What are THEY teaching?

Alas! To my astonishment, in many supplementary books of Mathematics I see the most tedious methods of solving even the easiest problems. In one (so very famous??) supplementary book of Maths XI, I found that the author was explaining the two forms of ellipse (One having major axis along X axis and another having major axis along Y axis) in most ridicules way, where this book says: always make ‘a’ and ‘b’ the denominators of X and Y respectively for both the type of ellipse. This means for first type of ellipse ‘a’ shall represent major axis, and for second type of ellipse ‘a’ shall represent minor axis.

What rubbish? This makes even the prudent student scare of problems related with conic section because he will have to remember two different sets of formulae for two types of ellipse which he would not have done, had he would have taken ‘a’ always a major axis (This is what is precisely done by NCERT). Similar problem arises in case of Hyperbola if the student goes by the opinion of author of that supplementary book.

In the same book for XII Maths, in Relations and Functions, the author defines two functions, f and g; and asks the students to work out ‘fog’ and ‘gof’ and writes in brackets ‘if they exist’. This question gives the impression that ‘fog’ or ‘gof’ may either exist or may not exist, which otherwise means that occurrence of ‘fog’ (or ‘gof’) is one of two mutually exclusive events, i.e. occurring or not occurring.

Preposterous. Isn’t it? For, for any given two functions ‘f’ and ‘g’, the ‘fog’ or ‘gof’ may exist for segmented intervals, and may not exist for many other segmented intervals. For example, if ‘f’ is sin x, and ‘g’ is log x; then ‘fog’ is ‘sin log x’ and ‘gof’ is ‘log sin x’. Obviously, ‘fog’ i.e. ‘sin log x’ exists for all x belonging to positive real numbers but does not exist for negative real numbers. Similarly, ‘gof’ i.e. ‘log sin x’ exists for segmented intervals like, {0,π}, {2π,3π}, {4π,5π}, {6π,7π},…., {2nπ,(2n+1)π} but does not exist for {π,2π}, {3π,4π}, {5π,6π},…., {(2n-1)π, 2nπ}. There are question galore in this (these) supplementary book(s) where the छात्र मात्र अपना सिर धुन सकता है.

I find that almost all school teachers of Maths are heavily banked upon making use of supplementary books in the class. Why? The reason is clear. This activity does not promote the (mathematical) intellect of the student; rather promote the sale of the book.