CBSE Class 12 commerce Maths
Maths is considered one of the most difficult subjects in CBSE Class 12 Commerce. One should be attentive and practice Maths regularly. In CBSE Class 12 Maths, the level of difficulty is high, as you get introduced to complex topics like integration and differentiation. Our Maths experts simplify complex Maths problems by assisting you with the right methods to solve them so that you can score full marks. You may still have doubts while referring to the Maths revision notes or Maths NCERT solutions. Get these doubts resolved by Maths experts through the UnDoubt section of our website.
CBSE 12 Maths Commerce Chapters
Chapter 1 Relations and Functions
The CBSE Class 12 Relations and Functions chapter talks about relations and functions, types of relations, types of functions, composition of functions, invertible functions and binary operations with many examples. Students get to learn about empty relation, universal relation, reflexive relation, symmetric relation, transitive relation and equivalence relation.
Chapter 2 Inverse Trigonometric Functions
The CBSE Class 12 Maths chapter explains inverse trigonometric functions in detail. This chapter includes the definition, range, principle value branch and graphs of inverse trigonometry. Trigonometric functions are also known as arc functions. The function of inverse trigonometry is the opposite of the trigonometric functions. This means the opposite of sine, cosine, tangent, cosecant, secant and cotangent. These six points are used in a right-angled triangle to find the measure of an angle and when the lengths of two sides of a triangle are known.
Chapter 3 Matrices
The CBSE Class 12 Matrices chapter gives the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of transpose of the matrix, symmetric and skew symmetric matrices, elementary operation or transformation of a matrix and inverse of a matrix by elementary operations along with several examples.
Chapter 4 Determinants
The CBSE Class 12 Determinants chapter explains the definition and meaning of determinants, remarks based on the order of determinants, properties of determinants, finding the area of a triangle using determinants, minors and cofactors of determinants, adjoint of a matrix, inverse of a matrix, applications of determinants and matrices with many examples. Students will also learn about consistency and inconsistency in numbers.
Chapter 5 Continuity and Differentiability
The CBSE Class 12 Maths chapter of Continuity and Differentiability focuses on derivatives of composite functions, chain rule, derivatives of inverse trigonometric functions and derivatives of implicit functions. The chapter then goes on to explain the concept of exponential and logarithmic functions and the meaning of derivatives of logarithmic and exponential functions. The chapter also elaborates on logarithmic differentiation and derivatives of functions expressed in parametric forms, including second-order derivatives. After the main pillars are explained, it then focuses on Rolle’s and Lagrange’s mean value theorems and their geometric interpretation.
Chapter 6 Applications of Derivatives
The CBSE Class 12 Maths chapter of Application of Derivatives is a sub-topic of Continuity and Differentiability and focuses on the areas where derivatives can be applied. In the previous chapter, we learnt about the concept of exponential and logarithmic functions and the derivatives of logarithmic and exponential functions. This chapter focuses on the applications of derivatives on the rate of change of bodies, increasing/decreasing functions, tangents and normals. It then moves on to the usage of derivatives in approximation, maxima and minima.
Chapter 7 Integrals
This CBSE Class 12 Maths chapter teaches Integrals in an elaborate manner. Integration is the inverse process of differentiation. Integration denotes the summary of hidden data. Integrals are used to calculate and find the functions to describe area, displacement or volume which occurs due to a small collection of data and things which cannot be measured singularly. Integration is an amalgamation of a variety of functions by substitution, by partial fractions and by parts. This chapter also explains definite integrals and the fundamental theorem of Calculus.
Chapter 8 Applications of Integrals
This CBSE Class 12 Maths chapter continues to discuss integrals with proper definitions. It then moves on to discuss how to find the area under simple curves, area of the region bounded by a curve and a line, area between two curves etc.
Chapter 9 Differential Equations
This CBSE Class 12 chapter teaches us about differential equations and the change rate of a function. Applications studied here are also extensively used in the fields of Engineering, Biology and Physics. The main objective of differential equations is to observe the solution that completes the equation. One of the easiest approaches to solving problems in differential equations is to use the explicit formula. This chapter also talks about the method of separation of variables and solutions of homogeneous differential equations of the first order.
Chapter 10 Vector Algebra
The CBSE Class 12 Maths chapter of Vector Algebra explains vectors and their functionalities. A vector defines the movement of an object from point A to point B. It can be pictured as a straight line, where the straight line is called the magnitude of the vector, and the angle at which the vector is inclined shows the direction of the vector. You will learn about the tail and head of a vector and more about Vector Math in this chapter.
Chapter 11 3-Dimensional Geometry
The CBSE Class 12 Maths chapter of 3-Dimensional Geometry video explains how direction cosines and direction ratios of a line join two points. It further goes on to explain the Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines, and finally, Cartesian and vector equation of a plane. It also explains the angle between two lines, two planes, a line and a plane, and the distance of a point from a plane.
Chapter 12 Linear Programming
The CBSE Class 12 Maths chapter of Linear Programming introduces students to terminology such as constraints, objective function and optimisation and different types of linear programming problems. It also covers the mathematical formulation of linear programming problems, the graphical method of finding the solutions in two variables, feasible and infeasible regions (bounded and unbounded) and optimal feasible solutions (up to three non-trivial constraints).
Chapter 13 Probability
The CBSE Class 12 Maths chapter of Probability defines several aspects of concepts like conditional probability and multiplication theorem on probability. Probability means possibility. It is a branch of Mathematics which deals with the occurrence of a random event. The value is expressed between zero and one. Probability helps us to predict how likely an event is to happen.
At TopperLearning, you can find study resources such as sample papers, mock tests, CBSE Class 12 Maths NCERT solutions and more. These learning materials can help you understand concepts such as differentiation of functions, direction cosines, integrals and more. Also, you can practise the Maths problems by going through the solutions given by our experts.
Why are study resources for CBSE Class 12 Commerce Maths important?
Maths is a subject which requires practising a variety of problems to understand concepts clearly. By solving as many problems as you can, you’ll be able to train your brain in thinking about the logical way to solve Maths problems. For practising problems, study materials such as sample papers, previous years’ papers and NCERT solutions are needed.
Our Maths experts give you the best solutions for Maths textbook questions and sample paper questions. Chapter-wise NCERT solutions for CBSE Class 12 Commerce Maths are easily accessible at TopperLearning. Use these solutions to practise problems based on concepts such as direction ratios, probability, area between lines, inverse trigonometric functions and more.
To prepare for your Maths exam, you need to attempt solving different kinds of Maths questions. One of the best ways to assess your problem-solving abilities is to attempt solving previous years’ papers with a timer set. Our Maths solutions for previous years’ papers will come in handy to help you with checking your answers. So, to score more marks in your Class CBSE 12 board exams, make use of our Maths study resources.
Where can I find the important questions for the CBSE Class 12 exam?
Our Most Important Questions or MIQs are a dedicated section which lists the important questions which are most likely to be asked in the exam.
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