How to prepare and score Good marks in Math Paper?

As far as competitive exams are concerned, especially those related to the engineering field, Mathematics becomes a very important subject. It is easy to score a 100 in Mathematics in board examination. You just need to work hard with dedication.

  1. Prepare a good Timetable – Have an ample amount of sleep and small breaks in between your study time. A minimum of 4 hours a day is necessary to score well in Maths. Sleep and proper diet will help you increase your concentration power. Also, try to make your timetable in a way that is able to complete the harder and boring chapters first. So that you remain free from any kind of stress and can prepare well for board exams.
  2. Keep a reference material at hand (CBSE Study Material/CBSE Study Notes) – The best reference material is the one that has maximum accuracy and least scope for errors. These CBSE Study Material/CBSE Study Notes are just the right thing to keep as a reference. You can also find Toppers’ notes online, for free. Just like the CBSE materials, Topper’s notes are also a very good source of accurate and up-to-date information.
  3. Solve the CBSE previous years’ question paper – The most reliable way to test your preparation is to solve the CBSE previous years’ question paper. This will help you identify the chapters where you need to give extra attention to. This way you’ll be able to prepare good answers for boards.
  4. Try online test of maths class 12 – After solving the previous years’ papers, you can solve these class 12th practice tests. These online tests of maths class 12 will help in enhancing your skills by the variety of questions they offer. The pattern of questions asked in these class 12th practice tests will prove to be useful in strengthening your concepts and analytical thinking.

Here Are The Important Chapter-Wise Topics In Mathematics

Relations and Functions

  1. Types of relations:
    1. Reflexive Symmetric
    2. Transitive
    3. Equivalence relations
    4. One to one and onto functions
    5. Composite functions
    6. The inverse of a function
  2. Binary operations

Inverse Trigonometric Functions

  1. Range, domain and principal value branch
  2. Graphs of inverse trigonometric functions
  3. Elementary properties of inverse trigonometric functions

Matrices

  1. Understanding of notation, order, equality of matrix, types of matrix, zero and identity matrix
  2. Types of matrices, zero and identity matrix
  3. Questions based on transpose of a matrix, symmetric and skew-symmetric matrices, operation on matrices (i.e. Addition and multiplication and multiplication with a scalar)
  4. Invertible matrices and proof of the uniqueness of inverse, if it exists

Determinants

  1. The determinant of a square matrix (up to 3 × 3 matrices)
  2. Properties of determinants
  3. Adjoint and inverse of a square matrix
  4. Consistency, inconsistency and number of solutions of a system of linear equations
  5. Solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix

Continuity and Differentiability

  1. Continuity & differentiability
  2. Differentiation of –
    1. Composite functions
    2. Inverse trigonometric functions
    3. Implicit functions
  3. Concept of exponential & logarithmic functions
  4. The derivative of functions expressed in parametric forms
  5. Second-order derivatives
  6. Questions based on Rolle’s and Lagrange’s Mean Value Theorems

Application of Derivatives

  1. Rate of change of bodies
  2. Increasing/decreasing functions
  3. Tangents and normals
  4. Use of derivatives in approximation
  5. Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool) very important
  6. Simple problems that illustrate basic principles and understanding of the subject as well as real-life situations

 

Integrals

  1. Integration of a variety of functions
    1. by substitution
  2. by partial fractions
  3. by parts
    1. Evaluation of simple integrals of the following types and problems based on them
    2. Definite integrals as a limit of a sum
    3. Fundamental Theorem of Calculus (without proof)
    4. Basic properties of definite integrals and evaluation of definite integrals

Application of Integrals

  1. Applications in finding the area under simple curves
  2. Especially lines, circles/parabolas/ellipses (in standard form only)
  3. The area between any of the two above-said curves (the region should be clearly identifiable)

Differential Equations

  1. Order and degree
  2. General and particular solutions of a differential equation
  3. The Formation of a differential equation with the given general solution
  4. The solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of the first order and first-degree
  5. Solutions of a linear differential equation

Vector Algebra

  1. Vectors and scalars (magnitude and direction of a vector)
  2. Direction cosines and direction ratios of a vector
  3. The position vector of a point dividing a line segment in a given ratio
  4. Properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, the scalar triple product of vectors

Three Dimensional Geometry

  1. Direction cosines and direction ratios of a line joining two points
  2. Cartesian equation and vector equation of line
  3. Coplanar and skew lines
  4. The shortest distance between two lines
  5. Cartesian & vector equation of a plane
  6. Angle between
    • two lines
    • two planes
    • a line and a plane
  7. The distance of a point from a plane

Linear Programming

  1. The mathematical formulation of L.P. problems
  2. Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded)

Probability

  1. Conditional probability
  2. Multiplication theorem on probability
  3. Independent events
  4. Bayer’s theorem
  5. Random variable & its probability distribution
  6. Mean and variance of random variable
  7. Repeated independent (Bernoulli) trials and Binomial distribution