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Rank: Frosh
Joined: 12/4/2011
Posts: 1
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My class just started vectors.
I did okay at calculus, but I can't really seem to understand vectors :@/ interpreting the questions correctly is really difficult for me.
Makes me realize why I failed the vectors unit last year in physics LOL
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Rank: Senior Student  Joined: 1/27/2011 Posts: 131
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Did any of you guys cover matrices in vectors? If you did, how did you find them difficulty wise? Bachelor of Health Sciences '16
McMaster University
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Rank: Senior Student
Joined: 1/25/2011
Posts: 75
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Why did high school take out Integrals?
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Rank: Senior Student
Joined: 5/9/2012
Posts: 98
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I have no idea why high school took out intergrals, but I have such a good teacher and yet I found Vectors ridiculously hard. I found Calculus really easy and got 94% for that (which is mid-term). Now I am getting 93% after the test and now my mark is creeping down...what makes my average go down is the "thinking" questions on the test. Oh my god - they are just hard that will make you gauge your eyes out!!!!!
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Rank: Senior Student
Joined: 4/23/2012
Posts: 161
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mhz wrote:Why did high school take out Integrals? because they took out year 13 and put vectors into a freakin calculus course
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Rank: Senior Student
Joined: 4/23/2012
Posts: 161
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KingKhan wrote:Sigh, this course is killing my average. I'm currently sitting at a 71%, hopefully the replacement test will bring it up to atleast an 85.
By the way, is my school the only one that does replacement tests for math courses? Do any of you guys have it aswell? and people say grade inflation doesn't exist..... LOOOOOOOOOOL. the only "replacement" tests we have is students having the ability to drop the course and take it in private school for a free 96+. we started off with 29 students and after the first unit test there were 14 people left. our math department got a lot of complaints but they didn't do anything. class median was 62%, after half the class dropped it rose to 74%, lol.
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Rank: Student Council
Joined: 5/5/2012
Posts: 412
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I have a genuine concern about the Vectors portion (regardless of whether or not you are taking an AP Calculus AB/BC course, if it exists in your school). How much 3D graphing do you have to do in it? It appears to me that I cannot do anyting with 3D graphs (damn, I am going to major in Math). If there are too many graphs, I will not know what I can do. Grade in 2011-2012: 11 Math Courses in 2012-2013: Advanced Functions, Calculus and Vectors, Mathematics of Data Management    Class of 2017Applied to 01 University of Waterloo - Mathematics (Co-op) - Major Area of Interest: Combinatorics and Optimization [Alternate Offer of Admission - Honours Mathematics, Regular, Combinatorics and Optimization] [2013-05-07] [OFFER ACCEPTED]02 University of Toronto - St. George - Faculty of Arts and Science - Studies in Computer Science [Conditional Offer of Admission - 2013-02-13] [OFFER DECLINED]03 McMaster University - Mathematics and Statistics I - Major Area of Interest: Mathematics/Computer Science [Conditional Offer of Admission - 2013-04-24] [OFFER CANNOT BE DECLINED]Current top 6 average: 85 (I attend a non-semestered school) Razear is found dead at around 9 PM on May 19, 2013, his body is buried in
StudentAwards' server. He has now resurrected and in good condition, please
execute him!
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Rank: Senior Student
Joined: 4/23/2012
Posts: 161
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randint wrote:I have a genuine concern about the Vectors portion (regardless of whether or not you are taking an AP Calculus AB/BC course, if it exists in your school). How much 3D graphing do you have to do in it? It appears to me that I cannot do anyting with 3D graphs (damn, I am going to major in Math). If there are too many graphs, I will not know what I can do.
Grade in 2011-2012: 11
Math Courses in 2012-2013: Advanced Functions, Calculus and Vectors, Mathematics of Data Management there's a lot of x/y/z axis graphing if that's what you mean by 3d graphing p.s. is your name "randint" named after a command in java and/or turing? p.p.s. ap calculus bc is a joke, only semi-hard part to understand is all the tests for divergence/convergence but once you understand it it's easy. ap exam was a joke and i cannot believe they're handing out a credit for such an easy exam
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Rank: Student Council
Joined: 5/5/2012
Posts: 412
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My username (randint) is a function in turing Syntax randint (int a, int b) Parameters - 2 integers specifying the range of the random number Returns - an integer that is within the range, where a < <returned value> < b if a > b. Oh (****), I'm screwed for the Vectors portions. Oh crap, I hope that it is not the end of the world! (MATH X4X courses in UW CO, CS) Class of 2017Applied to 01 University of Waterloo - Mathematics (Co-op) - Major Area of Interest: Combinatorics and Optimization [Alternate Offer of Admission - Honours Mathematics, Regular, Combinatorics and Optimization] [2013-05-07] [OFFER ACCEPTED]02 University of Toronto - St. George - Faculty of Arts and Science - Studies in Computer Science [Conditional Offer of Admission - 2013-02-13] [OFFER DECLINED]03 McMaster University - Mathematics and Statistics I - Major Area of Interest: Mathematics/Computer Science [Conditional Offer of Admission - 2013-04-24] [OFFER CANNOT BE DECLINED]Current top 6 average: 85 (I attend a non-semestered school) Razear is found dead at around 9 PM on May 19, 2013, his body is buried in
StudentAwards' server. He has now resurrected and in good condition, please
execute him!
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Rank: Frosh
Joined: 12/11/2010
Posts: 8
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randint wrote:My username (randint) is a function in turing
Syntax
randint (int a, int b)
Parameters - 2 integers specifying the range of the random number
Returns - an integer that is within the range, where a < <returned value> < b if a > b.
Oh (****), I'm screwed for the Vectors portions. Oh crap, I hope that it is not the end of the world! (MATH X4X courses in UW CO, CS) Relax, vectors is not that complicated. Three-space vectors just require lots of drawings and imagination. Take out your three pencils and play around with the dimension. Or draw planes, that's always fun. Graphing 3d is similar to graphing 2d, you have x then y, then z components. Making equations for 3D, finding solution sets, etc. just require you to know some basics of the graphs. It's a lot like 2d graphing imo! Waterloo Environmental Planning '16
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Rank: Senior Student
Joined: 4/23/2012
Posts: 161
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randint wrote:My username (randint) is a function in turing
Syntax
randint (int a, int b)
Parameters - 2 integers specifying the range of the random number
Returns - an integer that is within the range, where a < <returned value> < b if a > b.
Oh (****), I'm screwed for the Vectors portions. Oh crap, I hope that it is not the end of the world! (MATH X4X courses in UW CO, CS) that's funny, because i named one of my characters in an online game the same as yours exactly after that same command in turing, LOL. except my ign was randintxy and not just randint XD turing was definitely fun in grade 10 computer science, i hated java so i never took computer science again >_> and vectors is easy, lol. harder than calculus, but manageable. i'm cramming for a vectors test i have in 10 hours as i speak.
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Rank: Student Council
Joined: 5/5/2012
Posts: 412
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Haha, I have an AP meeting next week, that is, I get some form of summer homework from my future AP teacher for practise purposes (I wished that he knew that I can do derivatives! [I'm in Grade 11]) Calculus is super easy (at least for derivatives)... P.S. anyone know how to integrate a product or quotient or composite function? Example: Calculate the indefinite integral of (x + 3) / (x + 1) with respect to x OR Calculate the indefinite integral of sin (x^2 + 10x + 24) with respect to x OR Calculate the indefinite integral of (x + 4) * (x + 7) without expanding the product into x^2 + 11x + 28 so to generate the integral as x^3 / 3 + 11 / 2 x^2 + 28 x + C Class of 2017Applied to 01 University of Waterloo - Mathematics (Co-op) - Major Area of Interest: Combinatorics and Optimization [Alternate Offer of Admission - Honours Mathematics, Regular, Combinatorics and Optimization] [2013-05-07] [OFFER ACCEPTED]02 University of Toronto - St. George - Faculty of Arts and Science - Studies in Computer Science [Conditional Offer of Admission - 2013-02-13] [OFFER DECLINED]03 McMaster University - Mathematics and Statistics I - Major Area of Interest: Mathematics/Computer Science [Conditional Offer of Admission - 2013-04-24] [OFFER CANNOT BE DECLINED]Current top 6 average: 85 (I attend a non-semestered school) Razear is found dead at around 9 PM on May 19, 2013, his body is buried in
StudentAwards' server. He has now resurrected and in good condition, please
execute him!
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Rank: Student Council  Joined: 3/22/2012 Posts: 465
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My Calculus teacher is planning to teach us integrals/integration stuff in a couple of the last days of class to prepare us for university since we have extra days if we stay on schedule (I think we're ahead, anyways). ilikebones wrote:turing was definitely fun in grade 10 computer science, i hated java so i never took computer science again >_> Turing was okay, I suppose. We never did Java; we did Visual Basic (ICS4U). Turing, Flash, and some other stuff were in grade 11 (ICS3U) for us as the grade 10 class was cancelled the year I was in grade 10 (so I took ICS3U in grade 10, and ICS4U in 12). University of Guelph
Software Engineering, 2016
Applications (for Fall 2012):
University of Waterloo - Computer Science (Alternate offer to Geomatics, May)
University of Guelph - Software Engineering (Accepted, March)
Carleton University - Computer Science: Game Development (Accepted, February)
Carleton University - Interactive Multimedia and Design (Accepted, March)
The University of Western Ontario - B.Sc. Computer Science (Cancelled application)
First semester (mixed w/ grade 11 marks) average: low-mid 80s
Second semester midterm average: 81.33%
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Rank: Senior Student
Joined: 4/23/2012
Posts: 161
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randint wrote:Haha, I have an AP meeting next week, that is, I get some form of summer homework from my future AP teacher for practise purposes (I wished that he knew that I can do derivatives! [I'm in Grade 11]) Calculus is super easy (at least for derivatives)...
P.S. anyone know how to integrate a product or quotient or composite function?
Example:
Calculate the indefinite integral of (x + 3) / (x + 1) with respect to x
OR
Calculate the indefinite integral of sin (x^2 + 10x + 24) with respect to x
OR
Calculate the indefinite integral of (x + 4) * (x + 7) without expanding the product into x^2 + 11x + 28 so to generate the integral as x^3 / 3 + 11 / 2 x^2 + 28 x + C first one, use partial fraction decomposition then u-substitution i don't know if the second one is even possible with my current knowledge.. third one you HAVE to expand it and integrate each part separately, there's no other way. unfortunately there's no "chain-rule" equivalent or product/quotient rule for integration.. if only integrating was that easy, lol. that's what's hard about calculus 2, you actually have to think how to integrate because there's limited rules and you have to be clever algebraically in most of the simplifying (even trig functions ahh) unfortunately i bombed my vectors quiz today after an all-nigther cram. NEVER CRAM GUYS! trying to learn 2 chapters in 1 night is not possible :/ @above: turing was so fun and easy! XD
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Rank: Student Body President  Joined: 12/20/2010 Posts: 1,129
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You can integrate the 3rd one by parts. UW/WLU Math/Business DD - 2016
President - Double Degree Club
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Rank: Student Council
Joined: 5/5/2012
Posts: 412
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So, Calculus 2 deals with integrals? Oh, what is the precise method that you could use to integrate a f[g(x)] dx type function? Does anyone know how to do that? Or do I have to take it apart? What is sin (a + b + c) expanded? Could anyone tell me? I do not know how to integrate sin (x^2 + 10x + 24) with respect to x: I know how to do them with linear function: sin (x + 10) dx = sin x cos 10 + cos x sin 10 dx = cos 10 * (-cos(x)) + sin 10 * (sin x) + C Class of 2017Applied to 01 University of Waterloo - Mathematics (Co-op) - Major Area of Interest: Combinatorics and Optimization [Alternate Offer of Admission - Honours Mathematics, Regular, Combinatorics and Optimization] [2013-05-07] [OFFER ACCEPTED]02 University of Toronto - St. George - Faculty of Arts and Science - Studies in Computer Science [Conditional Offer of Admission - 2013-02-13] [OFFER DECLINED]03 McMaster University - Mathematics and Statistics I - Major Area of Interest: Mathematics/Computer Science [Conditional Offer of Admission - 2013-04-24] [OFFER CANNOT BE DECLINED]Current top 6 average: 85 (I attend a non-semestered school) Razear is found dead at around 9 PM on May 19, 2013, his body is buried in
StudentAwards' server. He has now resurrected and in good condition, please
execute him!
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Rank: Student Council
Joined: 6/29/2011
Posts: 370
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randint wrote:So, Calculus 2 deals with integrals? Oh, what is the precise method that you could use to integrate a f[g(x)] dx type function? Does anyone know how to do that? Or do I have to take it apart?
What is sin (a + b + c) expanded? Could anyone tell me?
I do not know how to integrate sin (x^2 + 10x + 24) with respect to x:
I know how to do them with linear function:
sin (x + 10) dx
= sin x cos 10 + cos x sin 10 dx
= cos 10 * (-cos(x)) + sin 10 * (sin x) + C You can expand sin (a+b+c) by grouping. sin(a+b+c) = sin[(a+b)+c], for example. = sin(a+b)cos(c)+cos(a+b)sin(c) = cos(c)[sin(a)cos(b)+cos(a)sin(b)]+sin(c)[cos(a)cos(b)-sin(a)sin(b)] = sin(a)cos(b)cos(c)+cos(a)sin(b)sin(c)+cos(a)cos(b)sin(c)-sin(a)sin(b)sin(c) I do not know how to integrate sin(x^2+10x+24) either, the integral of f(g(x)) is not necessarily elementary, and sometimes you cannot express it. If you ever have f(g(x)), the only way that I know of is to attempt to simplify first then integrate, and it usually has little do with either f(x) or g(x). In fact, the integral of that function came back with imaginary numbers. Check this page if you want to see: http://www.numberempire..../integralcalculator.php
You can integrate easily only if you have the derivative of g(x) (inner function) multiplied to some f(g(x)). ∫(x^4+5x^2-3x+2)^3*(4x^3+10x-3)dx = (1/4)(x^4+5x^2-3x)^4 + C (since d/dx (x^4+5x^2-3x+2) = 4x^3+10x-3) ∫sin^4(x)cos(x)dx = sin^5(x)/5 + C (since d/dx sin(x) = cos x) ∫2cos(ln(x^2))/x dx = sin(ln(x^2)) + C (since d/dx ln(x^2) = 2/x) The world is not over and I'm still kicking butt!
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