UP Board Class 12 Maths Syllabus 202021 (PDF): Revised & Reduced By 30%
Mayank UttamCheck UP Board Class 12 Maths Syllabus 202021 (Revised & Reduced By Almost 30%). Link to download reduced UP Board Class 12 Maths Syllabus 202021 is given at the end of this article. Links to access some other important articles for board exam preparation are also available here.
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UP Board Class 12 Maths Syllabus 202021 (PDF): Revised & Reduced By 30%
As the regular teaching – learning in schools, during the session 202021, 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 :
UnitI 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.
UnitIII 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.
UnitVI 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.
UnitII: 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.
UnitIII: 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 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 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.
UnitIV: Vectors and ThreeDimensional 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.
UnitV: 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 nontrivial constraints).
UnitVI: 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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