Manage your time properly. Math does require lots of focussed, diligent, hard work. By focussed I mean - find a quiet place, turn off the tv, msn, sms, etc., and do your math then! No talking on the phone, no internet. Plan for breaks, stretch, have a snack, but make it short.
Doing math is frustrating, at times it might look overwhelming. Do not rush thorugh the material. It is better to cover 2/3 of it well than to rush through just to make sure that you 'covered' all of it.
THINK on the test/exam ... works better than trying to recover things from memory! Memorizing things without understanding will not get you too far (not only in calculus, but in other courses as well). Thus, if necessary, modify your approach to studying adequately; learn to think! When doing a question, keep asking yourself questions: why does this work? why is this true? is there another way of doing it? why was I able/not able to apply such-and-such theorem in this situation? what's the message? can I apply this method to other questions?
*** learning from other people's mistakes: look at this test question, and the way it was solved (the solution is done in pencil; the red curve - correct solution - was drawn by the marker)
THINK! You have x|x|, and |x| is x or -x ... so x|x| is either x^2 or -x^2 ... then how can the graph consist of straight lines? Also, the question states 'sketch the graph of the FUNCTION ...' Is what is given as solution the graph of a function?
"Being able to think will help you build your confidence."
*****Key to success in calculus is practice!"
*** learning from other people's mistakes:
The solution is started correcly, using L'Hopital's rule. What happened then? Obviously, due to lack of practice, the student did not know how to proceed. After doing a dozen LH questions, you realize that some require that you apply LH several times to get a result, and that's what was needed here.
Also remember: when doing limits, the first thing you do is to substitute - this will ALWAYS give you an idea on how to proceed. Had the student substituted x=0 into the last line, she/he would have gotten 0/0 ... so, it's clearly LH
***It does not make much sense to read somebody else's solutions. Try the question yourself, see how far you can get ... if you get stuck, make an effort to understand why you got stuck. THEN look at solutions to see how that particular problem/issue has been resolved.
'Studying' solutions will not help you identify difficult and/or important parts of a solution - so, when you encounter similar situation in another question (or, on a test/exam), you might not be able to understand/solve it. Also, memorizing a solution and applying it to a question which is similar (but not the same) as the one you memorized usually leads to a disaster.
**In math, very small differences can lead to completely different solutions and answers.** For instance, to integrate xe^x you use integration by parts. But integration by parts will not help you to integrate xe^(x^2), you need to do substitution.
Key to success in calculus is practice: the only way to really master techniques is to do MANY problems, ON YOUR OWN. At least, attempt first by yourself. Again, reading a solution or watching somebody else do it for you is not a good way of learning. Not only will you not learn it, but (because you did not do it yourself) you will forget it quickly.
The textbook is full of exercises with exponential function, logarithms, fractions, trig functions ... if needed, do them all!
Key to success on tests and exams is practice. If you are well prepared, the disturbances (that will always be present!) will not really affect you. Think of a military: a soldier is trained to perform and execute precise orders in highly stressful, emotional, or dangerous situations.
If you are not sure whether or not ln(x^3) is equal to 3 ln(x), or if 1/x is derivative or antiderivative of ln(x), of whether or not tan(x) has period pi or 2*pi, that means that you lack practice!
*** learning from other people's mistakes:
the student correctly identified the limit as infinity - infinity ... the first association HAD to be L'Hopital's rule! How do you get the right association, and quickly? Do many LH questions! ... And critical numbers, or integration by parts questions (at the same time, you practice lots of other things, such as simplifying, laws of exponents and logarithms, fractions, etc.)
*** learning from other people's mistakes:
question asks for states critical numbers (critical points) ... your first association MUST BE: this is related to derivatives. So, f'=0, not f=0 !!! What was likely the problem here: due to nervousness, stress, etc. the student got confused. Remedy (I guess by now you know): PRACTICE!
*** learning from other people's mistakes:
Computing common denominator problem ... you cannot afford to lose points this way. If you feel rusty with things like this, use Math Review Manual, go over the first chapter.
How to solve the inequality x^2+x>0 ... convert to x^2+x=0, then factor ... or graph. Both are standard techniques that appear all over the place. You have plenty of examples in you class notes; also, look at solved examples in your textbook.
about your tests/exams:
* There is no relationship between blank space after a question and the expected length of your solution; if a question is worth more points, it does not mean it is more difficult
* If you think that you will not have enough time, concentrate on some things and do them right - it does not make sense to jump from one question to another without finishing any one of them.
* What you wrote is what is marked, and not what you thought ...
* Because of circumstances (especially on the final exam - stress, large room, noise, lots of people, disturbances, etc.), when you first look at the exam, it might appear to be impossible to do; spend 1-2 minutes reading the questions first, identify what you can do right away, and work on those questions first.
TO PREPARE: as I said many times - practice! there is no magic, no quick fix to learning something. Perhaps not fun, but it works - you need to gain routine. It is not just that you have to know the stuff, but you need to solve problems in the given amount of time. For instance: it should not take you more than 1-2 minutes to sketch the graph of sin(x)+4 from sin(x); or cos(2x) from cos(x), or tan(x+pi/2) from tan(x). If it takes you 10 minutes do figure out the limit of (x-4)/((x^2-x-12) as x approaches 4, then you will not have enough time to finish the whole test/exam.
*** learning from other people's mistakes:
Read the question! It asks you to do the derivative at zero - which is a lot simper than doing it at a general x, and then plugging in x=0. Also, doing it in this general way you encounter technical problems that are not that easy to resolve.
*** learning from other people's mistakes:
look at the first line of the solution ... should have been square root of x divided by 1/ln x. Quite probably, this was due to nervousness, or momentary lack of concentration (rest of the question is done correctly!).
To boost your concentration and energy, during a test/exam: drink water or juices, bring a chocolate bar or something else with lots of sugar in it.
*** learning from other people's mistakes:
Study your notes! Newton's method was fully explained in the notes ... here you are asked to reproduce the construction, and state it in your own words.
HINT: make sure you know and understand statements of theorems ,,, to make sure you know them, try to explain a theorem or a definition IN YOUR OWN WORDS to somebody else.
*** learning from other people's mistakes:
If it takes lots of writing to do a question, and you do not seem to be close to a solution ... HINT: you made a mistake somewhere (last line above is incorrect)! start again from scratch, (usually) it's quicker than trying to locate an error ... or, change the approach to solving if possible.
final message:
If you get a bad mark, that is overall not that bad. But if you do not identify the reasons why that happened and if you do not modify/ change/ adjust things approprietely, it will happen again. And that's not good.
****Please read this, think about it, and apply it! Good luck on your remaining tests and the exam,
--- THIS IS TAKEN FROM SOME BOOKS AND SOME OF THE TIPS ARE GIVEN FOR ME ( and for my college mates )BY "ONE OF THE LIVING LEGENDS OF MATHS Mr.DHARMAPADAM sir "
I DEDICATE THIS ARTICLE TO MY" PROFESSOR"
HOPE THIS WOULD BE OF GREAT USE -----striker
"IMAGINATION IS MORE IMPORTANT THAN KNOWLEDGE"
Moderation Team
![[Post New]](/templates/default/images/icon_minipost_new.gif){kind=icon}
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
44
