Welcome to the second post under "Mathematics Strategy". I am going to discuss the strategies and techniques of a chapter named "2D Geometry".
The importance of the chapter: -
As the name suggests, 2D means two dimensional. Roughly speaking, the plane you are standing on now is an example of a 2D object. From the engineering point of view, almost all of the engineering branch uses the knowledge of 2D geometry to solve real-life problems. From JEE point of view, it is one of the most important chapters and there are certainly 3/4 questions going to be asked directly, 2/3 more indirectly in JEE main and advanced respectively. You can not neglect this chapter to score well in the mathematics part, and my suggestion is you should not neglect this chapter because it can be a mark fetching chapter if the preparation is done correctly.
The important concepts inside the chapter: -
This chapter consists of the following sub-chapters, which are equally important.
1 - Point
2 - Straight line and pair of straight lines
3 - Circle
4 - Parabola
5 - Ellipse
6 - Hyperbola
I will be discussing the important concepts, loopholes and a strategy here so that aspirants can prepare well.
Today I will discuss the first two, "Point" and "Straight line and pair of straight lines".
Preparation Strategy: -
Book recommendation - I have used " Skills in mathematics, Coordinate geometry, by Dr. S.K. Goyal ". And this book alone is sufficient for both JEE Mains and Advanced.
Many aspirants do a mistake in this chapter, they try to remember the formula. But the formula can not help you to solve a lengthy question, in fact, the equation of the formula will make the question more lengthy. Try to learn the derivation of the formula, I mean the small concept that was used to make a formula.
For example, you know the formula to find in-center when you are given the coordinates of the three points of a triangle. Now there is a direct formula for this problem, but that formula is lengthy. If you know the small concept behind the formula of in-center, i.e. the distance of in-center from the sides of the triangle is equal, then you will never face problems while solving lengthy questions, you can easily write the straight-line equation and solve.
The book, that I suggested has the derivation for almost all formulas, you should learn them also and solve problems by the process instead of using the formula.
For the straight line chapter, there can be questions directly or indirectly. Divide this chapter into small parts as I am giving below.
- Different forms of equations of the straight line
- Reduction and conversion from one form to another.
- Manipulation of point and line
- Area problems
- Family of lines
- Bisector equation
- Image and reflections
Pair of the straight line is relatively easy but you have to be careful while dealing with so many unknowns and variables. There are many conditions in this chapter and JEE Main asks direct questions on those conditions.
The problem practice and problem-solving strategy: -
In this chapter, the one and the only way to master techniques is your visualization power. During the exam, you are not going to get that much time to draw a geometry diagram of the given problem or to write the equations. Your visualization power is the savior.
Visualization means understanding the question and making a virtual diagram inside your brain, which can help you to solve problems. While practicing questions initially, make accuracy as your priority, draw the diagram, understand clearly what the questions are asking, solve it step by step. Slowly, you will achieve speed and accuracy both with your practice. Then after some hours of practice, a time will come when you never need to draw a diagram or write the full equation. You can solve the question by writing only the important calculations instead of lengthy equations.
There are many other techniques given in the book and those techniques are helpful for a limited time problem-solving.
I would also suggest the following video from Youtube and the playlist related to it.
Mohit Sir is one of the best teachers on youtube. I never prepared with his videos but as suggested by some of my friends, I watched Combinatorics video on his channel, and that was really very helpful.
Final Words: -
JEE mathematics is all about practice and analytical skills. Obviously, this chapter has many formulas and concepts, but with a strategy, you can practice all the concepts along with the analytical skills required to solve the problems in coordinate geometry, i.e visualization.
Prepare well, All the best.
By,
Abhijit Tripathy
Admin, Dropper's Den.