UP Board Class 12 Maths Syllabus 2020-21 (PDF): Revised & Reduced By 30%

Check UP Board Class 12 Maths Syllabus 2020-21 (Revised & Reduced By Almost 30%) & other important updates. 

Created On: Jan 18, 2021 14:45 IST
UP Board Class 12 Maths Syllabus 2020-21 (PDF): Revised & Reduced By 30%
UP Board Class 12 Maths Syllabus 2020-21 (PDF): Revised & Reduced By 30%

Check UP Board Class 12 Maths Syllabus 2020-21 (Revised & Reduced By Almost 30%). Link to download reduced UP Board Class 12 Maths Syllabus 2020-21 is given at the end of this article. Links to access some other important articles for board exam preparation are also available here.

UP Board Time Table 2021: UP Board Date Sheet 2021 - 10th & 12th 

UP Board Class 12 Maths Syllabus 2020-21 (PDF): Revised & Reduced By 30%

As the regular teaching – learning in schools, during the session 2020-21, has widely been affected due to the Covid – 19 pandemic, the subject experts committee, after due consideration, has recommended to reduce the syllabus by 30% in the following manner :

Almost 30% reduced syllabus :- 

Unit-I Relations and functions 

Relations  and  functions-  Composite  functions,  Inverse  of  a function, Binary Operation. 

Inverse   Trigonometric   function-   Graphs  of  inverse   Trigonometric functions, Elementary Properties of inverse Trigonometric functions. 

Unit-III Calculus 

Continuity and differentiability – 

Roll’s  and  Lagrange’s  mean  value  theorems  (without  proof)  and  their geometric interpretations.  

Unit- IV Vectors and three Dimensional Geometry

Vectors- Scalar Triple Products of Vectors 

Three Dimensional Geometry- 

Angle between (i) Two lines, (ii) Two planes, (iii) A line and a plane.

Unit-VI Probability 

Mean  and  variance  of  random  variable,  Bernoulli  trials  and  Binomial distributions.

Class : 12  

Subject : Mathematics Only Paper

Time : 3 hours, Marks : 70 

Sr.No.

Name of Unit

Marks

1

Relations and functions

10

2

Algebra

13

3

Calculus

44

4

Vectors and three dimensional Geometry

17

5

Linear Programming

06

6

Probability

10

 

Total

100

 

Approximately -70% Syllabus

Unit I : Relations and Functions

Marks : 10 

1) Relations and Functions

 Types  of  relations:  Reflexive,  symmetric,  transitive  and  equivalence relations. One to one and onto functions.

2) Inverse Trigonometric Functions

Definition, range, domain, principal value branches. 

Unit-II: Algebra

Marks : 13

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.

Non- commutativity of multiplication of matrices and existence of non- zero matrices whose product is the zero matrix (restricted 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                                                              

Marks : 44

1- Continuity and Differentiability 

Continuity and differentiability, derivative of composite functions, chain rule, derivative 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.

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 real-life 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 properties of 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 Three-Dimensional Geometry     

Marks : 17 

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. 

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. Distance of a point from a plane.

Unit-V: Linear Programming                                           

Marks : 06 

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 or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability                                                 

Marks : 10

Probability

Conditional  probability,  multiplication  theorem  on  probability, independent events, total probability, Bayes’ theorem. Random Variable and its probability distribution.

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