What concept do you feel like you mastered this nine weeks? What concept did you struggle with the most? Why? What can you change this nine weeks in your study habits, etc to improve your grade?
What concept do you feel like you mastered this nine weeks? -I think the one concept I mastered this nine weeks was chapter one, which was everything dealing with limits. I really understood the limit process, whether it was plugging in limits, having to create a table, or just looking at the graph. It was a very simple concept, and it was easy to remember. There also wasn’t a lot of steps to solving it.
What concept did you struggle with the most? -The thing I struggled with the most would have to be all the word problems. The application problems we learned at the beginning of chapter two, and the last ones we learned in chapter two were pretty difficult. I understood them when I was told what I was dealing with, but when I had to figure everything out they got harder. I don’t know all the formulas, which is the problem.
What can you change this nine weeks in your study habits, etc to improve your grade? -I can work more problems instead of just the homework problems, and maybe ask more questions in class. I can also use the help handouts on edline.
This 1st 9-weeks, I feel that I mastered derivatives. Taking derivatives can be super simple if you study and know the rules. We spent a lot of time on derivatives in class and had a lot of homework problems on them, so I feel really confident about it. It helped that we did so many example problems in class with different types of derivatives, whether it was with the taking a simple derivative, implicit, product and quotient rule, or even the chain rule. On the other hand, I struggled with the word problems. I get the basics and I can do simple area or volume problems, but as the word problems got more complicated and into stuff like “the rate of a falling ladder” or “the area of a swimming pool,” I was totally lost. I have a hard time connecting the problem to a formula when the problems doesn’t straight out state “find the rate of the changing area” or “what’s the volume if…”. I think we should’ve done more different kinds of example problems in class and gone over the homework more thoroughly. Not to mention that I need to memorize some for geometry formulas, such as the volume and surface area of a cube. Personally, to improve I should probably get in the habit of using CalcChat more often when doing my homework and maybe ask more questions in class the next day.
The first nine weeks, i have to say i did not impress myself... I grasped derivatives almost completely, but implicits and related rates are kinda still hard to work through all the way, maybe its just me. we did have a ton of homework and notes. I think what i can change to improve my study habits/grades is to practice the problems that are confusing, ask around more, get help after attempting to the best of my ability and apply my understanding of things more, aka gain independence when it comes to word problems. I'll get used to asking more questions and using CalcChat soon, maybe feel a little more confident when i start getting things right. I don't think theres much i can do to improve my grade, we are working on AP test stuff tomorrow and wednesday if I heard correctly, and keep up with blogs, i think i only missed 1 this year so far so that's surprising. To sum it up I need to work much harder and memorize my important information i.e. formulas and steps
What concept do you feel like you mastered this nine weeks? I feel like I really mastered the methods of taking regular derivatives. I feel really confident when required to use the limit process, when required to use the short cut method, when required to use the product rule, when required to use the quotient rule, when the chain rule is involved ((finally!)) and when it’s necessary to take the second derivative. I also feel like I may have mastered implicit derivatives.
Example of using the limit process: f(x) 2(x+&x)-3-(2x-3)/ &x &x-> 0
Expand:
2x+2&x – 3 – 2x + 3 / &x
Take out what cancels: 2x + 2&x -3 -2x +3/&x
And you’re left with: 2&x/&x
Simplify:
2 &x/ &x Therefore the answer is 2
Example of using the short cut method: d/dx[x^3] = 3x^2
Example of using the product rule: 3x-2x^2) (5+4x) First I take the derivative e of each so that when I plug in I already know what the derivatives are to be plugged in D/Dx [3x-2x^2]= 3-4x Therefore F prime= 3-4x D/Dx [5+4x]= 4 Therefore G prime= 4
Now you plug into the formula Therefore 3x-2x^2(4)+ 5+4x (3-4x) Distribute 12x^2x-8x^2+15-20x+12x-16 Simplify -24x^2 + 4x +15 Because this equation cannot be simplified any further Dx= -24x^2+4x+15
Example of using the Quotient rule: The quotient rule is recognized as F(x)/G(x) The formula for solving with the quotient rule is D/Dx [F(x)/G(x)] = G(x) Fprime(x)- F(x) Gprime(x)/ [G(x)]^2 Example: 5x-2/x^2-1 First I take the derivative of each so that when I plug in I already know what the derivatives are to be plugged in D/dx [ 5x-2] = 5 Therefore F prime= 5 D/dx [x^2 – 1] = 2x Therefore G prime = 2x Now you plug into the formula Therefore (x^2+1)(5)-[(5x-2)(2x)]/(x^2+1)^2 Distribute 5x^2+5-[10x^2-4x]/(x^2+1)^2 Distribute the negative 5x^2+5-10x^2+4x/(x^2+1)^2 Simplify -5x^2 + 4x+5/ (x^2+1)^2 Because this equation cannot be simplified any further DX= -5x^2 + 4x+5/ (x^2+1)^2
Example of a chain rule problem: Square root of 3x^2-X+1 = (3x^2-X+1)^1/2 First, take the derivative of the outside: ½(________)^-1/2 Second, recopy just the inside ½(3x^2-X+1)^-1/2 Finally, multiply by the derivative of the inside ½(3x^2-X+1)^-1/2 (6x-1) Simplify 6x-1/2(3x^2-x+1)^1/2
Example of implicit derivatives:
Sqrtxy= x^2y+1 (xy)1/2=x^2y+1 X^ 1/2 y^ ½ = x^2 y +1 First take the derivative X^1/2 (1/2y^-1/2 dy/dx) + y^1/2 (1/2x^-1/2)= x^2 (1dy/dx+y(2x)) 1/2x^1/2y^-1/2 dy/dx + 1/2x ^-1/2 y^1/2 = x^2 dy/dx + 2xy Second gather all d*/dx 1/2x^1/2y^-1/2 dy/dx- X^2 dy/dx= 2xy - 1/2x^-1/2y^1y^1/2 Third solve for d*/dx
Dy/dx = 2xy -1/2x^-1/2y^1/2 / ½ x^1/2 y^-1/2 – x^2
What concept did you struggle with the most?
I really had a hard time when we were learning the chain rule in the beginning but since I think I may have a pretty good handle on the chain rule problems now, I guess the concept I am struggling most with is the word problems.
I had a hard time with the chain rule derivatives because there is no set list of steps to follow. I have a very logic and methodical oriented habitual mind and to try to understand a concept that doesn’t have an order of operations really threw me. I think it finally clicked for me when I had worked enough problems to figure out a specific method of solution for each general type of problem. Im having a hard time with the word problems now only because there are some problems where I have no clue what they are asking for. I understand how to lay out the given variables of the problems and I also understand how to follow the given steps for these types of problems. The only step catching me is the second step where we have to find a formula to plug in to. Some problems are obvious as to what formula they require however there are problems where I have no Idea what formula is being called for.
What can you change this nine weeks in your study habits, etc to improve your grade?
I have no idea what im doing wrong in my study habits. I do every problem when homework is assigned. Majority of the time when only odds are assigned I’ll do evens too. I take the class notes written on the projector and I take notes specifically on what is said by mrs, robinson. I also study for each quiz and test thoroughly. I guess the only other study habit I could start doing is making note cards every day on what key elements were taught each day and review them daily.
What concept do you feel like you mastered this nine weeks?
This first nine weeks went by very quickly, and feel I mastered taking simple derivatives and using the chain rule and product rule and quotient rule really well. I feel totally comfortable with derivatives now, the simple ones at least. Now for implicit derivatives, those are a whole different story.
What concept did you struggle with the most?
I feel like I mainly struggled with implicit derivatives, and I still struggle with those complex derivatives and then to take it a step further you have to take a second derivative of an implicit derivative function. That really got me. Well obviously I struggled a lot in the first nine weeks because I made a 66 on the exam without the curve, which is very unusual for me, I figured I would at least make a B. Oh well.
What can you do this nine weeks to improve your study habits, etc, to improve your grade?
I think I can definitely use more study time and at least try the next nine weeks.
*What concept do you feel like you mastered this nine weeks?
I feel like I've mastered limits and derivatives pretty good. Limits especially because we learned that concept last year and the beginning of this year was sort of just refreshing my memory. So I definitely have that down pat. Derivatives are sooooooooo easy now! I have no idea why I was stressing over them so much in the beginning..But really that goes to show you how much practice really helps. And now that we've been doing it a while, I don't have to stare at the problem for like 5 minutes JUST to figure out what I have to do with it (product/chain rule, etc) So yeah I'm glad I grasped that concept..The only thing I'm still a little iffy with (for derivatives) is 2nd derivatives when it's like a really complicated problem with trig functions involved. *The concept I think I've struggled with the most is definitely the word problems..Like I may have mentioned before earlier this year or last year, I am not a fan of word problems or any kinds of shapes..I don't know, that's just a pet peeve in math for me. I mean the simple word problems I understand completely..it's just the problems where you pretty much have to make up your own rules along the way and pull formulas and equations out of thin air..that's where I get lost. But hopefully since we'll be going back to this concept frequently, it'll stick in my brain sooner or later.
*What can you change this nine weeks in your study habits to improve your grade? Well honestly I should do more practice on the concepts we learn. Whatever the homework assigned I'll do mostly all of it, and attempt the ones I think are difficult..then ask questions (a million of them) the next day. Usually before a test, I won't do practice problems on the things I already know. I mainly focus on what I'm kinda struggling with and just basically look over my problems and the work with them. I guess I'm more of a visual learner because once I see something in front of me, it usually clicks in my mind. And also, typically when I get things wrong on a test it's because of stupid mistakes..so I should work on that too
What concept do you feel like you mastered this nine weeks? -I think that the one concept that I have mastered this nine weeks would be the "short-cut" to taking derivatives. Using the formula that involved deltaX kind of confused me. So straight taking the derivative is much easier for me. What concept did you struggle with the most? Why? -At first, I struggled with the Chain Rule, but after Brandi gave us a worksheet on the chain rule, it became much easier. By the end of the nine weeks, I have a new dilema. I don't understand related rates. I can determine what the variables are, but I cannot firgure out which formulas to plug the different variables into to find the rate of change. What can you change this nine weeks in your study habits, etc to improve your grade? -I think that I could have studied a little harder for the tests and it would have helped my grades on the tests. There isn't much more that I could have done since I had done all of my homework.
what do i feel like i mastered this nine weeks? hmm, I think I'll go with "nothing"…final answer
what did I struggle with the most? Umm, everything!…"Survey Says!" 48 points! why? because I just couldn't pick up on it and actually understand it
what can I do to improve my study habits and all that? first thing to do would be to get music to not be stuck in my head all the time; second would be to actually look up the answers i guess
Honestly I do not believe that I actually mastered any concept this nine weeks. For some reason this class is extremely difficult for me to keep up with.
But the only concept that I somewhat understood was the derivatives. After I memorized the formulas the derivatives equations became very easy for me to solve.
I had difficulty with almost every concept we went over this nine weeks. The concepts I had the most trouble with was probably the veloctiy equations, the area equations, the volume equations, and the surface area equations.
This nine week I will have to put more time in my studies to hopefully understand calculus better. I will have to do extra problems when I have time. Actually try to do all my homework instead of just a few problems. And I will have to go to that calc chat thing for help.
What concept do you feel like you mastered this nine weeks?
ReplyDelete-I think the one concept I mastered this nine weeks was chapter one, which was everything dealing with limits. I really understood the limit process, whether it was plugging in limits, having to create a table, or just looking at the graph. It was a very simple concept, and it was easy to remember. There also wasn’t a lot of steps to solving it.
What concept did you struggle with the most?
-The thing I struggled with the most would have to be all the word problems. The application problems we learned at the beginning of chapter two, and the last ones we learned in chapter two were pretty difficult. I understood them when I was told what I was dealing with, but when I had to figure everything out they got harder. I don’t know all the formulas, which is the problem.
What can you change this nine weeks in your study habits, etc to improve your grade?
-I can work more problems instead of just the homework problems, and maybe ask more questions in class. I can also use the help handouts on edline.
This 1st 9-weeks, I feel that I mastered derivatives. Taking derivatives can be super simple if you study and know the rules. We spent a lot of time on derivatives in class and had a lot of homework problems on them, so I feel really confident about it. It helped that we did so many example problems in class with different types of derivatives, whether it was with the taking a simple derivative, implicit, product and quotient rule, or even the chain rule. On the other hand, I struggled with the word problems. I get the basics and I can do simple area or volume problems, but as the word problems got more complicated and into stuff like “the rate of a falling ladder” or “the area of a swimming pool,” I was totally lost. I have a hard time connecting the problem to a formula when the problems doesn’t straight out state “find the rate of the changing area” or “what’s the volume if…”. I think we should’ve done more different kinds of example problems in class and gone over the homework more thoroughly. Not to mention that I need to memorize some for geometry formulas, such as the volume and surface area of a cube. Personally, to improve I should probably get in the habit of using CalcChat more often when doing my homework and maybe ask more questions in class the next day.
ReplyDeleteThe first nine weeks, i have to say i did not impress myself... I grasped derivatives almost completely, but implicits and related rates are kinda still hard to work through all the way, maybe its just me. we did have a ton of homework and notes. I think what i can change to improve my study habits/grades is to practice the problems that are confusing, ask around more, get help after attempting to the best of my ability and apply my understanding of things more, aka gain independence when it comes to word problems. I'll get used to asking more questions and using CalcChat soon, maybe feel a little more confident when i start getting things right. I don't think theres much i can do to improve my grade, we are working on AP test stuff tomorrow and wednesday if I heard correctly, and keep up with blogs, i think i only missed 1 this year so far so that's surprising.
ReplyDeleteTo sum it up I need to work much harder and memorize my important information i.e. formulas and steps
What concept do you feel like you mastered this nine weeks?
ReplyDeleteI feel like I really mastered the methods of taking regular derivatives. I feel really confident when required to use the limit process, when required to use the short cut method, when required to use the product rule, when required to use the quotient rule, when the chain rule is involved ((finally!)) and when it’s necessary to take the second derivative. I also feel like I may have mastered implicit derivatives.
Example of using the limit process:
f(x) 2(x+&x)-3-(2x-3)/ &x
&x-> 0
Expand:
2x+2&x – 3 – 2x + 3 / &x
Take out what cancels:
2x + 2&x -3 -2x +3/&x
And you’re left with:
2&x/&x
Simplify:
2 &x/ &x
Therefore the answer is 2
Example of using the short cut method:
d/dx[x^3] = 3x^2
Example of using the product rule:
3x-2x^2) (5+4x)
First I take the derivative e of each so that when I plug in I already know what the derivatives are to be plugged in
D/Dx [3x-2x^2]= 3-4x
Therefore F prime= 3-4x
D/Dx [5+4x]= 4
Therefore G prime= 4
Now you plug into the formula
Therefore
3x-2x^2(4)+ 5+4x (3-4x)
Distribute
12x^2x-8x^2+15-20x+12x-16
Simplify
-24x^2 + 4x +15
Because this equation cannot be simplified any further
Dx= -24x^2+4x+15
Example of using the Quotient rule:
The quotient rule is recognized as F(x)/G(x)
The formula for solving with the quotient rule is
D/Dx [F(x)/G(x)] = G(x) Fprime(x)- F(x) Gprime(x)/ [G(x)]^2
Example: 5x-2/x^2-1
First I take the derivative of each so that when I plug in I already know what the derivatives are to be plugged in
D/dx [ 5x-2] = 5
Therefore F prime= 5
D/dx [x^2 – 1] = 2x
Therefore G prime = 2x
Now you plug into the formula
Therefore
(x^2+1)(5)-[(5x-2)(2x)]/(x^2+1)^2
Distribute
5x^2+5-[10x^2-4x]/(x^2+1)^2
Distribute the negative
5x^2+5-10x^2+4x/(x^2+1)^2
Simplify
-5x^2 + 4x+5/ (x^2+1)^2
Because this equation cannot be simplified any further
DX= -5x^2 + 4x+5/ (x^2+1)^2
Example of a chain rule problem:
Square root of 3x^2-X+1
= (3x^2-X+1)^1/2
First, take the derivative of the outside:
½(________)^-1/2
Second, recopy just the inside
½(3x^2-X+1)^-1/2
Finally, multiply by the derivative of the inside
½(3x^2-X+1)^-1/2 (6x-1)
Simplify
6x-1/2(3x^2-x+1)^1/2
Example of implicit derivatives:
Sqrtxy= x^2y+1
(xy)1/2=x^2y+1
X^ 1/2 y^ ½ = x^2 y +1
First take the derivative
X^1/2 (1/2y^-1/2 dy/dx) + y^1/2 (1/2x^-1/2)= x^2 (1dy/dx+y(2x))
1/2x^1/2y^-1/2 dy/dx + 1/2x ^-1/2 y^1/2 = x^2 dy/dx + 2xy
Second gather all d*/dx
1/2x^1/2y^-1/2 dy/dx- X^2 dy/dx= 2xy - 1/2x^-1/2y^1y^1/2
Third solve for d*/dx
Dy/dx = 2xy -1/2x^-1/2y^1/2 / ½ x^1/2 y^-1/2 – x^2
What concept did you struggle with the most?
I really had a hard time when we were learning the chain rule in the beginning but since I think I may have a pretty good handle on the chain rule problems now, I guess the concept I am struggling most with is the word problems.
Why?
ReplyDeleteI had a hard time with the chain rule derivatives because there is no set list of steps to follow. I have a very logic and methodical oriented habitual mind and to try to understand a concept that doesn’t have an order of operations really threw me. I think it finally clicked for me when I had worked enough problems to figure out a specific method of solution for each general type of problem. Im having a hard time with the word problems now only because there are some problems where I have no clue what they are asking for. I understand how to lay out the given variables of the problems and I also understand how to follow the given steps for these types of problems. The only step catching me is the second step where we have to find a formula to plug in to. Some problems are obvious as to what formula they require however there are problems where I have no Idea what formula is being called for.
What can you change this nine weeks in your study habits, etc to improve your grade?
I have no idea what im doing wrong in my study habits. I do every problem when homework is assigned. Majority of the time when only odds are assigned I’ll do evens too. I take the class notes written on the projector and I take notes specifically on what is said by mrs, robinson. I also study for each quiz and test thoroughly. I guess the only other study habit I could start doing is making note cards every day on what key elements were taught each day and review them daily.
Taylor,
ReplyDeleteI don't think you have a lot to worry about changing. You did excellent on your exam. I think it just took a bit for everything to catch up with you.
What concept do you feel like you mastered this nine weeks?
ReplyDeleteThis first nine weeks went by very quickly, and feel I mastered taking simple derivatives and using the chain rule and product rule and quotient rule really well. I feel totally comfortable with derivatives now, the simple ones at least. Now for implicit derivatives, those are a whole different story.
What concept did you struggle with the most?
I feel like I mainly struggled with implicit derivatives, and I still struggle with those complex derivatives and then to take it a step further you have to take a second derivative of an implicit derivative function. That really got me. Well obviously I struggled a lot in the first nine weeks because I made a 66 on the exam without the curve, which is very unusual for me, I figured I would at least make a B. Oh well.
What can you do this nine weeks to improve your study habits, etc, to improve your grade?
I think I can definitely use more study time and at least try the next nine weeks.
*What concept do you feel like you mastered this nine weeks?
ReplyDeleteI feel like I've mastered limits and derivatives pretty good. Limits especially because we learned that concept last year and the beginning of this year was sort of just refreshing my memory. So I definitely have that down pat. Derivatives are sooooooooo easy now! I have no idea why I was stressing over them so much in the beginning..But really that goes to show you how much practice really helps. And now that we've been doing it a while, I don't have to stare at the problem for like 5 minutes JUST to figure out what I have to do with it (product/chain rule, etc) So yeah I'm glad I grasped that concept..The only thing I'm still a little iffy with (for derivatives) is 2nd derivatives when it's like a really complicated problem with trig functions involved.
*The concept I think I've struggled with the most is definitely the word problems..Like I may have mentioned before earlier this year or last year, I am not a fan of word problems or any kinds of shapes..I don't know, that's just a pet peeve in math for me. I mean the simple word problems I understand completely..it's just the problems where you pretty much have to make up your own rules along the way and pull formulas and equations out of thin air..that's where I get lost. But hopefully since we'll be going back to this concept frequently, it'll stick in my brain sooner or later.
*What can you change this nine weeks in your study habits to improve your grade?
Well honestly I should do more practice on the concepts we learn. Whatever the homework assigned I'll do mostly all of it, and attempt the ones I think are difficult..then ask questions (a million of them) the next day. Usually before a test, I won't do practice problems on the things I already know. I mainly focus on what I'm kinda struggling with and just basically look over my problems and the work with them. I guess I'm more of a visual learner because once I see something in front of me, it usually clicks in my mind. And also, typically when I get things wrong on a test it's because of stupid mistakes..so I should work on that too
What concept do you feel like you mastered this nine weeks?
ReplyDelete-I think that the one concept that I have mastered this nine weeks would be the "short-cut" to taking derivatives. Using the formula that involved deltaX kind of confused me. So straight taking the derivative is much easier for me.
What concept did you struggle with the most? Why?
-At first, I struggled with the Chain Rule, but after Brandi gave us a worksheet on the chain rule, it became much easier. By the end of the nine weeks, I have a new dilema. I don't understand related rates. I can determine what the variables are, but I cannot firgure out which formulas to plug the different variables into to find the rate of change.
What can you change this nine weeks in your study habits, etc to improve your grade?
-I think that I could have studied a little harder for the tests and it would have helped my grades on the tests. There isn't much more that I could have done since I had done all of my homework.
what do i feel like i mastered this nine weeks?
ReplyDeletehmm, I think I'll go with "nothing"…final answer
what did I struggle with the most?
Umm, everything!…"Survey Says!" 48 points!
why? because I just couldn't pick up on it and actually understand it
what can I do to improve my study habits and all that?
first thing to do would be to get music to not be stuck in my head all the time; second would be to actually look up the answers i guess
Honestly I do not believe that I actually mastered any concept this nine weeks. For some reason this class is extremely difficult for me to keep up with.
ReplyDeleteBut the only concept that I somewhat understood was the derivatives. After I memorized the formulas the derivatives equations became very easy for me to solve.
I had difficulty with almost every concept we went over this nine weeks. The concepts I had the most trouble with was probably the veloctiy equations, the area equations, the volume equations, and the surface area equations.
This nine week I will have to put more time in my studies to hopefully understand calculus better. I will have to do extra problems when I have time. Actually try to do all my homework instead of just a few problems. And I will have to go to that calc chat thing for help.