Tuition Coaching For Cbse Class 12 Mathematics In Arekere Bangalore
Course Structure
Unit I:
Relations and Functions
Unit II:
Algebra
Unit III:
Calculus
Unit IV:
Vectors and ThreeDimensional Geometry
Unit V:
Linear Programming
Unit VI:
Probability
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Mathematics Class 12 Syllabus
Course Structure
Unit

Topic

Marks

I.

Relations and Functions

10

II.

Algebra

13

III.

Calculus

44

IV.

Vectors and 3D Geometry

17

V.

Linear Programming

6

VI.

Probability

10

Total

100

Unit I:
Relations and Functions
1. Relations and Functions
Types of relations: reflexive,
symmetric, transitive and equivalence relations. One to one and onto functions,
composite functions, inverse of a function. Binary operations.
2. Inverse Trigonometric Functions
Definition, range, domain,
principal value branch. Graphs of inverse trigonometric functions. Elementary
properties of inverse trigonometric functions.
Unit II:
Algebra
1. Matrices
Concept, notation, order,
equality, types of matrices, zero and identity matrix, transpose of a matrix,
symmetric and skew symmetric matrices. Operation on matrices: Addition and
multiplication and multiplication with a scalar. Simple properties of addition,
multiplication and scalar multiplication. Noncommutativity of multiplication of
matrices and existence of nonzero matrices whose product is the zero matrix
(restrict to square matrices of order 2).Concept of elementary row and column
operations. Invertible matrices and proof of the uniqueness of inverse, if it
exists; (Here all matrices will have real entries).
2. Determinants
Determinant of a square matrix (up
to 3 x 3 matrices), properties of determinants, minors, cofactors and
applications of determinants in finding the area of a triangle. Adjoint and
inverse of a square matrix. Consistency, inconsistency and number of solutions
of system of linear equations by examples, solving system of linear equations
in two or three variables (having unique solution) using inverse of
a matrix.
Unit III:
Calculus
1. Continuity and Differentiability
Continuity and differentiability,
derivative of composite functions, chain rule, derivatives of inverse
trigonometric functions, derivative of implicit functions. Concept of
exponential and logarithmic functions.
Derivatives of logarithmic and
exponential functions. Logarithmic differentiation, derivative of functions
expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's
Mean Value Theorems (without proof) and their geometric interpretation.
2. Applications of Derivatives
Applications of derivatives: rate
of change of bodies, increasing/decreasing functions, tangents and normals, use
of derivatives in approximation, maxima and minima (first derivative test
motivated geometrically and second derivative test given as a provable tool).
Simple problems (that illustrate basic principles and understanding of the
subject as well as reallife situations).
3. Integrals
Integration as inverse process of
differentiation.Integration of a variety of functions by substitution, by
partial fractions and by parts, Evaluation of simple integrals of the following
types and problems based on them.
Definite integrals as a limit of a
sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof
definite integrals and evaluation of definite integrals.
4. Applications of the Integrals
Applications in finding the area
under simple curves, especially lines, circles/parabolas/ellipses (in standard
form only), Area between any of the two above said curves (the region should be
clearly identifiable).
5. Differential Equations
Definition, order and degree,
general and particular solutions of a differential equation.Formation of
differential equation whose general solution is given.Solution of differential
equations by method of separation of variables solutions of homogeneous
differential equations of first order and first degree. Solutions of linear
differential equation of the type:
dy/dx + py = q, where p and q are
functions of x or constants.
dx/dy + px = q, where p and q are
functions of y or constants.
Unit IV:
Vectors and ThreeDimensional Geometry
1. Vectors
Vectors and scalars, 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,
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, scalar triple product of vectors.
2. Three  dimensional Geometry
Direction cosines and direction
ratios of a line joining two points.Cartesian equation and vector equation of a
line, coplanar and skew lines, shortest distance between two lines.Cartesian
and vector equation of a plane.Angle between (i) two lines, (ii) two planes,
(iii) a line and a plane.Distance of a point from a plane.
Unit V:
Linear Programming
1. Linear Programming
Introduction, related terminology
such as constraints, objective function, optimization, different types of
linear programming (L.P.) problems, mathematical formulation of L.P. problems,
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 nontrivial constraints).
Unit VI:
Probability
1. Probability
Conditional probability,
multiplication theorem on probability. independent events,
total probability, Baye's theorem, Random variable and its probability
distribution, mean and variance of random variable. Repeated independent
(Bernoulli) trials and Binomial distribution.
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