__Class 12 Maths
Chapters__

__Class 12 Maths Chapters__

**1 ****Relations and Functions**** –** This Chapter is consists of 5
exercises based on the following concepts: Equivalence relations:
reflexive, symmetric, transitive, Injective(one-to-one) and Surjective(onto),
composite functions, concepts of inverse function and Binary operations.

**2 ****Inverse
Trigonometric Functions** – This chapter has 2 exercises and 1
Miscellaneous based on the following concepts: Definition, Range, Domain, Principal
value of the trigonometric function, Graphs of inverse trigonometric
functions. Elementary properties and use of formulas of inverse
trigonometric functions.

**3 ****Matrices** – This Chapter has 4
exercises and Miscellaneous exercise: Concept, notation, order, equality, types of matrices: Square, Rectangular,
Diagonal, Scalar, zero and identity matrix, transpose of a matrix, concepts
of symmetric and skew-symmetric matrices and how to express as a sum of both.
Operation on matrices. properties related to addition, multiplication and
scalar multiplication. Noncommutativity of multiplication of matrices and
existence of inverse matrices

Elementary row and column operations to find inverse of matrices. Invertible
matrices and proof of the uniqueness of inverse, if it exists; (Here all
matrices will have real entries).

**4 ****Determinants** – This Chapter
Includes 6 exercises and 1 Miscellaneous exercise which has the following concepts:
Introduction, Determinant of a square matrix (up to 3 x 3 matrices),
properties of determinants, minors, area of a triangle. Adjoint and inverse of
a square matrix. Consistency, inconsistency, and number of solutions of a
system of linear equations by examples, solving system of linear equations
in two or three variables with the use of inverse matrix concepts.

**5 ****Continuity
and Differentiability**** –** This Chapter
comprising of 6 exercises and 1 Miscellaneous exercise with the following
concepts: Definition of Continuity and differentiability and question
based on this, Chain rule, derivative of the following function: composite
functions, inverse trigonometric functions, implicit functions. exponential
and logarithmic functions, derivatives of functions expressed in
parametric forms. Second-order derivatives. Rolle’s and Lagrange’s Mean Value
Theorems (without proof) and their geometric interpretation.

**6 ****Applications
of Derivatives** – This Chapter has 5
exercises and 1 Miscellaneous exercise which includes following concepts: rate
of change, Concept of increasing/decreasing functions, how to tangents
and normal and equation of tangent and normal, use of derivatives in approximation,
maxima, and minima using first derivative test and second derivative test.
Simple problems (that illustrate basic principles and concepts of the chapters
as well as real-life situations).

**7 ****Integrals** – This Chapter has 11
exercises with 1 Miscellaneous exercise and contains following concept: Methods
of Integration; Simple Integration, Integration
of a variety of functions by substitution, by partial fractions and by
parts, Definite integrals as a limit of a sum, Fundamental Theorem of Calculus
(without proof). Basic properties of definite integrals and evaluation of
definite integrals.

**8 ****Applications
of the Integrals** – This chapter has 2
exercises and 1 Miscellaneous exercise with the following concepts: finding
the area under simple curves especially lines, circles/parabolas/ellipses
(in standard form only), Area between any of the two curves, circle,
parabola, and ellipse.

**9 ****Differential
Equations** – This chapter is comprising of 6 exercises
and 1 Miscellaneous exercise which includes the following concepts: Definition,
order and degree, how to general and particular solutions of a differential
equation. Formation of differential equations whose general solution is
given. Solution of differential equations by the method of homogeneous
differential equations of first order and first degree. Solutions of
linear differential equation.

** **

**10 ****Vectors** – This Chapter has 4 exercises and one Miscellaneous exercise. It includes
the following concepts; Vectors or scalars, graphical displacement, magnitude
and direction of a vector. Direction cosines and direction ratios of
a vector. Types of vectors: equal, unit, zero, parallel and collinear
vectors, position vector of a point, negative of a vector, components of a
vector, addition of vectors using triangle law and parallelogram law, multiplication
of a vector by a scalar, position vector of a point dividing a line
segment in a given ratio. Definition, Geometrical Interpretation,
properties and application of scalar (dot) product of vectors, vector (cross)
product of vectors, Projection of vector on a line, scalar triple product
of vectors.

**11 ****Three–Dimensional
Geometry** – This chapter has 3
exercises and one Miscellaneous exercise which contains questions based on Direction
cosines and direction ratios of a line joining two points. Cartesian equation
and vector equation of a line, equation of plane in: Normal form,
Perpendicular to vector and passing through point, Passing through three non
collinear points, Intercept form and passing through intersection of planes, Coplanarity
of two lines, equations of lines under planes conditions, coplanar and skew
lines, shortest distance between two lines. Angle between

· two lines

· two planes

· a line and a plane.

·
Distance of a point from a plane.

**12 ****Linear
Programming** – This Chapter has 2
exercises and 1 Miscellaneous exercise which includes questions based on: Introduction,
Linear Programming problem and its Mathematical Formulation, mathematical
formulation of problem, definition of constraints, objective function,
optimization, graphical method of solution for problems in two variables,
feasible and infeasible regions(bounded and unbounded), feasible and
infeasible solutions, optimal feasible solutions (up to three non-trivial
constraints).

**13 ****Probability** – This Chapter has 5 exercises and 1 Miscellaneous exercise which includes
questions based on: Conditional probability and its properties,
multiplication theorem, independent events, Bayes’ theorem (partition of a
sample space), Theorem of total Probability, Random variable and its
probability distribution of a random variable, mean and variance of a random variable.
Bernoulli trials and Binomial distribution.

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