OMG I ALMOST FORGOT!
To B-ROB: you are an AMAZING teacher. I don't care what anyone says, hands-down.. best teacher at riverside academy. you have so much dedication for your students and you believe in all of us. even the annoying ones in the class... ;) you are one of the only teachers i know that will work with you in all of your extra hours UNTIL you get it. no matter how long it takes, you will make it click in our brains. which you did for most of us. i wish i could put a note on here for all incoming calc students saying that brob is willing to help as long as you're willing to put forth the effort. that is one thing that i've learned also, which i'm very glad i did. i can honestly say i think i'm speaking on behalf of the entire class when i say: WE LOVE YOU BROB. thank you for believing in us.
Sunday, May 9, 2010
Kaitlyn's Final Reflection
Well after anticipating all year, it's finally here. My last few days of high school. First I just want to say how bittersweet this class was for me. The class itself, i loved it! The people, the messing around, the stressing out, the late night mini van trips, it was unforgettable. I really enjoyed getting to know everyone and love our ability to have fun yet still get a lot of work done. Now for the bitter part...the actually calculus. I'm pretty sure it's safe to say i suck at it. But hey, it's not the end of the world. Don't worry, i don't plan on building bridges or roller coasters in my future, so y'all should be safe ;)
Now onto the "concept" that never gave up on me and kept running into my skull until it finally got into my brain...
what else could it be..... AVERAGE VALUE!
It's just such a simple integral problem, how can anyone get this wrong. The formula is 1/b-a bSa f(x). You simply just plug in to the formula with what you were given. And half the time it's in the calculator portion so you just have to plug the integral in your calculator then times it by 1/b-a. Voila, you get a beautiful answer that you actually think is right :) AMEN to that.
Just so i don't seem like i only accomplished one thing in calculus all year, some other things i understood were average rate of change, mean value theorem, simple derivatives and integrals, HORIZONTAL TANGENTS, and i'm sure there are a couple of others.
So onto my farewells:
my seniors- We've had an amazing run. We're all so close and we worked hard to get where we are. No matter how mean i may come off sometimes, I love each and every one of y'all and wish every one luck in their future endeavors. Now let's finish this year off right and make a name.
oh let's doooo it
the juniors- i absolutely love y'all. i never really talked to y'all much before this class but i'm so glad that we had it together. Every one of y'all cracks me up, and i know y'all will be successful b/c of how determined you are. Keep it up and don't slack off, and have fun in calculs bc next year. I might miss you guys ;)
B-robbbb- thanks for putting up with me these last two years. You believed in me and kept pushing me even when i said it was impossible to stick this what i call "garbage" in my brain. I know i didn't catch on to a lot at first, but i did try and i truly believe no other teacher could put up with us as well as you did. You're an awesome person and i truly admire you and all of your accomplishments. Thanks again for everything :)
Now i think it's time to close this blog, my LAST one.
Goodbye Calculus, Goodbye Riverside, Hello Life :)
Now onto the "concept" that never gave up on me and kept running into my skull until it finally got into my brain...
what else could it be..... AVERAGE VALUE!
It's just such a simple integral problem, how can anyone get this wrong. The formula is 1/b-a bSa f(x). You simply just plug in to the formula with what you were given. And half the time it's in the calculator portion so you just have to plug the integral in your calculator then times it by 1/b-a. Voila, you get a beautiful answer that you actually think is right :) AMEN to that.
Just so i don't seem like i only accomplished one thing in calculus all year, some other things i understood were average rate of change, mean value theorem, simple derivatives and integrals, HORIZONTAL TANGENTS, and i'm sure there are a couple of others.
So onto my farewells:
my seniors- We've had an amazing run. We're all so close and we worked hard to get where we are. No matter how mean i may come off sometimes, I love each and every one of y'all and wish every one luck in their future endeavors. Now let's finish this year off right and make a name.
oh let's doooo it
the juniors- i absolutely love y'all. i never really talked to y'all much before this class but i'm so glad that we had it together. Every one of y'all cracks me up, and i know y'all will be successful b/c of how determined you are. Keep it up and don't slack off, and have fun in calculs bc next year. I might miss you guys ;)
B-robbbb- thanks for putting up with me these last two years. You believed in me and kept pushing me even when i said it was impossible to stick this what i call "garbage" in my brain. I know i didn't catch on to a lot at first, but i did try and i truly believe no other teacher could put up with us as well as you did. You're an awesome person and i truly admire you and all of your accomplishments. Thanks again for everything :)
Now i think it's time to close this blog, my LAST one.
Goodbye Calculus, Goodbye Riverside, Hello Life :)
sarah's final blog.
wow. I can't believe it's finally over. In a few days, i'll no longer by an underclassmen. I never realized how hard this was gonna be until it actually happened. I sound like i'm leaving the earth or something. ha, sorry. This is only my junior year and I'm already freaking out. I'm a big baby.
To my seniors: I love you guys more than you know. Every last one of you. Including Mher, although he always seems to not be in class. Yall had an awesome year, I can tell. I hope my senior years proves to be just as great. You guys will be missed, EXTREMELY. especially those of you who have been at RA since I first walked in the front door when I was 4. I always looked up to you guys... cuz yall were older :) and it's so weird to think that next year, we will be the role models. It still hasn't hit me yet.
To my juniors: Well, what can I say. it's been one heck of a ride.. From preschool, to middle school, to soon-to-be seniors. The five of you in the calc class are the people I am most close to out of the ENTIRE jr class. because I spend 90% of my day with you mon-fri... on weekends @ math trips, and during the summer @ practices. I love yall more than you can imagine. I can't wait for next year's calc BC class, it will be fun with just the six of us :)
So i'll stop being all mushy for a moment and talk about calc this year.
Most helpful thing: working in groups at the end of year to go over what you missed on the practice ap tests. one-on-one with another student that will actually make you do your work (thanks ellie) helped me more than you can understand. best idea yet B-ROB.
Thing i struggled with most: integration. i honestly still am not 100% with it, idk what it is. substitution, ln, tan inverse. none of it came to me easily. more practice was needed probably? idk.
Thing I picked up on the quickest: the derivative formulas. I can still say them to you probably quicker than anyone in the class. all those derivative practice sheets in the beginning were SOOOO helpful.
My epiphany of the year: the riemann sum formulas!!!!!!!!! honestly, i didn't understand all that f(a) + f(2 + a) stuff. and multiply by delta x whatever. it must easier when taught that TRAM is
b' + b'' / 2 (n) + b'' + b''' /2 (n). also the LRAM and RRAM are easier when taught that you add to x's divide by n (start all the way to left with LRAM and 2nd number with RRAM). that literally clicked in my head 2 days before the exam.
so, even though I don't want it to, this year is coming to a close. and quick too. I'm going to miss all you entirely too much. I will probably cry... a lot. just because I'm about to be a senior. i'll be sad everyday in calculus when i realize how small the class is. (& when i realize that mher IS actually not there). we had a great year, from partying it up with mr. st pierre to re-partying it up with brob. & of course getting people to sneak out of school to buy us some soft drinks because ricky never brings his stuff! i will miss it all.
GOOD LUCK TO YOU, seniors of 2010. you're gifted in more ways than you can imagine. embrace that.. you can do anything you want in your life. be proud of yourselves. i hope for the best for everyone and i'll remember you everytime i walk the halls of riverside academy.
To my seniors: I love you guys more than you know. Every last one of you. Including Mher, although he always seems to not be in class. Yall had an awesome year, I can tell. I hope my senior years proves to be just as great. You guys will be missed, EXTREMELY. especially those of you who have been at RA since I first walked in the front door when I was 4. I always looked up to you guys... cuz yall were older :) and it's so weird to think that next year, we will be the role models. It still hasn't hit me yet.
To my juniors: Well, what can I say. it's been one heck of a ride.. From preschool, to middle school, to soon-to-be seniors. The five of you in the calc class are the people I am most close to out of the ENTIRE jr class. because I spend 90% of my day with you mon-fri... on weekends @ math trips, and during the summer @ practices. I love yall more than you can imagine. I can't wait for next year's calc BC class, it will be fun with just the six of us :)
So i'll stop being all mushy for a moment and talk about calc this year.
Most helpful thing: working in groups at the end of year to go over what you missed on the practice ap tests. one-on-one with another student that will actually make you do your work (thanks ellie) helped me more than you can understand. best idea yet B-ROB.
Thing i struggled with most: integration. i honestly still am not 100% with it, idk what it is. substitution, ln, tan inverse. none of it came to me easily. more practice was needed probably? idk.
Thing I picked up on the quickest: the derivative formulas. I can still say them to you probably quicker than anyone in the class. all those derivative practice sheets in the beginning were SOOOO helpful.
My epiphany of the year: the riemann sum formulas!!!!!!!!! honestly, i didn't understand all that f(a) + f(2 + a) stuff. and multiply by delta x whatever. it must easier when taught that TRAM is
b' + b'' / 2 (n) + b'' + b''' /2 (n). also the LRAM and RRAM are easier when taught that you add to x's divide by n (start all the way to left with LRAM and 2nd number with RRAM). that literally clicked in my head 2 days before the exam.
so, even though I don't want it to, this year is coming to a close. and quick too. I'm going to miss all you entirely too much. I will probably cry... a lot. just because I'm about to be a senior. i'll be sad everyday in calculus when i realize how small the class is. (& when i realize that mher IS actually not there). we had a great year, from partying it up with mr. st pierre to re-partying it up with brob. & of course getting people to sneak out of school to buy us some soft drinks because ricky never brings his stuff! i will miss it all.
GOOD LUCK TO YOU, seniors of 2010. you're gifted in more ways than you can imagine. embrace that.. you can do anything you want in your life. be proud of yourselves. i hope for the best for everyone and i'll remember you everytime i walk the halls of riverside academy.
Stephanie's Final Blog
As this year comes to a close, I'd like to tell everyone how great our class was this year. Especially with our mad covert partying skills, our ability to goof off and still get our work done, and lastly, our great personalities. The seniors this year are great, and i'll miss every one of yall. To my juniors, LETS GET THIS PARTY STARTED. I'm ready to own the school, yall bout it?
So, something i couldn't understand then it just smoked me in the face is substitution. I think it took Ryan Breaud just yelling at me about how to substitute, then somehow making it involve either a mean girl quote, bonquiqui, or darrel, spelt like darrel, but pronounced like darrel. I can't explain how it really stuck in my head besides taht. But give me something today, and i'll substitute the numbers out of it. Watch out.
This was definately one of my favorite classes this year, besides the MASSIVE struggles i've had in this class, it definately taught me that i can achieve what I strive to do. And to the seniors leaving, i'm glad i got to take this class with yall, and yall better remember the good times we had..and if anyone gets famous remember the girl who mission impossibled it to the cafeteria to get ice for our cups.
To the juniors, well seniors now, lets make this year the greatest ever. I mean i'm already great, and yall have class with me, so that makes you offliated with greatness, which means you're semi-great..and so add that together, then you get that we're all great. because of me, of course. :)
Also, thanks to Mrs. Robinson for helping me this year and not giving up on me when i answer free response questions without thinking. I know i couldn't of done it with out you.
Lastly, i have to tell everyone thanks for making my first hour great, and you better not ever forget me. :)
So, something i couldn't understand then it just smoked me in the face is substitution. I think it took Ryan Breaud just yelling at me about how to substitute, then somehow making it involve either a mean girl quote, bonquiqui, or darrel, spelt like darrel, but pronounced like darrel. I can't explain how it really stuck in my head besides taht. But give me something today, and i'll substitute the numbers out of it. Watch out.
This was definately one of my favorite classes this year, besides the MASSIVE struggles i've had in this class, it definately taught me that i can achieve what I strive to do. And to the seniors leaving, i'm glad i got to take this class with yall, and yall better remember the good times we had..and if anyone gets famous remember the girl who mission impossibled it to the cafeteria to get ice for our cups.
To the juniors, well seniors now, lets make this year the greatest ever. I mean i'm already great, and yall have class with me, so that makes you offliated with greatness, which means you're semi-great..and so add that together, then you get that we're all great. because of me, of course. :)
Also, thanks to Mrs. Robinson for helping me this year and not giving up on me when i answer free response questions without thinking. I know i couldn't of done it with out you.
Lastly, i have to tell everyone thanks for making my first hour great, and you better not ever forget me. :)
Ellie's Final Reflection
Alright you guys!!! We've gotten through calculus and we've all made it. When this class first started, I wasn't stressed out by the least. Having a teacher like Mrs. Robinson the year before, I knew what I was getting into. The first week was oddly enough, expected! We got so many formulas to memorize and so many ways of taking a derivative a lot of us were going crazy, but not me, I was kind of like "whatever" with it. Turns out two or three weeks into it, I got really scared, my grades weren't really slipping but I wasn't getting the new, or harder, derivatives. After that, I buckled down and got to work. Here's what I've learned throughout the year...
Easy Concepts For Me:
--How to Take a Derivative:
You take the exponent and times it by the coefficient, what you get is the new coefficient and you're new exponent will be the original exponent minus one!
--The First Derivative Test:
You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.
--The Second Derivative Test:
You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.
--Maximums, minimums, critical values, increasing, decreasing:
All of these are related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.
--Point of inflection, concave up, concave down:
It's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.
--Finding Critical Values:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.
--Limits:
If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
Some Concepts that...after reviewing over and over for weeks/months...it just clicked:
--Slope of a normal line:
Take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.
--Absolute Extrema:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.
--Average Rate of Change:
f(b)-f(a)/(b-a)
--Average Value:
This is just an integral times by 1/(b-a).
--Equation of a Tangent Line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
And-of course-the things that I always struggled with, and hope to never encounter again even though I know I will....:
--linearization:
Identify the equation
Use the formula f(x)+f ' (x)dx
Determine your dx in the problem
Then determine your x in the problem
Plug in everything you get
Solve the equation
--Riemanns Sums:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals
--Volume by Disks:The formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph
--Volume by Washers:
The formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.
--OPTIMIZATION...
I just can't do it =(
Just a shout out:
To the seniors in the Calculus Class of 2010 - - I'll Miss Yall, we've grown up together basically. I won't lie, I didn't like MANY of yall when I first came here because of different things that happened; however, we've all matured [thank God] and we've become friends. Although some of us aren't best friends I can honestly say that I will miss each and every one of you all because yall are the people I spent all day every day with for the past 6 years.
To the juniors in the Calculus Class of 2010 - - I'll miss yall just as much. There's many reason's why I will..some were my first friend at Riverside Academy because of the Cheerleading Squad, some have always been in my life because we grew up living next door to each other, some have been with me through the years with dancing and just being friends, some HOWEVER have become my friend in this past year and believe me I love yall just as much!
So back to the FARWELLS:
No, I'm not sad I'm graduating. My parents say that it hasn't hit me yet...but most of yall know me already and I'm so happy to finally be just about OUT of Riverside Academy that nothing else matters. Also, I'm not sad that I'm leaving any of yall. Yall have been great friends and I'm glad we've become as close as we have or, not as close as we have in some cases, because LIFE GOES ON..We cannot dwell in the past much less live it. I won't be back at Riverside once I'm out, there's no need....I'm finally getting my life started and I CAN'T WAIT!! =) Yeah, I'll miss yall when certain things come up and I realize what [so and so] would've said and they wont be there..but most of all .. I'll miss US as a class together and how we are with each other! So to everyone - - THANKS! And have a GREAT time either being a senior, or going out into the REAL WORLD and EXPERIENCING everything!
Love Always,
Ellie Kliebert
Easy Concepts For Me:
--How to Take a Derivative:
You take the exponent and times it by the coefficient, what you get is the new coefficient and you're new exponent will be the original exponent minus one!
--The First Derivative Test:
You have to take the derivative of the function and set it equal to zero. Then solve for the critical values (x values). Set those values up into intervals between negative infinity and infinity. Plug in numbers between these intervals into the first derivative to see if there are max or mins or if the graph is increasing or decreasing.
--The Second Derivative Test:
You take the derivative of the function twice and set it equal to zero. Solve for the x values and set them up into intervals between negative infinity and infinity. Plug in numbers between those intervals into the second derivative to see where the graph is concave up, concave down, or where there is a point of inflection.
--Maximums, minimums, critical values, increasing, decreasing:
All of these are related to first derivative test. it's simple. you take the derivative, set equal to 0, solve for x. Set up some intervals using these numbers. Plug in numbers and test your intervals. pos to neg is a min. neg to pos is a max. pos = increasing, neg = decreasing. simple stuff. remember it.
--Point of inflection, concave up, concave down:
It's the second derivative test. set up intervals, if the intervals change signs, it is a point of inflection there. also, if its negative, that interval is concave down, positive is concave up.
--Finding Critical Values:
To find critical values, first take the derivative of the function and set it equal to zero, solve for x. The answers you get for x are your critical values.
--Limits:
If the degree on top is smaller than the degree on the bottom, the limit is zero.
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, you divide the coefficients to get the limit.
Some Concepts that...after reviewing over and over for weeks/months...it just clicked:
--Slope of a normal line:
Take derivative, plug in x. get a slope. however, make sure you use the negative reciprocal of the slope (normal means perpendicular to). use point-slope formula.
--Absolute Extrema:
If you are given a point, plug those numbers into the original function to get another number. Alos, solve for critical values and plug those into the original function. Once you get your second numbers, you set each pair into new sets of points. The highest point is the absolute max and the smallest point is the absolute min.
--Average Rate of Change:
f(b)-f(a)/(b-a)
--Average Value:
This is just an integral times by 1/(b-a).
--Equation of a Tangent Line:
Take the derivative and plug in the x value.
If you are not given a y value, plug into the original equation to get the y value.
then plug those numbers into point slope form: y − y1 = m(x − x1)
And-of course-the things that I always struggled with, and hope to never encounter again even though I know I will....:
--linearization:
Identify the equation
Use the formula f(x)+f ' (x)dx
Determine your dx in the problem
Then determine your x in the problem
Plug in everything you get
Solve the equation
--Riemanns Sums:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals
--Volume by Disks:The formula is pi times the integral of the [function given] squared times dx. so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one. then graph
--Volume by Washers:
The formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the in between number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. then graph.
--OPTIMIZATION...
I just can't do it =(
Just a shout out:
To the seniors in the Calculus Class of 2010 - - I'll Miss Yall, we've grown up together basically. I won't lie, I didn't like MANY of yall when I first came here because of different things that happened; however, we've all matured [thank God] and we've become friends. Although some of us aren't best friends I can honestly say that I will miss each and every one of you all because yall are the people I spent all day every day with for the past 6 years.
To the juniors in the Calculus Class of 2010 - - I'll miss yall just as much. There's many reason's why I will..some were my first friend at Riverside Academy because of the Cheerleading Squad, some have always been in my life because we grew up living next door to each other, some have been with me through the years with dancing and just being friends, some HOWEVER have become my friend in this past year and believe me I love yall just as much!
So back to the FARWELLS:
No, I'm not sad I'm graduating. My parents say that it hasn't hit me yet...but most of yall know me already and I'm so happy to finally be just about OUT of Riverside Academy that nothing else matters. Also, I'm not sad that I'm leaving any of yall. Yall have been great friends and I'm glad we've become as close as we have or, not as close as we have in some cases, because LIFE GOES ON..We cannot dwell in the past much less live it. I won't be back at Riverside once I'm out, there's no need....I'm finally getting my life started and I CAN'T WAIT!! =) Yeah, I'll miss yall when certain things come up and I realize what [so and so] would've said and they wont be there..but most of all .. I'll miss US as a class together and how we are with each other! So to everyone - - THANKS! And have a GREAT time either being a senior, or going out into the REAL WORLD and EXPERIENCING everything!
Love Always,
Ellie Kliebert
Dylan's last post
Well school is finally over. The only thing that is left is graduation. Hut there are a few things I have learned this past year that will definitely stick with me.
Derivatives
The derivative of simple equations such as x^3+9x^2+7x-3. The derivative is 3x^2+18x+7.
Integrals
S 3x^2+4x-8
=x^3+2x^2-8x
Implicit derivatives
All that you do is take the derivative like normal but of x's and y's but put dy/dx right after where you take the derivative of the y then sove for dy/dx.
Limit rules
1) if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents.
2) If the highest exponent is on the top then the limit is infinity.
3) But if the highest exponent is on the bottom then the limit is 0.
Product rule is copy the first times the derivative of the last plus copy the first times the derivative of the second.
Quotient rule is copy the bottom times derivative of the top minus copy the top times the derivative of the bottom all divided by the bottom squared.
Those are the main things that I have learned that have stuck with me all year and will probably stay with me. Calculus this year has been and interesting experience that will stick with me forever. I wish everyone good luck with everything they do.
Derivatives
The derivative of simple equations such as x^3+9x^2+7x-3. The derivative is 3x^2+18x+7.
Integrals
S 3x^2+4x-8
=x^3+2x^2-8x
Implicit derivatives
All that you do is take the derivative like normal but of x's and y's but put dy/dx right after where you take the derivative of the y then sove for dy/dx.
Limit rules
1) if the highest exponent is the same on the top and bottom then the limit is the top coefficient over the bottom coefficient of the highest exponents.
2) If the highest exponent is on the top then the limit is infinity.
3) But if the highest exponent is on the bottom then the limit is 0.
Product rule is copy the first times the derivative of the last plus copy the first times the derivative of the second.
Quotient rule is copy the bottom times derivative of the top minus copy the top times the derivative of the bottom all divided by the bottom squared.
Those are the main things that I have learned that have stuck with me all year and will probably stay with me. Calculus this year has been and interesting experience that will stick with me forever. I wish everyone good luck with everything they do.
Well here it goes.. every thing comes to an end sooner or later right?
I think over the past couple of days I’ve understood that statement more than anything and to begin I would like to say thank you to everyone who was there for me over these past couple of days because even though it doesn’t make it hurt any less, it does make it somewhat easier and for that I am forever thankful.
What can I say, calculus was calculus, we loved it and hated it at the same time. I don’t think anyone will ever be able to understand just how if feel besides all of the people who were in there with me. It was truly memorable and brought everyone closer together. One person needed help and others didn’t hesitate to lend a hand which is awesome to me. We truly excelled this year because of EACHOTHER, it was a team effort =)
To our coach, haha teacher, Brandi, words cannot express how truly thankful I am for you both as a teacher and as a person. Without you, we surely would not have been as successful as we were this year in calculus. You prepared us as much as humanly possible and even after Sara-Rachelle was born you got back to us as quickly as you could so that we would stay on track, that’s dedication. You stuck with me, you didn’t give up, and you always believed in me which means the world to me, thank you so much for an amazing couple of years and you will always be remembered.
OKAYY lets get to some calculusss!
So some things that will stay with me forever and I actually get excited when I see them:
Mmkay, well I realized I love derivatives. Of course the slope formula because it’s on AP free response and I loveeeeeeeee it. Limit rules and the basic integrals.
For derivatives
x^4 + 3x^3 + 6x
multiply the coefficient in front of your variable by it's exponent, then subtract 1 from your exponent.
4x^3 + 9x^2 + 6
Hmmm, some things that I never really caught on to, only because I didn’t focus on them, were substitution and of course how to integrate a fraction, ahhhah I never looked at the comment on my blogs =)
MY Epiphany: I FINALLY HAVE A RELATIONSHIP WITH MY CALCULATER AND IT DOES AMAZING THINGS FOR ME, I LOVE IT.
To my seniors: it’s been a great run guys, I love ALL of y’all. We’re such a close group, I consider each of you family and I don’t know where I’d be today without y’all. It’s all coming to an end, what we’ve waited for our whole high school careers, so let’s hit up my pool these next couple weeks, walk across that stage and never look back. I have complete confidence that everyone will be successful in what ever they chose to do. I LOVE Y’ALL!
To the juniors: yall have also made my senior year one of the best. Yall are an amazing bunch of kids with an extraordinary about of talent, don’t let any one tell y’all differently. I hope that y’all will also have an amazing year next year and remember not to take this time for granted, or anything for that matter. Good luck, I love every one of you.
so this is it, goodbye blogggggerrr!
I think over the past couple of days I’ve understood that statement more than anything and to begin I would like to say thank you to everyone who was there for me over these past couple of days because even though it doesn’t make it hurt any less, it does make it somewhat easier and for that I am forever thankful.
What can I say, calculus was calculus, we loved it and hated it at the same time. I don’t think anyone will ever be able to understand just how if feel besides all of the people who were in there with me. It was truly memorable and brought everyone closer together. One person needed help and others didn’t hesitate to lend a hand which is awesome to me. We truly excelled this year because of EACHOTHER, it was a team effort =)
To our coach, haha teacher, Brandi, words cannot express how truly thankful I am for you both as a teacher and as a person. Without you, we surely would not have been as successful as we were this year in calculus. You prepared us as much as humanly possible and even after Sara-Rachelle was born you got back to us as quickly as you could so that we would stay on track, that’s dedication. You stuck with me, you didn’t give up, and you always believed in me which means the world to me, thank you so much for an amazing couple of years and you will always be remembered.
OKAYY lets get to some calculusss!
So some things that will stay with me forever and I actually get excited when I see them:
Mmkay, well I realized I love derivatives. Of course the slope formula because it’s on AP free response and I loveeeeeeeee it. Limit rules and the basic integrals.
For derivatives
x^4 + 3x^3 + 6x
multiply the coefficient in front of your variable by it's exponent, then subtract 1 from your exponent.
4x^3 + 9x^2 + 6
Hmmm, some things that I never really caught on to, only because I didn’t focus on them, were substitution and of course how to integrate a fraction, ahhhah I never looked at the comment on my blogs =)
MY Epiphany: I FINALLY HAVE A RELATIONSHIP WITH MY CALCULATER AND IT DOES AMAZING THINGS FOR ME, I LOVE IT.
To my seniors: it’s been a great run guys, I love ALL of y’all. We’re such a close group, I consider each of you family and I don’t know where I’d be today without y’all. It’s all coming to an end, what we’ve waited for our whole high school careers, so let’s hit up my pool these next couple weeks, walk across that stage and never look back. I have complete confidence that everyone will be successful in what ever they chose to do. I LOVE Y’ALL!
To the juniors: yall have also made my senior year one of the best. Yall are an amazing bunch of kids with an extraordinary about of talent, don’t let any one tell y’all differently. I hope that y’all will also have an amazing year next year and remember not to take this time for granted, or anything for that matter. Good luck, I love every one of you.
so this is it, goodbye blogggggerrr!
Trina's Final Reflection
This year in calculus has definitely been a whirlwind for me. I came into the class worried that everything was not going to click for me right away and guess what.... i was right.. I struggled with grasping different concepts throughout the first half of calculus but with the help of some friends.. i caught the hang of a few things. Limit rules were the easiest to catch onto because all you had to do was follow the rules. When we learned how to do derivatives i understood the basic derivatives but when it came to e derivatives and ln derivatives, those took a little bit longer... but with a lot of practice and a lot of studying i came to understand those too.
When we were introduced to integrals i did not understand the concept at all... it took weeks of practice and help from my friends for me to finally grasp a piece of the concept. But like derivatives, once i had worked integrals over and over again, the concept became very easy.
Tangent lines were a pain at first as well. One day Mrs. Robinson explained how to do them once more and everything just clicked in my mind. I don't know why but it just did lol. Whenever i would see problems like that on the AP's i would be so happy because i knew i had at least one right :).
Finding volume and area on the free response portions were very easy for me. Mrs. Robinson explained how to do those during lunch after we had taken the tests and i caught on right away. If felt proud knowing that i could at least attempt these problems knowing what i was doing.
One thing i struggled with to the very end was Riemann sums, i don't know if if was because i couldn't remember the formulas or if i just didn't know what to do with them.. but eventually i got a little bit better at them :).
This class definitely helped me in preparation for any math courses i will have to be taking in college and i am glad i got the chance to take the class with my wonderful classmates. A big thanks to everyone who helped me study and for those who supported me throughout the year. A a huge thank you to Mrs. Robinson for helping me understand different concepts and calming my nerves throughout the year. I will miss you all very much and good luck to the juniors who will be taking Calculus BC next year.
Goodbye everyone :)
When we were introduced to integrals i did not understand the concept at all... it took weeks of practice and help from my friends for me to finally grasp a piece of the concept. But like derivatives, once i had worked integrals over and over again, the concept became very easy.
Tangent lines were a pain at first as well. One day Mrs. Robinson explained how to do them once more and everything just clicked in my mind. I don't know why but it just did lol. Whenever i would see problems like that on the AP's i would be so happy because i knew i had at least one right :).
Finding volume and area on the free response portions were very easy for me. Mrs. Robinson explained how to do those during lunch after we had taken the tests and i caught on right away. If felt proud knowing that i could at least attempt these problems knowing what i was doing.
One thing i struggled with to the very end was Riemann sums, i don't know if if was because i couldn't remember the formulas or if i just didn't know what to do with them.. but eventually i got a little bit better at them :).
This class definitely helped me in preparation for any math courses i will have to be taking in college and i am glad i got the chance to take the class with my wonderful classmates. A big thanks to everyone who helped me study and for those who supported me throughout the year. A a huge thank you to Mrs. Robinson for helping me understand different concepts and calming my nerves throughout the year. I will miss you all very much and good luck to the juniors who will be taking Calculus BC next year.
Goodbye everyone :)
Ryan's Final Reflection
So I don't really know how to start this, but I guess I'll try.
Well, I guess I'll have to say that Calculus was one of my favorite classes this year, not just because I liked the subject, but also because I loved my classmates.
To all the seniors (Aimee, Jessie, Ricky, Ryan, Ryne, Chelsea, Mamie, Trina, Kaitlyn, Mher, Steven, Ellie, John, and Dylan): I'm really going to miss you guys.
To all of my fellow juniors (Sarah, Stephanie, Abbey, Malerie, and Ashley): Let's make our senior year the best Riverside Academy has ever seen. And just think that we're the first Calculus BC class EVER.
(**hopefully I didn't forget anybody)
To our teacher, Mrs. Robinson aka B-Rob, thanks for teaching us one of the "hardest subjects" in high school this year.
Something I really believe I've grasped this year is taking derivatives, from just the basic x^2 to chain rules like cos(5x^3)sin(e^8x).
Something I had a struggle with this year was Riemann sums. It took me basically to the last couple of days before the AP to really understand them.
To finish it off
Class of 2010: have a great life in college, and don't forget about us :).
Class of 2011: Let's Get It!
Love you guys,
Ryan B.
Well, I guess I'll have to say that Calculus was one of my favorite classes this year, not just because I liked the subject, but also because I loved my classmates.
To all the seniors (Aimee, Jessie, Ricky, Ryan, Ryne, Chelsea, Mamie, Trina, Kaitlyn, Mher, Steven, Ellie, John, and Dylan): I'm really going to miss you guys.
To all of my fellow juniors (Sarah, Stephanie, Abbey, Malerie, and Ashley): Let's make our senior year the best Riverside Academy has ever seen. And just think that we're the first Calculus BC class EVER.
(**hopefully I didn't forget anybody)
To our teacher, Mrs. Robinson aka B-Rob, thanks for teaching us one of the "hardest subjects" in high school this year.
Something I really believe I've grasped this year is taking derivatives, from just the basic x^2 to chain rules like cos(5x^3)sin(e^8x).
Something I had a struggle with this year was Riemann sums. It took me basically to the last couple of days before the AP to really understand them.
To finish it off
Class of 2010: have a great life in college, and don't forget about us :).
Class of 2011: Let's Get It!
Love you guys,
Ryan B.
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