This week consisted of APs again and Friday a clicker quiz! My gosh, I cannot believe how close the AP is!
Let's see...
How about some quick tips?
1. Limit from h->0 (DON'T LOOK AT THE COEFFS!!)-- it's a definition of a derivative
2. When you're asked about the Average Rate Of Change, you simply take the derivative.
3. When they ask you about relative maximum, you take the derivative, solve for x, and check intervals.
4. When you're asked about maximum value, take the derivative, solve for x, then plug in to get y.
5. Maximum acceleration = slope = derivative
6. When asked to find the vertical tangents, take the derivative.
Some things I'm confused about:
1. Keywords in free response - I never know what to do...oh and for slope field, 0 is a straight line, -1 is bottom of the line points to [left or right?] while +1 is where the bottom of the line points [left or right?]...also, what do you do if the number is bigger than 1?
2. Acceleration, velocity, and [[the other word that I cannot remember]] - what is the trick to remembering what to do?
3. Related Rates - how do I recognize them?
4. TRAM - It goes like thisish right? delta/2[f(a)+2f(a+2(delta))+2f(a+3(delta))+2f(a+4(delta))+2f(a+5(delta))+f(b)]
5. e! or ln! I cannot grasp these two..each time I see them in a problem I skip it or save it for last...
6. OH!!! Calculator help! I'm still amazed at what it can do, but there's still lots I don't know about...also, do we ever use degrees?
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Slope fields:
ReplyDeleteYou find the points given to you on the graph.
Then you plug in the points into the equation given.
If the answer is 0, then the slope field is -
If the answer is a negative, the slope field is \ (i remember by thinking of it as decreasing)
If the answer is a positive, the slope field is / (increasing)
The bigger the number is, the steeper the slope field will be.
The smaller the number, the slope field will not be as steep.
Example: dy/dx=y-1/x^2
(-1,0) = 0-1/(-1)^2 = -1 slope field is \
(-1,1) = 1-1 / (-1)^2 = 0 slope field is -
(-1,2) = 2-1/(-1)^2 = 1 slope field is /
(2,0) = 0-1 / (2)^2 = -1/4 slope field is \ (but less steep)
hope this helped.
The formula for TRAM is delta x/ 2 [f(a) + 2f(delta x + a) + 2f(2 delta x +a) ..... + f(b)]
ReplyDeleteHowever, for the questions most seen on the AP, you do not need to use the formula because the values are usually given.
If given the table x 0 0.5 1.0 1.5 2.0
f(x) 3 3 5 8 13
The question says: A table of values for a continuous function f is shown above. If four equal subintervals of [0,2] are used, which of the following is the trapezoidal approximation of S f(x) dx on [0,2]?
Since you have the table, you do not need to plug into the formula because the values are already given.
You need to find delta x, which is done by finding the pattern in the numbers. .5 -0 = 1/2 , 1-.5 = 1/2, etc.
Delta x = 1/2
divided by 2 because it is trapezoidal: 1/2/2 = 1/4
1/4 [f(0) + 2f(0.5) + 2f(1) + 2f(1.5) +f(2.0)]
(all you have to do is remember the first and last terms are not multiplied by two but the middle are)
Now plug in the numbers: 1/4 [3 + 2(3) + 2(5) + 2(8) + 13]
1/4[ 3 + 6 +10 + 16 +13]
1/4 {48]
48/4 = 12
The Position function will always be an original function... velocity is the first derivative and acceleration is the second derivative. If you have acceleration and you want to get to velocity or position.. you integrate... if you have velocity and want to get to position.. you integrate... just remember them in that order and you should be good to go!
ReplyDeleteNOPE...WE DO NOT USE DEGREES...JUST STAY IN RADIANS AND YOU'LL BE SAFE!
ReplyDelete[if is says __ degrees then put it in degrees but otherwise..NO]
related rates are always a long paragraph. explainging how oil is spilling in the ocean or filling up a tank or something. the most common first thing given is ... THE RATE AT WHICH OIL IS SPILLING IN THE OCEAN IS v(t)=whatever, v representing velocity.
ReplyDeleteand it will tell you a bunch of other stuff that is usually important. just write it all down on the side.
also, for related rates.... 9/10 times on free response. part A says something like the rate at which the oil spills from time = 0 to time =2. whenever it gives you an interval, you should INTEGRATE according to that interval. *calculators*
:)
position is the original function, then the velocity is the derivative of the position, then acceleration is the derivative of velocity, and to get between any of these all you need to do is either take the derivative to move up the ladder, or integrate to go down
ReplyDeletestay in radian mode the hole way any youll be okay. Also just remember this :
ReplyDeleteposition : Volicity : Acceleration
PVA
intergrate to move in chain of command and derive to move down : ) boom!