Class 12th Maths is extremely application based and has a lot of interrelated content as well. It is the class where calculus begins in detail after a brief introduction in class 11th. This year of Maths asks students to have very clear fundamentals and will help in all the upcoming years in a student’s life.

Syllabus for Class 12th Maths

• Relations and functions – What are the different types of relations, what are the different types of functions, finding the inverse of a function and a brief introduction to binary operations
• Inverse trigonometry – Understanding concepts of the domain of a function, range of a function and principle value of a function, plotting and analysing graphs of inverse functions, fundamental properties of functions associated with inverse trigonometry
• Matrices – What is a matrix, what is the order of a matrix, how to find the order of a matrix, what are the different types of matrices, finding the transpose of matrices, importance of identity matrix and different symmetric and skew-symmetric matrices, addition of matrices, multiplication of matrices by scalar quantities and other matrices, devising primary row and column operations of matrices, finding the inverse of matrices and proving their singularity
• Determinants – Finding out determinants of square matrices of order 3 x 3, understanding fundamental concepts like minors and cofactors of elements, using determinants in calculating the area of a triangle, calculating the inverse of a matrix, calculating adjoint of the matrix, applying the concept of determinants to find out solutions of linear equations
• Understanding continuity and differentiability in calculus – Finding derivatives of inverse functions in trigonometry, finding derivatives of implicit and composite functions, introduction to exponential and log functions, finding out derivatives of these functions, pursuing differentiation using log methods, devising derivatives of parametric functions, calculating second-order derivatives and theorems
• Derivatives applications – Using derivatives to find out the rate at which quantities change with respect to others, finding out whether a function is increasing or decreasing at a certain point or over a range, calculating tangents and normals, numeral approximation, maxima, minima, applying the test of second-order derivative
• Integration – How integration is the polar opposite of differentiation, different methods of integration like substitution, calculating integrals of simple functions, division theorem of calculus, introduction to definite integrals
• Integration applications – Simply finding the area swept across by curves like parabolas, finding out the area of a circle and also ellipses
• Differential equations – What are differential equations, how to find their degree, how to find their order, calculating particular solutions of these equations, different types of first-degree homogeneous equations, solving linear equations of differentiability
• Vectors and 3D geometry – Differentiation between vectors and scalars,  conceptualising the magnitude and direction associated with a vector, studying the various types of vectors, properties of a vector, multiplying a scalar and a vector, scalar product of vectors, dot product of vectors, how a vector segregates a line in a given ratio, properties of a line joining two points in terms of direction and ratios, cartesian equation of lines and their vector counterparts, different types of lines, finding out the shortest distance in between two lines as their perpendicular distance, equations of a plane, the distance between a given line and plane
• Fundamentals of linear programming – What are constraints, what is the function objective, what is optimization and how to achieve it, the graphical technique of finding solution of linear programming question, different types of bounded and unbounded regions, non-trivial solutions
• Probability – Introduction to probability with some attached conditional statements, theorems and probability distribution

Game plan for effective studying

• Understanding the syllabus – The word understanding means to analyse the syllabus in-depth and acknowledge the weightage given to each chapter. Some topics are more heavily weighted and so doing them will increase your chances of scoring more. Analysing the syllabus will also make sure you know what to study more and what to study just once/ twice.
• Focus on the long-form questions more – Calculus, differential equations and vectors along with 3D geometry carry the most amount of weightage so strategizing accordingly will prove to be fruitful. Refer to the RS Aggarwal Class 12 Solutions in PDF if you get stuck while solving questions from the RS Aggarwal Class 12 Maths book.
• Segregate your weak and strong points so that it is clear how much time should be invested in each topic and chapter.
• Practice sample papers and previous years’ question papers for a better overview of the exam pattern and even the type of questions that would come. It is best to be prepared in advance and always have some expectations
• Don’t try to rote learn – Mugging up maths is not an option. Instead, try and study every day so that there is ample time to understand everything completely
• Self-evaluate daily to find out about your speed and ability to solve a variety of questions. By doing this, you can find out your strong points and potential shortcomings too.
• Work in a managed and scheduled way – Never lose out on precious time. Try and establish a balance between the studying hours and rest hours. Time management is the key to excellence.

Tips for good marks

• Always make a separate copy containing all the theorems in short, identities and the formulas. Class 12th maths has a lot of these so planning out a separate copy would be extremely helpful.
• Write your exam neatly – Writing neatly is so crucial because it automatically increases the visibility of your answers and gives a good impression to the board checker.
• Never miss out on steps – steps are as important as the final answer. Make sure to write all the steps neatly and compactly for the convenience of the checker
• Never leave any doubts for the last minute
• Always revise each topic multiple times to improve mental retention
• Pay close attention to graphs as they are heavily weighted
• Make good use of the 15 minute reading time
• Check each question after its completion

Class 12th is a board class and maths can be a daunting subject but with sufficient and constant practice, there is an endless scope of scoring well. Try to visualise each concept to grasp it well and focus on your weak points so that no part of the syllabus is left uncharted.