Geometry is a stream of maths in which students have traditionally scored well. If you test middle and high school students and evaluate their performance stream-wise, it turns out that geometry and number systems, are the streams in which students score the most. So geometry, which has a 17% weightage in the Class 12 board exams, can be relied upon to give you those extra marks you finally need.
One of the reasons why students seem more comfortable with basic geometry may be that geometric problems are easier to visualise, and word problems deal with practical or physical situations which are simpler to understand. However, in the senior classes, the topic does become a little more abstract with the introduction of 3D coordinate systems, vectors and tabular representations. The challenge for students as they get into these topics is to retain the visual perspective, and to be able to continue to visualise the problems at hand in the new language of coordinates and vectors.
The shift from 2D geometry to 3D geometry, can best be described by the following example: Earlier, the question in a geometry paper could have been about finding the distance between two persons standing at two points on a floor. Now, the question type shifts to finding the distance between two persons standing at two points on two different floors. The root concept in solving these types of problems is the Cartesian coordinate system, which every student should understand.
Most of you must have heard the story of the fly that helped Rene Descartes come up with the idea of the Cartesian coordinate system. One day, Descartes was sitting in a room which had square tiles on its walls, and in a eureka moment, spied a fly in a corner of the room. Suddenly, it occurred to him that the exact location of the fly could be defined by its position on the ceiling tile. The idea of mapping any location using the XYZ coordinates, emerged as a result. Its application can now be seen everywhere, in simple maps, in the GPS systems, in computer graphics and image processing. Many of the questions in the Class 12 boards would relate finally to locating a position or various positions on a system of coordinates, and computing distances or areas or volumes related to points and planes in the defined space. At the root of all these problems is Rene’s Cartesian coordinate system.
A student preparing for the boards should do two things to be well prepared, once the key concepts have been understood. One, list down the various formulae required for computing various geometric spaces and distances, and revise them frequently. Quick recall of the right formulae will save a lot of time during the test. Second, look at each problem and visualise it before you try to solve it. If you like, sketch it on a piece of paper, and confirm from your teacher or coach whether you have conceptualised it right. If you have these two aspects covered, you will definitely do well.
The other tip for those preparing for the boards is a general one. Test yourself frequently, and you could avail of online options for testing. The important thing to do is to analyse your performance after each test and note down as to which problem types you failed in. Understand your weaknesses therefore very specifically and then work to clear your concepts and doubts in these areas. In your next test, check if you have cleared the hurdle on these weak areas, and you may also find that you have discovered some new areas where you have done badly and start working on them immediately.
This is a cyclical process, but one guaranteed to lead you to good results if you follow it with discipline.
The writer is founder & director, Second School Smart Tuitions