In higher secondary level or plus-one and plus-two standards (Class XI & XII) in some regions, also referred to as pre-college level, mathematics becomes an essential subject, and crucial topics of higher mathematics are introduced at this level. At this level, acquiring a clear and firm knowledge of the basics of higher mathematics is very important. Till the secondary level, students get familiarised with the concepts of basic algebra, which includes polynomials, types of polynomials, linear, quadratic and cubic equations, and how to find the solution of any equation using different methods. The geometry concepts are taught in detail – lines and angles, properties and essential theorems related to them, congruency and similarity criteria. Along with these fundamental concepts of statistics, commercial mathematics and probability are also taught.
Learning mathematics is a hierarchical process. Different concepts of each level provide the building block for the next higher level. Now, let us discuss what topics are addressed at the higher secondary level. With knowledge of fundamental concepts of algebra, we move on to introduce the basic notions of abstract algebra, such as sets, relations and functions. Higher-level trigonometry and elements of inverse trigonometry are taught with their applications. Some basic introductory concepts of linear algebra, like matrices and determinants. Then, one of the most crucial concepts of advanced mathematics, which has a wide range of applicability in both applied and pure mathematics, is calculus, which includes both differential and integral calculus.
In geometry, the equation of line and plane of different forms are introduced. The concept of directions ratios and direction cosines with basic knowledge of vectors are provided. These topics are the major topics from which questions of good weightage are asked every year in the board examinations. Students are advised to practise questions based on these concepts thoroughly to score well in examinations.
There is a very important theorem which establishes the connection between the integral of a function to that of the derivative of a function: that is the fundamental theorem of calculus which has two parts. The second fundamental theorem of calculus provides the definition of a definite integral of a function. This definition of definite integral has great importance in finding the area under the curve and the area in between the curves. In higher secondary mathematics, a vast revelation of differentiation and integration is provided, which is also required for many concepts of physics at this level.
A glance at advanced statistics and probability is also introduced at this level, and how both the branches are related to each other. In probability, a very important concept of reverse probability is introduced through Bayes’ theorem and conditional probability. Then, basic ideas of different types of distributions are also raised. From all these topics, necessarily 2-3 questions are asked every year on board examinations. At last, a brief vision of linear programming problems are put forward, which deals with actual real-life problems related to production and management. For an advanced level, this idea of linear programming will definitely create a basis for operations research which nowadays is in huge demand from a vocational point of view.
To sum up, the subject mathematics itself is indispensable in our daily life; we all are well aware of it. And almost in every stream of study, we will always find mathematics a part of it. So if you are opting out mathematics as a subject in your higher secondary, the mentioned concepts are of utmost importance and will surely be helpful to you for your further studies, whether it be for a master’s course, any vocational course or may it be any competitive examinations. More or less, questions from these areas are asked to test your knowledge and aptitude. Hence, it is very necessary to have thorough and firm knowledge of these. By knowledge, it does not mean being able to solve questions; rather it means understanding the actual meaning and implementation.