Help with getting better at calculus (for exam in 4 months)

[GeorgieB]

Hello all, I am preparing for national exams which I take in about 4 months but In order to get in the department I want I'd have to score 75+/100 in maths,the sad part is that I am pretty much lost because at the start of this semester I shifted my focus to physics which has always been the most difficult subject to me and chemistry which I had never studied before and needed to build some foundations. Now 4 months before the exams I have reached a very good level at both physics and chemistry but I am really struggling with mathematics!

My syllabus is:

. . .Function Continuity
. . .Limits (+ x-->infinite)
. . .Bolzano Theorem +Generalizations
. . .Tangents
. . .Rate Of Chang
. . .Derivatives- Function/Derivative monotony
. . .Function/Derivative Curvature
. . .Rolle Theorem
. . .Medium Price Theorem +Generalizations
. . .Fermat Theorem
. . .Integration

Typical Excercises include:

. . .Show /or find that a function or a derivative has a root
. . .Analyse and draw the function:....
. . .Calculate the rate of change
. . .Calculate the area between 2-3-4 functions
. . .Calculate the limit of...

(those are just some simple examples of exercises)

I Have always been rather good at math so I have a pretty good understanding of the concepts and theory and when I study a solution most of the time I understand it,the thing is I haven't studied math seriously a quite a while so I have a hard time solving anything about medium difficulty. Any advice on how to get to a good level rather fast? All help is greatly appreciated,Thank you for taking the time to read this!

PS:I understand that this thread is mainly for help with exercises but I did not know where else to post this!

 

[j-astron]

Hi GeorgieB,

Just out of curiosity, what "department" are you trying to get into? I ask because if this calculus is at the high school level, it includes some things I was never taught in high school calculus (Bolzano's theorem is apparently something from Real Analysis, which is like the rigorous theoretical underpinnings of calculus). On the other hand, your example exercises sound like straightforward high-school or first-year-university level calculus problems. I will defer to people with a more pure math background to weigh in on the more obscure topics, but for the general calculus stuff, have you tried things like:

- Khan Academy (online video tutorials that are very thorough and well explained)?
- The lessons on this website (freemathhelp), which I admit I have not looked at?
- Calculus practice problem books or textbooks from your local library (or on Amazon)?
- Old math competitions (may be available online)?

Four months is a feasible amount of time to get up to speed if you have good mathematical intuition, which it sounds like you do. I think the key is to do as many problems as you can. Also, don't just look at a solution. Even if you think you understand it at the time you're reading it, it's no substitute for having to work through the steps yourself. Granted, at first, you may have to look at a few worked examples to see what the general approach is to various classes of problems. But after that, definitely make sure you try to tackle a problem all the way through, or until you're absolutely stuck, before resorting to looking at the solution.

Good luck!

 

[mmm4444bot]

… I am really struggling with mathematics!

… I Have always been rather good at math … the thing is I haven't studied math seriously a quite a while so I have a hard time solving anything about medium difficulty.

… Any advice on how to get to a good level rather fast?

If your algebra and precalculus skills are good, then I'd suggest working with one of the free introductory calculus courses online. There are also free calculus textbooks. You wouldn't need to complete the entire course or book; use them as self-study guides, to learn the terminology and find your weaknesses. (You may need to check out more than a couple sources, to find presentations that work for you.)

If you find that you've forgotten a lot of algebra or precalculus, you ought to plan on studying more than 20 hours per week, to both catch up and learn the calculus.

Typical [calculus] exercises include:

Show /or find that a function or a derivative has a root
Analyse and draw the function:....
Calculate the rate of change
Calculate the area between 2-3-4 functions
Calculate the limit of...

We can help with these topics, if you post a specific exercise and show how far you got. (Please start new threads for new exercises.)

For example, I could talk about finding function roots (or to show that some given value is a root), but I might be repeating something that you already understand.

Be sure to check out the forum guidelines, too. :cool:

 

[GeorgieB]

Hi GeorgieB,

Just out of curiosity, what "department" are you trying to get into? I ask because if this calculus is at the high school level, it includes some things I was never taught in high school calculus (Bolzano's theorem is apparently something from Real Analysis, which is like the rigorous theoretical underpinnings of calculus). On the other hand, your example exercises sound like straightforward high-school or first-year-university level calculus problems.

Hello and thank you for the response,
I want to get into the department of chemical engineering at the university and for that I need to take exams on Math,Physics and Chemistry and score an average of 82/100,however the university entrance system in my country is a bit peculiar,meaning that it is not each university that dictates which subjects should the students take exams on in order to get in one of their departments but rather it is the state that categorizes universities under 4 categories:Humanitarian studies (for which you have to take History.Latin,Ancient Greek),Medical studies (Biology,Physics,Chemistry),STEM(Math,Physics,Chemistry) and Economics/Computer Science (Economic Principles,Applied Programming,Math) so each student at their final year has to choose one of those 4 fields and at the end of the year you take exams on 3 subjects depending on the field you chose.As for the differences in syllabus the university entrance system in my country is notoriously hard,our math syllabus contains almost everything from first year college in other countries of europe and our physics syllabus contains almost everything from the first two years of college in physics departments across the world (Electromagnetism,Fields,Relativity,all known oscillations,Waves,Liquid Mechanics,Neutonian mechanics)
Hope this answers your question and again thanks for the help!