WE understand class 12 maths is no child’s play. School Connect Online provides you NCERT solutions for class 12 Maths to help students as well as tutors. NCERT solutions for each subject, chapter and topic are available for students to read and learn.
NCERT solutions can help the students learn and understand the subject better. With pre researched and expert revised solutions to questions, students can learn and understand how to solve or answer a questions.
It gives students a sample of how and what should be the answer to the question. Also with tons of homework and work pressure on students, NCERT solutions for maths for class 12 can make the homework easier and less confusing.
Benefits of Ncert solutions class 12 maths
In the final exam, questions are asked from these NCERT exercise problems. The questions are designed to increase students analytical skills and learning. Thus, should at least practise once all the exercise problems from the textbooks before the exams.
Sometimes students get stuck and are not able to solve the questions. So, to help them we have provided detailed step by step NCERT Solutions for class 12 maths. These solutions will also help students in writing the answers in a better way from the exam perspective, so that they score more marks in exams.
|CBSE Maths Notes For Class 12|
|Chapter 1 – Functions and Relations|
|Chapter 2 – Inverse Trigonometric Functions|
|Chapter 3 – Matrices|
|Chapter 4 – Determinants|
|Chapter 5 – Continuity And Differentiability|
|Chapter 6 – Application of Derivatives|
|Chapter 7 – Integrals|
|Chapter 8 – Application of Integrals|
|Chapter 9 – Differential Equation|
|Chapter 10 – Vector Algebra|
|Chapter 11 – Three Dimensional Geometry|
|Chapter 12 – Linear Programming|
|Chapter 13 – Probability|
Chapter 1 – Functions and Relations
Relations and Functions are an integral part of Mathematics, which helps to define the different concepts, along with different types of specific valued functions along with their graphs.
Chapter 2 – Inverse Trigonometric Functions
The inverse trigonometric functions is an important aspect of trigonometric functions, included in the syllabus for class 12 students. Inverses of trigonometric functions exist solely due to the restrictions existing on the domains and their respective ranges. Being able to solve inverse trigonometric function problems starts by understanding the trigonometric ratios first.
The behavior of these trigonometric functions is usually represented in the form of graphical methods. They play an essential role in calculus as they help to define different integrals. The major applications of inverse trigonometric functions in everyday life are in the fields of science and engineering.
Chapter 3 – Matrices
Matrices are an important branch of mathematics, which also helps students understand other mathematical concepts due to the interrelatedness to other branches. A matrix can be defined as an array of numbers or functions arranged in a rectangular order.
A matrix which possesses rows titled “X” and columns titled as “Y” is called as a matrix of an order of X x Y. The major operations carried out with Matrices are the Addition, Subtraction, and Multiplication.
Chapter 4 – Determinants
When a square matrix “A” of an order “n” is associated with a number, then it is titled as a determinant of the aforementioned matrix. The number involved in this square matrix can be a real number or a complex number.
Chapter 5 – Continuity And Differentiability
In continuity and differentiability class 12, we will learn important concepts of differentiability, continuity, and relationship between them. Also, other important concepts like the differentiation of inverse trigonometric functions and new functions like logarithmic and exponential functions.
Chapter 6 – Application of Derivatives
There are various applications of derivatives not only in maths and real life but also in other fields like science, engineering, physics, etc. In previous classes, you must have learned to find the derivative of different functions, like, trigonometric functions, implicit functions, logarithm functions, etc. In this chapter, you will learn the use of derivatives with respect to mathematical concepts and in real-life scenarios. This is one of the important topics covered in Class 12 Maths as well.
Derivatives have various important applications in Mathematics such as:
- Rate of Change of a Quantity
- Increasing and Decreasing Functions
- Tangent and Normal to a Curve
- Minimum and Maximum Values
- Newton’s Method
- Linear Approximations
Chapter 7 – Integrals
Integration is referred to the process which is inverse to that of differentiation. In the integration, we will be responsible for finding the function whose differential is provided to us. Integrals are the functions which satisfy a given differential equation.
Chapter 8 – Application of Integrals
There are a number of methods of calculations among which are functions, differentiation and integration. Application of Integrals is applied in various fields like Mathematics, Science, Engineering etc.An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Therefore, finding the integral of a function with respect to x means finding the area to the X-axis from the curve. The integral is also called as anti-derivative as it is the reverse process of differentiation.
Chapter 9 – Differential Equation
The equation which involves the derivative of the variable which is dependent with respect to the independent variable is known as differential equations. The order here is given to the highest order of the occurring derivative. The degree is given to the presence of the polynomial equation in the derivatives.
Chapter 10 – Vector Algebra
Vector algebra is one of the essential topics of algebra. It studies the algebra of vector quantities. As we know, there are two types of physical quantities, scalars and vectors. The scalar quantity has only magnitude, whereas the vector quantity has both magnitude and direction.
In essence, vector algebra is an algebra where the essential elements usually denote vectors. We perform algebraic operations on vectors and vector spaces. This branch has rules and hypotheses based on the properties and behaviour of vectors.
Chapter 11 – Three Dimensional Geometry
Three Dimensional Geometry for class 12 covers the important topics such as direction cosine and direction ratios of a line joining two points. Also, we will learn here the equation of lines and planes in space under different conditions, the angle between line and plane, between two lines etc. You need to practice the questions to understand the topic better and based on the formulas as well.
Chapter 12 – Linear Programming
Here, the variables are non-negative and satisfy a set of linear inequalities (called linear constraints) and the problems have the goal to find the optimal value (maximum or minimum) of a linear function of several variables (called objective function) with respect to the conditions. Variables are sometimes called decision variables and are non-negative in nature.
Chapter 13 – Probability
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.
The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
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NCERT Question Papers
The question papers are prepared by the CBSE and other boards in accordance with the NCERT exam guidelines. Here, we have provided the question papers for class 6 to 12. By solving them students will get an idea about the question paper pattern, types of questions asked, marks distribution and important topics. These question papers will be more helpful for the class 12 maths and competitive exams.