class 12 maths NCERT solutions

Preparing for Class 12 Maths Exam – Most Important Topics

Mathematics is considered to be among the most scoring subjects in class 12. If you have a clear understanding of the concepts and practice regularly, you can even score full marks. But, it is important to note that doing this is not a cakewalk. You need to put in extra effort and be consistent with your studies the whole year. NCERT textbooks are the ones you need to use as your main study material. You can get class 12 maths NCERT solutions pdf online. Read on to learn some of the most important topics of the class 12 Maths syllabus:

  1. Relations and Functions

With a total weightage of 10 marks, you can expect one six marks question from this topic. Here are the important topics you need to focus on:

  • Composition of Two Functions
  • Types of Relations
  • Invertible Functions

The most commonly asked questions from this section are based on the Composition of function and Equivalence relation. You can practice using NCERT and other reference books. Range and domain are important concepts of this chapter, so make sure that you practice a lot of questions based on these. 

  1. Inverse Trigonometric functions

This is the foundation for trigonometry. If you skip this chapter, you will have issues later. The most important topic from this chapter is the properties of inverse trigonometric functions. Make sure that you know the range and domain of all the trigonometric functions and their inverse. Try questions from NCERT and other reference books.

  1. Matrices

This is a new chapter with a weightage of about 5 marks. The expected questions from this chapter are one question for 4 marks and two questions of 1 mark. Important topics of this section include:

  • Multiplication of matrices and other related properties
  • Using elementary transformations for finding the inverse of a matrix
  • Symmetric and skew-symmetric matrices
  1. Determinants

Just like matrices, this is also a completely new and interesting chapter for you. Its weightage is about 5 marks. You can expect one question of 6 marks or 4 marks in the exam. These questions can be finding the inverse of a matrix or a problem on determinants. Here are the important topics of this chapter you need to focus on:

  • Properties of determinants
  • System of Linear Equations’ solution
  • Inverse and adjoint of a matrix
  1. Continuity and Differentiability

This chapter is very important as it serves as a prerequisite to several other chapters of Calculus. Also, if you practice these questions well, you will be able to easily score 2 to 3 marks. Here are the important topics from this chapter:

  • Logarithmic differentiation
  • Continuity of a function
  • Second-order derivatives
  • Differentiating functions in parametric form
  1. Application of derivatives

This is a kind of tricky chapter. There are some sections in this that are easy and scoring like Approximations using differentials and Normals and Tangents to the Curves. The chapter’s weightage is about 12 marks. If you observe question papers from previous years, you will find that there is always one question worth 6 marks from the ‘Application of Maxima Minima’ topic. Here are the important topics from this chapter you need to focus on:

  • Increasing and Decreasing functions
  • Normals and Tangents to Curves
  • Rate of Change of Quantities
  • Finding Local Maxima and Minima Points through first and second derivative tests
  1. Integrals

This is the most scoring and lengthiest chapter of the subject. All of its sections are important as one is usually the base for the other. You cannot skip any topic from this. However, you can focus more on the following:

  • Integration by the Substitution and Partial Fractions method
  • Integration by parts
  • Properties of definite integrals
  • Definite integrals as a limit of a sum
  1. Application of integrals 

Since this chapter is based on the integral formulas, you must learn all the formulas that are used in this chapter. Here are the important topics from this chapter:

  • Area under simple curves
  • Area bounded by two curves, a curve and a line
  1. Differential equations

This is another scoring chapter. Check out the important topics:

  • Formation of differential equations
  • Linear differential equations
  • Homogeneous differential equations
  • Solving differential equations with variable separable
  1. Vector algebra

The important topics from this chapter are:

  • Scalar product of vectors
  • Vector product of vectors
  • Projection of vector on a line
  1. Three Dimensional Geometry

This is considered to be a difficult and time-consuming chapter. But, you can make your preparation efficient by focusing more on the following topics:

  • Direction ratios or direction cosines of line
  • Coplanarity of lines
  • Equation of a line
  • Angle between two lines
  • Equation of a plane in the Normal form
  • Shortest distance between two skew lines
  • Equation of a plane that is passing through a given point and perpendicular to a given vector
  • Equation of a plane that is passing through three noncollinear points
  • Plane that is passing through the intersection of two planes
  • Distance of a point from a plane
  • Angle between two planes
  1. Linear programming

The important topic from this chapter is the graphical solution of linear programming problems.

  1. Probability

Here are the important topics of this chapter you need to focus on:

  • Bayes’ theorem
  • Multiplication theorem on probability
  • Random variable and its probability distribution
  • Independent events
  • Binomial distribution
  • Variance and mean of a random variable

It is important that you focus on the examples and problems given in the NCERT textbooks. Write all the formulas in a separate notebook so that you can use them for revising right before the exam. During the exam, if you come across a question that you don’t know how to solve and there isn’t much time left to figure it out, try showing some effort by writing the introductory steps. If there are some figures relevant to the question, sketch them out. Don’t panic just because you get stuck while solving a question. Leave some space and don’t cross out any of the steps that you have written. This way, even if you don’t have time for solving this question, you will get some marks because of the stepwise marking system followed by CBSE.

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