Karnataka Board Class 12 Maths Syllabus

15-07-2021 jAzÀ

15-09-2021 gÀvÀgÉUÉ

(Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.)

2. Inverse Trigonometric Functions 2.1

(Definition, range, domain, principal value branch.)

6 hours

3 hours

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, Invertible matrices; (Here all matrices will have real entries)

7 hours

applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.)

8hours

(Limits and Derivatives first PUC revision 2 hours)

(Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.)

12hours

13-09-2021 jAzÀ

15-09-2021 gÀvÀgÉUÉ

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16-09-2021 jAzÀ

30-11-2021gÀvÀgÉUÉ

(Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives)

6.               Applications of Derivatives 6.3 to 6.6

(increasing/decreasing functions, tangents and normals, 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)

7.            Integrals 7.1 to 7.6

(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

1                           1                          1                            1                             1                          1

types∫             𝑑𝑥, ∫            𝑑𝑥, ∫            𝑑𝑥, ∫                         𝑑𝑥, ∫            𝑑𝑥, ∫             𝑑𝑥,

𝑎2+ 𝑥2                        𝑎2−𝑥2                         𝑥2−𝑎2                         √𝑥2−𝑎2                                            √𝑥2+𝑎2                     √𝑎2−𝑥2

and problems based on them. )

12. Linear Programming

(Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems. Graphical method of solution for problems in two variables, feasible and infeasible regions (bounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

7hours

7hours

14hours

5 hours

20-11-2021 jAzÀ

30-11-2021 gÀvÀgÉUÉ

01-12-2021 jAzÀ

30-01-2022gÀvÀgÉUÉ

Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

8.            Applications of the Integrals 8.1

6hours

parabolas; area of circles /ellipses (in standard form only) (the region should be clearly identifiable)

equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree of the type: 𝑑𝑦/𝑑𝑥 = f(y/x). Solutions of linear differential equation of the type: dy/ dx + py = q, where p and q are functions of x or constant.)

6 hours

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)

7 hours

equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane.

Distance of a point from a plane.)

7 hours

events, total probability, Bayes’ theorem, Random variable and its probability distribution.)

28-01-2022 jAzÀ

01-02-2022 jAzÀ

31-03-2022gÀvÀgÉUÉ

(Composite functions, Invertible functions and Binary operations)

2.            Inverse Trigonometric Functions

(Properties of Inverse trigonometric functions and problems)

3.            Matrices

(Inverse of a matrix by elementary operations)

4.            Determinants

(Properties of Determinants and problems)

5.            Continuity and Differentiability

(Mean Value Theorem andRolle’s Theorem)

6.            Application of Derivatives

(Rate of change of quantities and Approximation) 7.Integration

( Definite integral as alimit of a sum)

8. Application of Integrals

(Area bounded by curve and line Area between two curves) 9.Differential Equation

(Formation of a Differential Equation whose General Solution is given. Solution of Linear differential equation of the type dx/dy +py=q)

10.  vector

(Scalar triple product of three vectors and problems)

11.  Three Dimensional Geometry

(Angle between two lines, Angle between two planes and Angle between line and planes)

13. Probability

(Mean and Variance of a Random variable. Bernoulli Trials an Binomial Distribution)

4 hours

24-03-2022 jAzÀ

30-03-2022

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