CBSE 12 Maths Commerce
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 Class 12-commerce Textbook Solutions, Videos, Sample Papers & More
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.
CBSE Class 12-commerce MIQs, Subjective Questions & More
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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.
FAQs
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.
Will online study help me score more marks?
TopperLearning’s intense practice and revision-based study materials ensure that if students practise and revise with dedicated effort, they will do well in the exams.
What should I read during CBSE Class 12 exam revision?
Besides enabling you with the appropriate preparation, our chapter and revision notes are great for a quick brush up before your exams.
If I find a concept difficult to understand, whom should I ask?
If you struggle to understand a concept, you can refer to our video lessons. Should you still have some doubts, you can always use our UnDoubt (Ask the Expert) forum and get them clarified as soon as possible.
Is TopperLearning equipped enough to help me?
Yes, we have 950+ video lessons, 200+ revision notes, a question bank with 8500+ questions and 15+ sample papers (including CBSE Class 12 sample papers 2019) for CBSE students. TopperLearning’s CBSE Class 12 study materials are designed to give you clarity of the concepts that you study in class.
CBSE Class 12-commerce Maths Frequently Asked Questions
All chapters of class 12-commerce Maths CBSE, in the prescribed syllabus by the CBSE and based on the NCERT curriculum have their importance and weightage. TopperLearning have taken into consideration all minute details from the curriculum to ensure that the syllabus of class 12-commerce Maths CBSE is aligned properly. Each chapter of class 12-commerce Maths CBSE has various concepts that are aligned to the NCERT Learning outcomes and plays a specific role in improving outcomes. CBSE class 12-commerce Maths chapter list will give you an idea of the entire course curriculum coverage.
To start with Class 12-commerce Maths CBSE, one should clearly understand the syllabus and course structure first. Teachers will help giving an introduction and of the syllabus and ways it will help them to improve their learning levels. Once a learner slowly understands the concepts, it is recommended to initiate practice a habit. ToppeLearning can aid students to practice with tests and do a quick revision of the concepts learnt in the class with important resources like Video lessons, notes and sample papers. Practicing and revising all these resources from initial will help them understand the concepts with clarity. Nowadays, the questions are asked keeping in mind the problem solving and applications of concepts into consideration. Always try to clear the concepts of Class 12-commerce Maths CBSE that you do not understand. Avoid skipping topics or concepts. Revise crucial topics watching concept and problem solving videos at TopperLearning after your school or online classes or as required.
To score good marks in Maths Class 12-commerce CBSE, one needs to understand the concepts really well. If a learner is well aware of the core concepts then it becomes very easy to attempt problems asked on those concepts. This also motivates learners to gain knowledge and excel in studies. Once a learner has understood the concepts in Maths Class 12-commerce CBSE then practice should become a daily ritual as it is the key to let know about strengths and weaknesses. For subjects like Maths, practice is the key. For Science, knowing how to apply a learnt concept into daily life and problem solving is crucial. Once a learner is able to know what is happening around, can relate to the theories learnt in the books. Writing answers is also a good habit as it strengthens your communication skills and keeps a check on areas to improve which will enable scoring good marks in exams. Keep revising crucial topics watching concept and problem solving videos at TopperLearning after your school or online classes or as required.
Some students consider Class 12-commerce Maths chapters as interesting than Science chapters. Actually, the interests vary from student to student as some like History chapters than Class 12-commerce Maths. It is very evident that most students who like Maths, chapters related to Algebra, Percentages, Profit and Loss, Trigonometry, etc. interested the most. Students who have planned for various scholarships, Olympiads or competitive exams mostly find chapters related to metals and non-metals, acids and bases, light, energy, work, power, etc. In Social Maths, students mostly find interests in stone and Iron Age history, about the medieval age, world history and India’s struggle for independence, etc. At TopperLearning you will get access to the bank of resources in the form of videos, notes, a huge question bank, Class 12-commerce Maths NCERT solutions etc., which will help you gain knowledge on the chapters that interest you the most. Just make sure to go through the TopperLearning Plans for your board-grade combination.
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.
TopperLearning’s intense practice and revision-based study materials ensure that if students practise and revise with dedicated effort, they will do well in the exams.
Besides enabling you with the appropriate preparation, our chapter and revision notes are great for a quick brush up before your exams.
If you struggle to understand a concept, you can refer to our video lessons. Should you still have some doubts, you can always use our UnDoubt (Ask the Expert) forum and get them clarified as soon as possible.
Yes, we have 950+ video lessons, 200+ revision notes, a question bank with 8500+ questions and 15+ sample papers (including CBSE Class 12 sample papers 2019) for CBSE students. TopperLearning’s CBSE Class 12 study materials are designed to give you clarity of the concepts that you study in class.