let's review shall we ^__^

A PARABOLA:
The equations:

If the x is squared, the parabola is vertical (either opens up or down) and if the y is squared the parabola opens horizontally (opens left or right). p is the distance from the vertex to the directrix and the focal point. If 4p is a big number, the stretch of the parabola is also big. If the number is smaller than one the parabola will be skinny.

A CIRCLE:
The equation:


r is the radius. In general form, the coefficients of x and y are squared and are the same. That's how you know it's a circle!

AN ELLIPSE:
The equations:

When a (the bigger number) is under x, the ellipse is horizontal. If it's under y then its vertical.
a is the length of the semi major axis. b is the length of the minor axis. Use c^2 = a^2 - b^2 if you have to find the distance between the origin and the focal points. In general form, the coefficients for x and y are different.

A(N) HYPERBOLA:
The equations:


When x is positive the hyperbola is horizontal (opens right and left). When y is positive it is vertical (up and down). a is the length of the semi transverse axis, while b is the length of the semi conjugate axis.

use c^2 = a^2 + b^2 to find c, the distance from the origin to the focal points.

hyperbola graphs have asymptotes! use the slope formula to figure out their equations.

To be alright for the test, all we need to know are the formulas and how to graph them. I'm sure everyone will do fine! ;D

Make sure to eat healthy, drink plenty of water and get some rest so you can be in top shape tomorrow morning!

~Bye bye! :D

Bob has a Perm ;D

This unit wasn't that bad, but I've had my down moments. Heck, i have had many more down moments with this unit then happy up moments but that's OK... well not really.

I'll start off with how I feel about this test tomorrow: Not that great. I thought I understood everything before I entered that classroom today but the pretest was... confusing, and the cards! OH MY GAWSH, the cards... I'm not a big fan of them, but I will learn to love them.

Here are some wonderful pieces of useful information that should be useful:

1. A PERMUTATION is used when ORDER MATTERS. The lock on your locker is a permutation lock because the order the numbers are chosen effects whether the lock opens or not. For example the combo 17-4-56 is not the same as 56-17-4.

The formula you would use would be nPr - read as n pick r - where n is the number of objects to pick from and r is the number of objects that need to be arranged.

If you have non-distinguishable objects (like repeated letters in a word that you want to rearrange), then n!/k1!k2!k3!... where n is the number of letters in the word and k is the number of repeated objects.

2. A COMBINATION is different from a permutation. This is when order DOES NOT MATTER. Picking people for committees is an example of a combination because there are no places or ranks to order them in.

The formula you would use is nCr - which is read as n choose r - where n is the total number of objects and r is the number of objects you want to choose for you combo.

3. The FUNDAMENTAL PRINCIPLE OF COUNTING should have been first on my list but oh well... it's when you have p number of things and q number of things and u multiply them together, you'll get the number of possible combinations. Yay!

The ! means factorial. Factorial means that you multiply a nunber by every number below it until 1. So 5! would be 5x4x3x2x1.

4. CIRCULAR PERMUTATIONS are when you must rearrange things in a circle. The formula for this is (n-1)! because one object is the starting point and it does not count.

There are SPECIAL CASES like when the circle is a bracelet or a necklace because you can flip it over. For these cases the formula would be (n-1)!/2

5. For objects that MUST ALWAYS STICK TOGETHER (people wanting to sit together, certain books have to be side by side etc.), but those objects in a bag and count the bag as one object. Figure out the number of possible ways to arrange those objects. Then find the number of ways to arrange the objects inside the bag. Then multiply the two answers together to get the final answer... does that make any sense ? Well it does to me. :D

6. The BINOMIAL THEOREM can blow your mind away. It can find a specific term in a binomial expansion without actually expanding the whole binomial. Here is the formula:
i is the term you want.
n is the exponent
a is the first term and b is the second in (a+b)^n

WHEN LOOKING FOR THE MIDDLE TERM. IF THE NUMBER OF TERMS OF THE EXPANSION IS EVEN THERE IS NO MIDDLE TERM. REMEMBER THAT.

7. Pa-pa-pa-poker face, pa-pa poker face [8]. Cards. Yeah. Look at aldrin's and john's BOBs, they have that covered... I can't really explain it becuase i don't really know it.

I hope I have everything covered. If I don't please don't hesitate to tell me. Or if I have something wrong.. correct me ;D

I hope I don't fail tomorrow.

BREAK A PENCIL EVERYONE ;D

BOB was sitting on a LOG...

Anyways, this is my BOB, and no I am not late since i didn't do my test yet.

Since I missed a whole week I have a feeling that all those word problems and questions involving e will be my downfall since that is what the class covered while I was away. Just saying.

Here is stuff that I should remember for the test:

a) A LOGARITHM IS AN EXPONENT.

b) When solving exponential equations, make sure the base is the same. If the base is not the same use log.

c)When dealing with quadratics, reject the negative answer since it will make the log/exponential function undefined.

d)Know how to draw these functions and describe them (range, domain, increasing/decreasing etc.)

e)Know the laws:
i) The product law
ii) The quotient law
iii) The power law
iv) The change of base law

f) Know the formulas, unless Mr. K is nice enough to have a formula sheet :D
i) A=P(1+r/n)^(t*n)
ii) A=Pe^rt
iii) The rule of 72 ?
iv)A=Ao(model)^t

g) Just know that ln is the natural logarithm.

Alright. I guess that's it... just eat, sleep and study right....

May I request that I do my test wednesday Mr. K? :)

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.

It's Raining Exponents... Hallelujah ?

Hi everyone! It's Ann here (oh wow my name is so short O__o) and I've been handed the torch of Scribedom. :)

Today, the first thing I heard as I walked into the classroom was something about dinosaurs and Jurassic Park. Apparently those topics will be brought up later in our...

NEW UNIT!!! Exponents and Logarithms ~!

First, we went into groups and with our brilliant minds thought up many ways to write numbers exponentially. The number 2 for example can be written as 2^1, 4^(1/2) and so on. Remember that there are an infinite number of ways to write a number.

Just a note! : Negative exponents give you the reciprocal of the base.

…and just to clarify the parts of a power so no one gets confused:

Now let us play the game that we all love to play: Solve for x!

Exponential equations are similar to what we have already done in the past, but now there is a new step: The powers that you are solving must have the same base because if the base is equal then the exponents must be the same. So if you don’t have the same base your answers going to be all wonky.

Some simple ones that we did today:

That seems easy enough right? But what if you have something like this?

You must still make the bases the same, but now we must take the exponents, turn it into an equation and solve for x.

If any of you are wondering where the 6x-3=1 came from, please look at the exponents. Multiply 3(2x-1) and since the exponent on the 3 is a one then let the equation equal one and solve.

Then we did other practice problems that were similar to that one. Then the bell rang. :D

REMEMBER THAT TOMORROW IS OUR IDENTITIES TEST!!! STUDY! STUDY! STUDY!

The next scribe is Jennifer ;D

BOB, Show Some Identification Please :D

Since our test is on Wednesday I've decided to BOB already. I know what some of you may be thinking... "It's Spring Break! Have fun! It's to early for a BOB!" But you know what ? I have lots of work and I might as well get this over with. >__<

I understand this topic. I really do. My quiz may state otherwise but I UNDERSTAND. I swear! It's just that I don't have many clever ideas and that I tend to do things the long way. I guess this means I have to study.. lots. :(

Well I guess this is basically what we need to know for this unit:

1. Work with the complicated side of the identity first.

2. Rewrite both sides of the identity in the terms of sine and cosine.

3. Use a Pythagorean identity to make a substitution (sin^2x + cos^2x = 1, 1 + cot^2x = csc^2x, sec^2x + 1 = tan^2x ). So if you have 1 - sin^2x for example, substitute it with cos^2x.

4. Simplify complex fractions or rewrite fractions of sums and differences with the same common denominator.

5. Factor (especially use difference of squares).

Oh wait I lied... there is ONE rule: NEVER EVER CROSS THE GREAT WALL OF CHINA !!

Then there are sum and difference identities...

sin(a+b) = sinacosb + cosasinb
sin(a -b) = sinacosb - cosasinb
cos(a+b) = cosacosb - sinasinb
cos(a-b) = cosacosb + sinasinb

Use them :D

Just substitute the values of a and b. Then evaluate. You might have to find out what the angles are but you guys are all geniuses ;)

Oh and then there are those double identities. Look those over because we are most likely going to need them :)

I guess that's it... well that was short :D

I just noticed that I use smiley faces a lot. :O

It's The BOB To My Heart :D

I was meaning to do this earlier but since we haven't had the test yet I'm good. xD

How I feel about this unit on a scale of 1-to-10 ? About an 8.5. I understand it, it's just that I make a lot of stupid mistakes... and I mean.. A LOT. The only real trouble that I can foresee is most likely the word problems and some reciprocal graphs. Actually just the word problems because sometimes I just don't read the problem right. =/

Here's basically what I (and you guys too!) need to know:

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

Parameter A: Stretches the graph vertically by a factor of a.
Parameter B: Stretches the graph horizontally by a factor of 1/b. Say if the value was 2, then the x coordinates would be multiplied by 1/2.
Parameter C: Moves the graph horizontally C units. WATCH OUT FOR THE SIGN OF C. When it is negative you move the graph to the right and vice versa.
Parameter D: Moves the graph vertically D units.

ALWAYS DO STRETCHES BEFORE TRANSLATIONS!! Just saying... ;)

In the case of trig equations (which you most likely need to know for the word problems)...

g(x)=AsinB(x-C)+D

Parameter A: Is the amplitude (the distance away from the sinusoidal axis).
Parameter B: IS NOT THE PERIOD! B determines the period with the little equation Period=2(pi)/B.
Parameter C: Shifts the graph C units. Watch out for the SIGN! :)
Parameter D: Shifts the sinusoidal axis up or down D units. (This is the average point between the max and min of the graph).

Also.. know how to figure out if a graph is odd or even (or neither!) Just plug in -x and see what you get ;)

When it is even f(-x)=f(x).

When it is odd -f(x)=f(x)

And when it's neither.. well.. its neither of those...

Also know how to graph reciprocal and inverse functions. THESE ARE NOT THE SAME GRAPHS. f^-1(x) DOES NOT EQUAL 1/f(x).

To graph the inverse of f(x) just basically switch the x and y values. Remember to find the invariant point and make sure your sketch goes through it =/ This graph should look like it's reflecting itself over the graph of y=x.

As for reciprocal graphs.. first you have to find the invariant points (where f(x)= 1 or -1). Then look for the asymptotes, then do the 'biggering and smallering' method. :D

I think that's it. It better be. Anyways, I hope we all do really good on the pretest and test :D

Break a pencil everyone~!

I'll BOB you ! :)

To tell you the truth I felt that I had everything down pact. Now I don't feel as confident. XD

I understand the values in the unit circle. Radians and degrees seem interchangable, and I remember my quadrants and my cos and sin and everything else!

Looking for the unknown values of theta? I'm good. Seeing if a point is on the unit circle. I'm fine. Just being pi. Sure. I like pi :)

BUT I don't understand anything with graphs, or this ABCD stuff. I looked at the slides,I looked at the blog, but I think I need someone to explain it to me before I go crazy. Today I sort of got it but I'm not sure if I'll be able to apply this bit of meagre knowledge to questions on the test tomorrow.

My goal is 100% + I'm scared I won't achieve it =(

But I'm going to wish everyone good luck! And break a pencil ! (x

Happy Valentine's (Approximation) Day! >:D

Hello there mon internet (stalker) classmates! It's ANNabanana here! Right now I am very tempted to say that all we did today in class was math.

>:D

Anywho, we started off the day with a little mental math. You know, the unit circle stuff our mental math's have been based on all week (click here if you need some practice with it). Then we went into small groups so our brain waves could be shared to solve the problems that were on the smartboard. If you would dare to look at Mr. K's slides you'll see what problems I'm talking about. Rather simple trigometric functions, it's just that I have to point out some things to you mon dearies. :D



I'd like you're eyes to be entranced by the slide directly below this.

You see that big red X? Well Mr. K showed us the wrong way to solve equations. Never ever ever EVER divide by a variable because you don't know the value of it and might potentially be zero. When you divide by zero the answer becomes undefined and you don't want that! Talking about undefined...

Why would I point this out? Because I had such a wonderful time writing out the (wrong xD) answers on the slide it was from. No, actually Mr. K pointed out that on our exam we have to write the answers that don't work or that are undefined seperate from the answers that DO work. Also, for those of you wondering why cos x = 2 is undefined, it's because the unit circle has a radius of one and the maximum unit that it can go up to is one. Two unfortunetly is too big. D=

Here's something new. Let's look for the answer in the domain of.. what's this! The set of real numbers?! Oh my! There are infinite answers for this question! How can we possibly write them all down?!?

It all comes down to k. A number in the set of intergers. Something that tells you how many times it goes round and round (with pi). For any tangent say that the answer is (tan x) + k(pi) because every tangent is an unit of pi (half a circle) away from eachother. For all other answers it should be (your answer here) + 2k(pi) because it's going to take one whole revolution around the unit circle to reach that answer again.

The homework for the weekend is the rest of exercise 5 and the last 10 quesitons on exercise 6.

LOL, look what I found on youtube.

Hmmmm... let's see. The next scribe is Mary. :D

"Insert math quote here"