What to know in Maths for KVPY:
There is no specified syllabus for KVPY. Going through the previous years’ question papers reveals to some extent what the examiners are looking for. For anyone preparing for other competitive or entrance exams like JEE, the syllabus seems to be very similar. The KVPY SA exam is for class XI students and the common SB/SX question paper is for class XII and first year students in basic science courses.
The maths questions in the KVPY are complex and need a good understanding of the fundamentals. Some of the most commonly asked questions involve polynomial algebra, set theory and trigonometry. These form the backbone of the class XI and class XII maths along with calculus. Hence they are taught quite extensively in schools. Apart from these, there are questions based of shapes and their properties. This needs special attention especially because these questions seem to draw from shape properties whose solutions can be difficult to arrive at in situ in a short time. Also owing to the fact that these types of questions have been asked consecutively in the last few years, it is better to spend some time on shapes and their properties. This includes ellipses, simple geometrical shapes and their properties like shortest distances, radius of the circum-circle for instance. Information and material on this topic will most likely be available under the heading Planar geometry.
Polynomial algebra including set theory, calculus and planar geometry form a bulk of the questions asked. In the total number of mathematics questions in the papers for SB/SX exams for the last six years, the above topics cover about 25%, 25% and 20% respectively. They are also slightly biased towards property based questions than pure problem questions, although both types of questions are present. Sequences and series, trigonometry and probability form another bulk of the questions in the last six years coming to a combined contribution of about 20%. While the calculus and Sequences and series questions are fairly advanced, the probability questions seem to stick to the property based questions theme. In addition to these topics, there have been questions from statistics, combination and permutation, vector algebra and matrices. These seem to be appearing on and off and do not seem to follow any specific trend. It is to be noted that these topics have covered only 10% of all questions asked and so at least one question can be expected from these topics.
Apart from these there have been one or two questions on complex numbers. In addition to the subject oriented questions, mathematical puzzles have also been asked sporadically. These puzzles require a good working knowledge of algebra, planar geometry and, combination and permutation.
Thus, it can be concluded that most of the topics are broadly covered in classes in school but the depth of the questions asked is very complex. Sticking to just the school’s curriculum will most definitely not be enough. It is advised that the aspiring student practice more complex problems making use of several resources!