So you have a few months to your board exam ? And you are doing ok but not great in Math - The Achilles heel for many students.
How about we try to approach acing the exam in a different way ? Discipline.
Looking at the blueprint, the Math exam weightage by chapter is as follows...
Relations and functions - 10
Algebra - 13
Calculus - 44
Vectors & three-dimensional Geometry - 17
Linear programming - 6
Probability - 10
Clearly calculus is the big chapter.
Reminder - calculus is the chapter with integration - the one with the snake like symbol or like a karate pose whatever fancies you, and differentiation - where 'd' is divided by 'dx' but you dont get to cancel the 'd' in numerator and denominator ( i am sure some students feel like your teachers are cheating - after all in algebra, we were allowed to cancel the 'd' ).
But before we get into calculus, an obvious question that will come into every student's mind ( especially the day before the exam ) -
Why should I be reading calculus ? I have never seen any adult doing calculus as part of their job.
Fair question...If you plan to remotely take up a career ( job where you work and get money and then buy fancy clothes and phones ) anything related to engineering and finance, calculus will come up.
So let me learnt it when i encounter it later - not now ?
Hmmm. Good question. Ask your cbse board. But very soon ( in a year or two ) in college, you will hit calculus again and again and again, unless you go into Arts or Humanities. ( too late, you are in Science group )
As you might have heard by now, calculus is used almost everywhere - biology, economics, surveys, buildings, statistics, computers and the list goes on.
So if you plan to do anything related to any of the above subjects, you will need to learn calculus. And to become a doctor, engineer, economist, finance consultant you need COLLEGE degrees. And all these degrees expect you know calculus.
So think of this as a building block ( like a brick for a house ). Mathematics learning always builds on your past math knowledge. So learning numbers is needed to learn arithmetic which is needed to learn algebra and geometry, which then leads to functions, sequences, limits and
which then helps to learn calculus and all of these to learn different fields like engineering, economics etc.
Here are some interesting links on uses of calculus - ( I did a google search - which by the way uses calculus for its algorithms - but that is for another day )...
Application of Calculus
Who uses calculus? You do. Every day.
Fun Exercise: Find a use of calculus beside the examples listed in this article or in the links above. ( Hint - video games, music )
If you have still not accepted importance of calculus not just for your exam but for your life, then look at the blueprint above and find which chapter gets the most weightage. Maybe that will convince you to learn calculus.
From here, it is just planning and understand concepts.
* Learn LIMITs well.
* Differentiation means figuring out 'rate of change'
* 'dx' means 'a small amount of x'
* 'dy/dx' means 'the ratio of the small amount by which y changes when a small amount of x is changed'.
* 'dy/dx' can be calculated only when y and x are related. That is, when x changes, y changes also. That is, y is a FUNCTION of x.
* Integration symbol is just a big "S" which means "sum" up all the small parts.
* Integration is understood easily by calculating the area under a curve. Slice up the area into small rectangles and sum them. The more the slices ( smaller they get ), the accuracy of the calculation gets better.
* Imagine we need to fill up water in a bucket. 'Differentiation' is the rate at which the water fills the bucket. Integrating the tiny amounts of water every second, gives us the volume. Hence 'integration'.
Now read your book chapter slowly. Once done, practice. When done, practice more. When done, practice more. You get it...
Finally a quote from here -
“There is a gold rush on calculus. It currently [makes] is responsible for billions of profit.”
To practice Calculus, for CBSE and JEE MAIN exams, try out http://clay6.com and click on the "CBSE Math" study plan and practice those tests and step-by-step solutions.
clay6 CBSE 12th Study Plan -
Miscellaneous good links to learn Calculus -
Some applications of calculus problems -