![]() |
The Mathematics Club ~ *ΜΑΘ* ~
Do you like math? Are you good at math? Do you need help with your math homework? Do you want to see what good of a lifestyle it is to be a Mathematheist Mathematician? The join this club and exercise the joy of Mathematics!
What are to be the topics of this club:
Anybody can come on in and ask for help with Math homework. For this, you don't have to have to like mathematics. However, if you like math and want to be recognized for active conversations, you should probably join as a full-pledge member. This is simple and can be done by filling this out: [B]Username: Overall Education Level: Mathematics Education Level (Or most recent/advanced math subject): Do you think you can be asked for help in your level or lower?: Just for fun~ You can also just say you want to be a Full-pledge member. Full-pledge Members:
Remember to follow the forum and global rules. Now lets ____∞____ \ \ \ \ talk(math(talk)) / / / / ___math(talk) = 0___ |
I want to join!
Username-Otherworld9)
Overall Education Level-4.0, so I think I'm straight A's....oh, I am. Mathematics Education Level-I'm an 8th grader, and currently taking Algebra Honors. Do you think you can be asked for help-Yes, I've been asked for help daily, so yes. What is the Derivative of 3X2?....I feel stupid, but I'm only in Middle School. :paranoid: 6x I want to be a full pledged member for as long as I live. |
omg math
Username: Lightning
Overall Education Level: In midst of an undergrad degree Mathematics Education Level: some second-year university courses :3 Do you think you can be asked for help in your level or lower?: Yup, though I may need a refresher on what things are. XD What is the derivative of 3X^2?: 6x Favourite math pick up line: I wish I were a derivative so I could lie tangent to your curves. You cannot have a math club without math pick up lines!!! 8D |
Username: BlooMilk C.
Overall Education Level: 8th or 9th grade. Mathematics Education Level: Pre-Algebra, but I know most topics in Algebra. Do you think you can be asked for help in your level or lower?: Yes. What is the derivative of 3X2?: 6x(we just did linear functions, so the rest is Wikipedia) Math catchprase 8D: Depressing lives are like pi, they need to be terminated. Also, I want to join as a full-pledge memeber. |
Username: Sammyskitty
Overall Education Level: 10th grade Mathematics Education Level: Currently taking Algebra II Do you think you can be asked for help in your level or lower?: Yes, I am like super amazing in Geometry whenever I remember how to do the stuff What is the derivative of 3X^2?: 6x I want to be a full-pledged member bro |
Hmm... plenty of members already ^__^ I was soo expecting you, Erica
And I really have tried your pickup line there before... needless to say those things are fails until you check out math majors >__> |
Requesting joinage 8D
Username: smile!, but you can call me Arc if you want (long story) Overall Education Level: Uhh, tbh, I'm not quite sure what level of the education in my country would be equivalent to yours. I'm guessing, around 12th grade? Mathematics Education Level: Currently taking Calculus I. Do you think you can be asked for help in your level or lower?: Mhmm.. Probably. What is the derivative of 3X2?: I had to search the meaning of derivative >.> I feel so lame! XD Uh, but yeah, I'm more used to y'. Anyway, 6x. Quote:
Uhh, math catchphrase? Can't think of any right now. I vaguely remember something about pi, but I can't recall the exact wordings. Though, what my maths teacher once said, (sounds something like this) If the temperature of a town is 0o Celsius today, and the temperature of tomorrow will be twice colder than today, then what is tomorrow's temperature? |
Ill try my best !!
Username: Murasaki_Paz28,, but you can jus call me Murasaki for short :)
Overall Education level: 11th grade Mathematics Education Level: Already took... pre-algebra, algebra 1 honors, geometry, and algebra 2. Going towardz Pre-cal then Cal 1 Do you think you can be asked for help in your level or lower: Bad memory but i can try :P Srry i dont get what everybodiez answering 3X2=6X,, i dont member what derivative meanz if i even learned it,, bad memory like i said :( I guezz full pledged member plz since everyone iz already... |
*pats* My high school curriculum didn't introduce derivatives until the second half of the grade 12 calculus/functions course so it's not weird if you haven't seen it before. :3
|
Username: Snow Phoenix
Overall Education Level: 11th Grade, GPA = 3.94. I regret the mistakes I made when I took High School classes in middle school @[email protected] Mathematics Education Level: I take Calculus at a community college via dual enrollment. I started off taking Pre-Algebra in 6th, Algebra 1 in 7th, Geometry in 8th. Algebra 2 in 9th, and then College Algebra, Plane Trig., and Pre-Calculus via Dual Credit. Dual credit classes are a semester each. Do you think you can be asked for help in your level or lower?: Yes :3 I tutor Netto every now and then <3 What did Pi say to i and what did i say back to Pi?: Err... I'd say something, but I'm probably overthinking things @[email protected] |
Quote:
The only difference is... he's Asian and I'm Mexican :X So yes, by Junior year I'll be taking Calculus III and modern Algebras... if the guys at the uni I'm in for concurrent let me, anyways >__> I'll be pissed if they don't let me. |
Sign me up! Even though I detest mathematics. ^_^
Username: Regeneration Overall Education Level: 10th grade? Mathematics Education Level: Everything except calculus Algerba, Trigonometry, Geometry. Do you think you can be asked for help in your level or lower?: Of course! What did Pi say to i and what did i say back to Pi?: You're incomplete without me. >D |
I'll get around to joining properly at some point, but I just finished enrolling in my undergrad uni course today. Including Mathematics IA and IB.
|
Quote:
|
ALGEBRA IS AWESOME!!!
Sorry to change things...but it isn't strange to find an 8th grader in an Algebra Honors class, right? It's completely normal, right? (note that Algebra and Algebra Honors aren't the same...Algebra Honors is ahead.)
|
Quote:
If you were Asian, it'd be strange you'd be so behind |
Quote:
(I am sorry if I am not allowed to post here) |
Username: I like Pokemon (...)
Overall Education Level: I'm in Year 10 in England. I'm 14, going on 15. Mathematics Education Level: Not much at all. Recently, we learned Sine and Cosine rule. I'm still rather young, so I haven't gotten much education. I'm self teaching (pre) calculus, though. Do you think you can be asked for help in your level or lower?: Definitely, yes. I'm used to helping students in my class, and lower. Hell, if I know the topic, I might be able to help those higher XD. What did Pi say to i and what did i say back to Pi?: "Get real", "Be rational". Oh, I would LOVE to be a full-pledged member. Oh, and Arc, I feel slightly betrayed T.T |
Quote:
Also, here's a history of math anecdote that you won't care about. Did you know that the earliest evidence of written mathematics dates back to the Sumerians, who adopted a basic number system, made multiplication tables, dealt with geometric exercises, and did division problems? "The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation to √2 accurate to five decimal places."(Wikipedia) |
Username:
Midnight Bear Overall Education Level: Eleventh grade, 4.0. Mathematics Education Level: Algebra 2, Geometry, Pre-Calculus Do you think you can be asked for help in your level or lower?: I could, because I'm really good at math, but I wouldn't advise asking me. I make a terrible teacher. I wish I were a _______ so I could lay tangent to your curves: Derivative. I'm sad to say that I had no idea (still in Pre-Cal), and just googled it. |
Quote:
Why do you feel betrayed? XP Sine and cosine rule, as in sin a/a = sin b/b or as in lim (x->0) sin h/h = 1? Self teaching... whoa I still remember your aim to study everything you'd learn in college now and when you do get to college, you're going to annoy your lecturer with your weird questions. XD Be rational, nice. XD |
Username: meerfall
Overall Education Level: year 10 Mathematics Education Level: (surrpose to be) higher Do you think you can be asked for help in your level or lower?: sure wynaut? I wish i was a improper fraction so i can contain a great deal of you! if you are an acute angle you are more then you seem if you are an right angle you know where to turn if you are an straight line you are as bright as the sun if you are an obtuse angle you are big and full of ideas if you are a reflex angle you can reach your true poltensal by beliving in yourself if you are a 360 degree angle you are all of the above and more! |
I found a quote about maths and... love. XD
Quote:
|
Quote:
Quote:
Quote:
At the moment, my aim is to do precalc, calc, maybe trig as well. If possible, I'd LOVE to go over non-euclidean geometry, or topology in general. Quote:
Also, can someone explain to me how maths is taught in USA? Because it's very different from the English system, it seems. |
Quote:
|
How's it taught in the English system?
In Canada, math doesn't branch out into separate topics until grade 12 (last grade). We learn a combination of algebra, geometry, trig, etc. until grade 11 and then it branches to... I forget what it is here in Ontario now. When I was in HS it was Calculus, Discrete Algebra, and Data Management. I think they merged the Discrete course and the Calculus course now (wtf). |
Quote:
Quote:
I wouldn't be able to properly explain how it works, though, since it seems to change JUST for my year group. Quote:
|
math O.O
I LOVE MATH :D May I join? Username: Pikagirl3 Overall Education Level: 12th Grade in High School Mathematics Education Level: regular math, Algebra I and II, Geometry (although not that good at geomertry ^^;), Advanced Functions and Modeling, and Discrete Math. Do you think you can be asked for help in your level or lower?: Yuppers ^^ I wish I were a _______ so I could lay tangent to your curves: Derivative ^^ Another Math Joke: (cause EVERYONE LOVES JOKES!) -What do you get if you divide the circumference of a jack-o-lantern by its diameter? PUMPKIN PI XD |
Quote:
In my case, I'll be brooming Multivar Calculus, Vector Calculus, Differential Equations, Analysis, Non-Euclid Geo, and Topology before graduating from High school ^__^ Hopefully. Of course, this means I had to concurrently enroll with an university because there doesn't seem to be any high school that offers anything above Calculus II or a second course relating to Statistics. Quote:
Quote:
And wow, so many people are joining already ^__^ So glad there's a significant population with an interest in math. |
Even with AK47's explaination I still don't get how Mathematics is taught in the US. Etymologically, Precalculus means everything before Calculus, which would include 1st-grade education, like addition of single-digit numbers. Yet apparently people have somehow limited it to something between Algebra and Calculus, but adding the split of Algebra to Algebra I and Algebra II just confuses me even more.
On topic now, I love Mathematics. That's why I am definitely going to join this group. Username: ShinyMeowth Overall Education Level: 9th grade Mathematics Education Level: No idea what course this would apply to, since I've been studying at home, but I have studied Calculus up to triple integration, in Cartesian, Cylindrical and Spherical coordinates, and am currently studying Probability. Do you think you can be asked for help in your level or lower?: Sure, always glad to help. I wish I were a _______ so I could lay tangent to your curves: Derivative. Anyway, Now that I have finished watching every Pokemon episode aired so far, 6 hours per day have been freed in my life. I plan to use these hours to study more, and I am planning to study, and finish number theory and group theory before I get to the 10th grade. Anyway, I would like to bring up a topic of conversation, what do you think of teachers teaching us incorrect rules that are to be removed or disproved later on? I personally have told my teacher off many times, but still she insists that negative numbers have no square root. My opinion is the same opinion I have about reproduction. Teachers should tell their students the truth, while leaving out unnecessary details. Teaching them something that is incorrect and even insisting on it when somebody refuses to take it? That is terrible teaching in my opinion. |
TEACHERS
Quote:
|
I disagree with insisting on it--if someone disagrees with it, teachers should go with the flow and sort of explain ahead a little bit if anyone's interested before going back to the curriculum.
In the case of negative fractions, I can see why they'd teach it that way. Quite often in the maths and sciences, they'll gloss over a lot of details and teach the general blanket rules before they start teaching the exceptions. I learnt that you couldn't take the root of a negative number and then a few years later (or later in the semester or the next year... I forget when I learnt square roots xD), we learnt about i and imaginary numbers. But for the most part, my experience is that a lot of people are only in math because their school requires it and for a LOT of people, tossing ~imaginary numbers~ into the mix just sounds silly and they can't grasp the material as easily so early on, or they just lose interest because "now it's getting ridiculous". :/ Sounds like you just have a bad teacher who thinks they have to follow the curriculum rigidly and with no wiggle room. (Relatedly, I know I learnt about imaginary numbers in 11th grade math but apparently it's not even in the high school curriculum in my province anymore and I think that is unacceptable, nevermind just coming back to it later. <_<) |
Quote:
The English system has a lot less room for choice, but we tend to cover a good variety of non-specific branches of mathematics. And then it depends on what course you take in university. Quote:
Quote:
Quote:
I always HATE it when my teacher says that something can't be done "you can't subtract a bigger number from a smaller number/you can't square root a negative number/etc." and then next year they contradict themselves. If I were a teacher, I would specifically mention this but I wouldn't go into much detail, instead telling the student "if you want to know more, you can research it or ask me after lesson, but you won't need to know for this module". This way, students who WANT to know this learn it, and those who don't need to know it now, won't. Quote:
I have a question. I don't know how to do integrals yet, but I've seen that it can be used to find the volume of a sphere. Can this be done to find the area of a regular shape (something simple, like a triangle or a square) and more specifically, can it be used to find the area of a trapezium? |
Quote:
And Pre-calculus should be thought of as a superset to Algebra II. First semester it's just accelerated Algebra II with preparation for skills in calculus. Second semester gets more abstract and gives advanced trigonometry and other subjects like polar coordinates in preparation for common topics in Calculus. Obviously, trig is abused in calculus like a doll under a dog o_o And other skills are also learned to apply calculus in other ways later on. Quote:
Quote:
Quote:
Then again, I also still remember my 3rd grade teacher saying a number can't be subtracted something larger than itself >__> They're called negative numbers, people. I swear, I was bored in elementary school all the time. Such interesting stuff I'm noticing, that more and more people seem to be advanced in their math studies, yet there's also many that are just normal or behind. I do wonder if legislatures for education should consider 'raising the bar'. Maybe the standard should be that advanced math studies should begin in 7th grade. It doesn't require too much compression of pre-algebraic mathematics, since it's a simple 10 year to 8 year compression. And I am confident that people should be perfectly capable of understanding advanced mathematics at a young age. So let Algebra and Geometry be things of 7th and 8th grade, and we have ourselves Advanced Algebra, Pre-calculus/Trigonometry, Calculus I, and Calculus II before college. Would it be a good idea to have that be the norm? |
My province outright lowered the bar. :/ Lots of idiots in standard schooling here.
(A lot of forum users are computer nerds who are more likely to be interested in math so you're gonna get a biased sample in this club. :P) |
Quote:
Quote:
Quote:
Quote:
|
Username: Pokemon Trainer Touko
Overall Education Level: Year 8 Mathematics Education Level: I study in Hong Kong so we have a different system. I might be the youngest here but I can beat year elevens :3 I've tried multivariate calculus and it wasn't that hard =] Do you think you can be asked for help in your level or lower?: I guess so :D I wish I were a _______ so I could lay tangent to your curves: Derivative Please don't smash me with super hard stuff- I'm only 12 ~~ |
Quote:
|
Quote:
I know for certain that everyone in this club, if they had been given the opportunity, would be like the prodigies I mentioned. That's the beauty of maths; if I want to, I can learn anything I want as early as I want, unless it develops on some other branches (like calculus and trig). The "dreadful" bit is that some ARE allowed to do higher level work much earlier than others who could, but aren't allowed. Take the example of ShinyMeowth and Pokemon Trainer Touko, they were allowed to do calculus and such at a young age, and we're feeling bad XD Quote:
Obviously, mathematics and literacy are INCREDIBLY important for getting jobs, correct? If you can't read/write or do arithmetic, then, well, you're screwed. But when you reach the age of, say, 14-15 at school, what you learn isn't really all that important for the average worker. Why do I need to learn to analyse a book, or learn quadratics? I don't. I think that all the really important things should really be pushed until Year 9 (which is the final year, in England, that all subjects are compulsory). After that, it should really be optional. Of course, others would disagree. Quote:
|
Skipping
Quote:
|
Joining~
Username: Nurse Barbra Overall Education Level: 3rd year (9th grade in american terms) Mathematics Education Level:I do the new irish project maths sylubus, more wordy and complex equations, its about the equalivent of 12th grade maths,I know alot of the equations such as the distance between 2 points [^1/2{(a1+a1)^2+(b1+b2)^2}] , Do you think you can be asked for help in your level or lower?: Sure I wish I were a _______ so I could lay tangent to your curves: n Angle of 35* or more~ |
members
Quote:
|
I am not impressed with the lack of productivity in the recent week.
Now to talk about why exactly you like math, or what you like about it and when did it get you so interested? Is there anything specific that had you hooked? |
Quote:
Why exactly I like math? I don't really know why. It's just... fun, I guess. Like my lecturer said once, "When you get to prove the trigonometric equations, it felt fun, isn't it? Just like orgasm." The best part is when you get an answer to a question that's been bugging you for days. Anything specific... I know someone is going to answer pi Speaking of that, I'd really to learn more about the history behind constants like pi, e, etc. But the syllabus is just more centered around "How do you apply this to this" etc. Anywayy.. Today entered the chapter derivative in graphing and application. The concavity part is still easy, but I have a feeling that the graph-sketching part is not going to be that simple. |
yeaaahh mathssss.
Username: Ninja Caterpie; NC, En-say Overall Education Level: Year 9 Mathematics Education Level (Or most recent/advanced math subject): eh idg this. Do you think you can be asked for help in your level or lower? Yes. Possibly a bit higher, too. Life = The Universe = Everything = 42/3 = 14. |
Quote:
|
...well, I like maths,
but right now in year 9 I am having some trouble with motion problems. can anyone help with this? I don't want to put the question because I want to try learn it myself, but does anyone know what I mean by motion problems? |
Quote:
|
okay, here's an example;
A motor cyclist makes a trip of 500km. If he had increased his speed by 10km/h, he could have covered 600km in the same time. What was his original speed? |
Quote:
Hint: Spoiler:
|
Quote:
Quote:
Quote:
500/x=600/(x+10) (5000+500x)/(x^2+10x)=600x/(x^2+10x) (making the denominators equal) 5000+500x=600x (multiplying both sides with x^2+10x) -100x=-5000 100x=5000 x=50km/h If you have trouble with any part of that explanation, don't hesitate to ask for more details. What those problems need to be solved, is for you to write them down as an equation, and solving them becomes trivial after that. Edit: Bah, ninja'd. |
Quote:
Why I like maths? That's... quite a hard question to answer, but I'll give it a go and probably write about e^3 pages worth of text. I felt the need to spoiler it: Spoiler:
|
thanks for the help, smile and shinymeowth :)
i think i get it now :) |
Behold some questions from todays test for me, i got all the right answers but im just gonna throw it out there for you all. (As Quoted directly from the test):
Spoiler:
...Have fun~ |
Quote:
Quote:
Quote:
Quote:
Quote:
|
Spoiler:
|
Quote:
Spoiler:
|
Quote:
|
Quote:
|
Quote:
b)i) is actually "x^2 -13x+36 = 0" Answer time: Spoiler:
correct answers are in BOLD yay for the irish maths system~ Edit: Note: These were 4 SEPERATE questions. In our maths system the "1) Algebra" is the section " a) " is the question , ergo : question A. and "i" is used for the seperate parts of the question. |
Quote:
Spoiler:
But from what I have seen, that was probably done due to a "5²=20"-type mistake. |
Quote:
and y+1 = 1/y When x = (√5 +1)/2 and when y = (√5 -1)/2 And when you get the fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, etc. where you take the previous number and add it to the last number to get the next number) and put it as a fraction (1/1, 1/2, 2/3, 3/5, 5/8, 8/13, etc.) the fraction converges to (√5-1)/2. When you flip the fraction (1/1, 2/1, 3/2, 5/3, 8/5, 13/8, etc.) the fraction converges to (√5 +1)/2. Which is also the golden ratio, which is supposed to be related to beauty or something like that. Quote:
I swear I'd have given that stuff a try if I came to the club earlier. |
who like algabra?! (puts hand up)
|
Quote:
|
Quote:
|
Well the formulas arent labeled and there like this in order of the questions(the test was 40 questions long):
-b+-√(b²-4(a)(c)) 2a ax²+bx+c (x+h)² = (x+xh+h) 4/3πr³ |
Quote:
|
Quote:
How so? Err.. The way I understood your sentence is that Maths = everything but then you limited to physics is just maths. What about Biology and Chemistry? |
Quote:
2a ax²+bx+c - General form of a linear equation in 2 variables. (x+h)² = (x+xh+h) - Aren't x and h supposed to be squared and isn't xh supposed to be 2xh? o.o 4/3πr³ - Volume of a sphere |
Quote:
And on my test papers, I have all of those as well as: Volume of a pyramid/cone: [base]*[perpendicular height]/3 Volume of a prism: [Area of cross section]*[length] Area of a trapezium: h(a+b)/2 |
Quote:
|
Quote:
and my teacher decided to give the class a directed investigation, and he's giving us a whole week. the questions are really hard (for me, anyway), and i've only managed to solve 3 out of 5 the first day. i wanna see how people here fair, i'm expecting for all of you to get it in like 5 seconds and make me feel stupid :P , but here they are; A girl thinks of 3 numbers. She adds these numbers in pairs, getting 11, 17 and 22. What are the three numbers? (This took me so long to get, it was like a sudden brain wave and i got the answer. i then spiraled into a 10 minute victory dance with my friend, because we conquered the maths) The sum of two numbers is 8 and the difference between their squares is 34. Find their difference. (This one annoyed me alot, took me a while to realise the seemingly obvious, but i got it) and the other ones a calendar one that i can't be bothered typing. as soon as i finish the others im going to post them and see if others can solve them too :) |
Oh my god~! My classmates are doing trigonometry and they don't even know what's the sine and cosine rules~?!?! :O Unbelievable~!
|
Quote:
Quote:
Basically, it's how you manipulate the algebra. For the first one, just assign the numbers as x, y and z. Then make an equation for each and solve them accordingly. For the second, it's about factorization. As long as you know that x2 - y2 = (x+y)(x-y), you should be able to do it. |
Quote:
how are you so good at maths? i'm so jealous. |
Uh, those questions aren't really that hard, unless you don't know algebra.
1) Let the numbers be x, y and z. x + y = 11 (1) x + z = 17 (2) y + z = 22 (3) As there are 3 unknowns and 3 equations we should be able to solve it. (1) + (3): x + 2y + z = 33 Subtract (2): 2y = 16 thus y = 8 The rest is just basic manipulation, x = 3 and z = 14. 2) Let the numbers be x and y, x > y. x + y = 8 (1) x^2 - y^2 = 34 (2) Again we have 2 equations and 2 unknowns, so it should be solvable. Rearranging (1): y = 8 - x Substituting into (2): x^2 - (8 - x)^2 = 34 Expanding: x^2 - 64 + 16x - x^2 = 34 Cancelling x squared and shifting -64 over: 16x = 34 + 64, thus x = 6.125 Then y = 1.875 If you want to get past your mental block at doing maths, just remember that if there are n equations and n unknowns, you should be able to solve for every unknown. Write down equations representing everything that is given to you in the question. Then solve those equations for the answers. At your level, only substitution and elimination are needed. My answers for the two questions you provided display both techniques (eliminating x + z in the first and substituting 8 - x in the second). If there are more unknowns than there are equations, then the question can't be solved! If there are 2 equations which mean the same thing (like x + y = 3 and 2x + 2y = 6), then you can totally ignore one of those equations. If this puts you in a situation where there are more unknowns than equations, then the question can't be solved. Oh, and if you want your equations to be displayed nicely on forums, try using Texify. It'll take some time to learn how to use, but you'll be able to display superscripts, subscripts, Greek letters, differential/integral signs, etc. Sadly I can't use it because I don't have 15 posts yet :( |
ahhh, imma try all the harder ones now :) ,
|
This thread needs more manly trigonometry questions. I have one if anybody is bored:
If sinθ + cosθ = √2cos(90° - θ), find cot θ. It's not really difficult, anyone wants to try? |
Let theta=x, it's easier than entering Greek characters.
cos(90-x) is sin x, substitute that in: sin x + cos x = sqrt(2) sin x Divide by sin x on both sides (assuming sin x is not 0): 1 + cos x/sin x = sqrt(2) cos x/sin x is cot x, which is sqrt(2) - 1. |
Quote:
My final examinations are fast approaching, so gotta practise lots of math. XD |
Quote:
Sin: Oh hell (O/H) Cos: Another Hour (A/H) Tan: Of Algebra (O/A) |
Quote:
Quote:
|
Username: Drekin
Overall Education Level: Highschool math plus 13 credit hours after this semester is over Mathematics Education Level (Or most recent/advanced math subject): College Calculus I Do you think you can be asked for help in your level or lower?: Definitely Life = The Universe = Everything = : 42 (shouldn't it be Life + The Universe + Everything = ? ) |
Quote:
here's my way of remembering; S.O.H.C.A.H.T.O.A. ..you all know what the letters represent |
Quote:
x + y = 8 ... (1) x2 - y2 = 34 ... Factorize (x+y)(x-y) = 34 From ... (1) 8(x-y) = 34 x-y = 34/8 Since the question asked for the difference of x and y, there's no need to solve for x and y. Quote:
Does someone has a formula for memorizing them? XD I know that you can basically just draw the unit circle and find the value, but I want to memorize them. It's way quicker to get, especially in exams. Quote:
Quote:
Quote:
|
Quote:
I learned only the values of Sin. (In degrees) Sin 0 = 0 = Cos 90 Sin 30 = 1/2 = Cos 60 Sin 45 = 1 /√2 = Cos 45 Sin 60 = √3/2 = Cos 30 Sin 90 = 1 = Cos 0 If you noticed, the values of Cos are just opposite of those of Sin. Then, Tan = Sin/ Cos Cosec = 1/Sin Sec = 1/Cos Cot = 1/Tan = Cos/ Sin That way, you can remember the values with the help of just memorising the values of just Sin. We get to use a log table for all other values. XD |
Yeah, that is a faster way of doing it. I guess it depends on whether you can spot such a shortcut right away or not.
I memorize all trigonometric values by imprinting a picture of their graphs in my mind (i.e. y = sin x, y = cos x, y = tan x). So I know right away that, for example, sin x starts at 0, goes up to 1, back down to 0, then -1, then 0 again. One more thing when converting between radians and degrees: pi/6 is 30 and pi/3 is 60. |
Quote:
Quote:
Memorizing graph pattern, cool. That could help. Thanks :) |
Quote:
And I agree with you on deriving any formulae, mainly because I don't trust my brain to get ALL the numbers correct when memorising, plus it's fun, and as you said it feels rewarding, and I can trust that I've gotten it right at the end. As for memorising constants, I would like to memorise up to about 6 decimals (an accuracy to a millionth) but I know that Pi is 3.1415926 (7 decimals), e begins with 2, and phi begins with 1.618. Quote:
|
Quote:
I never memorize trigonometric values, since those most commonly used ones can be easily found by constructing triangles, and whenever you need something like sin(17), you are definitely going to have access to a table anyway. |
I, on the other hand, always memorize formulas. I may have a go at deriving them when I have time, but I never derive formulas during tests/exams. Try deriving the ideal gas equation and tell me that memorizing PV = nRT is harder.
It actually isn't that hard, if you've done enough practice problems you can always fill in the correct numbers in the correct places. It's a bit like muscle memory. Writing down every necessary formula on a piece of paper also helps. I don't memorize constants like pi either - your answer is always either computed using a calculator, or given in terms of pi. |
Quote:
Quote:
THAT. I seriously need to do that. First Principles, Newton's Method, Rolle's Theorem, Local Linear Approximation... They're all scattered throughout my notes. XD We used to substitute pi for 22/7 or 3.142 in the high school, but now we give the answers in terms of pi instead. I love that better, because substituting pi for 22/7 or 3.142 doesn't really give a correct answer. Also, I don't know whether you guys already know about this, but. Speaking about pi, if you use 22/7 as pi, the equivalent value is 3.142857142857142857.... If you notice, we have a recurring sequence there, which is 142857. It's a roundabout number, i.e whenever you multiply that number by e.g 2, you get the same numbers, only in different sequence. 142857 x 2 = 285, 714 142857 x 3 = 428, 571 142857 x 4 = 571, 428 . . . 142857 x 7 = 999, 999 142857 x 8 = 1, 142, 856 (notice that 6+1 = 7 so essentially it's still 142, 857) I don't know how far this number will stay the same though. XD |
Derive a formula during tests? No way. Unless that is what the question asks. XD
Memorising formulae is not difficult at all if you're practising maths a lot. You'll keep using them and hence easily memorise them all. |
If there's one thing I hate more than trigonometry, it's modulus, I swear. They drive me nuts on limit questions. x.x I wonder if someone can help me with this?
Determine whether all the hypotheses of the Mean-Value Theorem are satisfied on the stated interval. If they are not satisfied, find all values of c guaranteed in the conclusion of the theorem. f(x) = |x-1| on [-2,2] ...I didn't even understand the last part of the question. o.o Anyone? :3 |
The hypotheses required are:
(1) f(x) is continuous on [-2,2], and (2) f(x) is differentiable on (-2,2) The first statement is easy to prove: |x-1| can be piecewise defined, as 1-x if x < 1, 0 if x=1, and x-1 if x > 1. Since x-1 is a polynomial, and all polynomials are continuous over R, f(x) is continuous over [-2,1) and (1,2]. Next, we must check for continuity at x=1. http://www.texify.com/img/%5CLARGE%5C%21%5Cnormalsize%20%5Clim_%7Bx%5Cto1%5E-%7Df%28x%29%20%3D%201-1%20%3D0.gif http://www.texify.com/img/%5CLARGE%5C%21%5Cnormalsize%20%5Clim_%7Bx%5Cto1%5E%2B%7Df%28x%29%20%3D%201-1%20%3D0.gif f(1) = 0 All 3 numbers match, so f(x) is continuous at x=1. The second statement can be seen as false graphically: there is a corner point at x=1. However, we must prove this rigorously (no graphical methods are acceptable). Start with the definition of derivative, calculate the left-hand derivative: http://www.texify.com/img/%5CLARGE%5C%21%5Cnormalsize%20%5Clim_%7Bx%5Cto1%5E-%7D%5Cfrac%7Bf%28x%29-f%281%29%7D%7Bx-1%7D%3D%20%5Clim_%7Bx%5Cto1%5E-%7D%5Cfrac%7Bf%28x%29%7D%7Bx-1%7D%3D%20%5Clim_%7Bx%5Cto1%5E-%7D%5Cfrac%7B1-x%7D%7Bx-1%7D%3D-1.gif Noting that f(1) = 0, and using the piecewise definition of f(x) as described earlier. Then calculate the right-hand derivative: http://www.texify.com/img/%5CLARGE%5C%21%5Cnormalsize%20%5Clim_%7Bx%5Cto1%5E%2B%7D%5Cfrac%7Bf%28x%29-f%281%29%7D%7Bx-1%7D%3D%20%5Clim_%7Bx%5Cto1%5E%2B%7D%5Cfrac%7Bf%28x%29%7D%7Bx-1%7D%3D%20%5Clim_%7Bx%5Cto1%5E%2B%7D%5Cfrac%7Bx-1%7D%7Bx-1%7D%3D1.gif Since they are not the same, f(x) is not differentiable at x=1, so (2) is false. One of the conditions was not satisfied, so no values of f'(c) are guaranteed. (1 - 3)/(2 - (-2)) = -0.5. The only values of f' at the points where it is differentiable are 1 or -1. p.s. I'm pretty sure the last part of the question is worded wrongly, because: 1) "not satisfied" = theorem doesn't count for anything 2) MVT involves f'(c), and does not state exactly which, or how many, values c could take. |
Quote:
And yeah, I don't know whether the last part of question is worded correctly. I'll ask my lecturer again to clarify. Anyway, thanks again! 8D I didn't quite get that last part, though. The last 2 lines before the postnote. |
This should be clearer.
f(2) = 1 f(-2) = 3. (f(2) - f(-2))/(2 - (-2)) = -0.5. d/dx (x-1) = 1 and d/dx (1-x) = -1. |
Quote:
|
i had my maths test today.
i feel pretty confident :) . i know i got one question wrong though (i accidentally added the dividends instead of leaving them, so the answer was too big) . but i managed to conquer the speed questions :D they were actually fun :) thanks for all the help on here, too :) |
Quote:
Although, I did one silly mistake by separating integral cos x sin x into integral cos x times sin x. =\ I thought you could do so, and only after the test when I checked I found out you cannot. >.< |
| All times are GMT -8. The time now is 4:22 AM. |
![]()
© 2002 - 2018 The PokéCommunity™, pokecommunity.com.
Pokémon characters and images belong to The Pokémon Company International and Nintendo. This website is in no way affiliated with or endorsed by Nintendo, Creatures, GAMEFREAK, The Pokémon Company or The Pokémon Company International. We just love Pokémon.
All forum styles, their images (unless noted otherwise) and site designs are © 2002 - 2016 The PokéCommunity / PokéCommunity.com.
PokéCommunity™ is a trademark of The PokéCommunity. All rights reserved. Sponsor advertisements do not imply our endorsement of that product or service. User generated content remains the property of its creator.
Acknowledgements
Use of PokéCommunity Assets
vB Optimise by DragonByte Technologies Ltd © 2023.