Bihar Board Class 12 Mathematics Syllabus

Bihar Board Class 12 Mathematics Syllabus

Bihar Board students who is preparing day and night to give exam for Bihar Board Inter Examination 2020. Inter students are well aware of the importance of marks in the board exams as it will not only help them in good grades but also in choosing the best colleges. 

There are famous sayings that Bihar students always fare well in mathematics and it’s quite true. Mathematics Exam 2020 is going to be bit difficult keeping it in mind. We are providing the complete Bihar Board Class 12 Mathematics Syllabus 2020.

The Mathematics syllabus for Class 12 of the Bihar Board will give you a better strategy for preparing of maths paper. The Bihar Board Class 12 Mathematics Syllabus includes various units such as Relations and Functions, Vectors and 3 Dimensional Geometry, Algebra, Calculus, Linear Programming, Probability etc. 

Bihar Board Class 12th Mathematics Syllabus with Marks Distribution

Bihar Board Inter students get detailed information about the latest Bihar Board 12th Mathematics Syllabus 2020. You know that Bihar Board Class 12th Mathematics Syllabus contains 6 Units that carry a total of 100 Mark. As there will not be any practical exam for mathematics subject. Before going into the details of Inter Mathematics Syllabus we are providing each chapter and associated weightage of each chapter. 

Bihar Board Class 12 Mathematics Syllabus (Complete)

Students can find the detailed Mathematics Syllabus for Bihar Board Class 12th. We suggest students take the help of NCERT books also for better planning. Bihar board.xyz is providing the complete Bihar Board Class 12 Maths Syllabus in PDF. You can download Bihar Board Inter Syllabus free. 

Unit Name

इकाई का नाम

Weightage

Unit 1: Relations and Functions इकाई1: संबंध एवं फलन 10
Unit 2: Algebra इकाई 2: बीजगणित 13
Unit 3: Calculus इकाई 3: कलन शास्त्र 40
Unit 4: Vectors and 3 Dimensional Geometry इकाई 4: सदिश एवं त्रि विमीय-ज्योमिति 18
Unit 5: Linear Programming इकाई 5: रैखिक प्रोग्रामन 09
Unit 6: Probability इकाई 6: प्रायिकता 10
Total 100 Marks

Detailed Chapterwise Bihar Board Class 12 Maths Syllabus

The Mathematics paper of Bihar Board Class 12 (Intermediate 2nd year) consists of total of 100 marks with 3 hours of time duration. While topics related to Calculus are allocated 40 marks, the rest of the topics are allocated 9 to 18 marks each. The syllabus below is as per the latest Bihar State Board Books.

Unit 1: Relations and Functions

i) 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.

ii) Inverse Trigonometric Functions

  • Definition, range, domain, principal value branch.
  • Graphs of inverse trigonometric functions.
  • Elementary properties of inverse trigonometric functions.

Unit 2: Algebra

i) 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 matrices
  • Concept of elementary row and column operations.
  • Invertible matrices and proof of the uniqueness of inverse

ii) Determinants

  • The 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 a system of linear equations by examples,
  • Solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Unit 3: Calculus

i) Continuity and Differentiability

  • Continuity and differentiability
  • Derivatives of composite functions, chain rule
  • Derivatives of inverse trigonometric functions
  • Derivatives 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.

 

ii) 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).

iii) Integrals

  • Integration as the 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.

Bihar board class 12 Maths Syllabus

  • Definite integrals as a limit of a sum
  • Fundamental Theorem of Calculus (without proof)
  • Basic properties of definite integrals and evaluation of definite integrals.

 

iv) Applications of 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).

 

v) Differential Equations

  • Definition, order, and degree, 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 separation of variables solutions of homogeneous differential equations of the first order and first degree.
  • Solutions of a linear differential equation of the type:

            dy/dx + py = q, where p and q are functions of x or constants.

Unit 4: Vectors and 3 Dimensional Geometry

i) 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.

 

ii) 3 – 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.
  • Angle between

(a) two lines,

(b) two planes

(c) a line and a plane

Unit 5: 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 non-trivial constraints).

Unit 6: Probability

  • Multiplication theorem on probability
  • Conditional probability
  • Independent events, total probability
  • Baye’s theorem, Random variable and its probability distribution,
  • Mean and variance of the random variable.
  • Repeated independent (Bernoulli) trials and Binomial distribution.

 

इकाई 1. संबंध एवं फलन (Relations and Functions)

संबंध एवं फलन

  • संबंधों के प्रकार
  • फलनों के प्रकार
  • फलनों का संयोजन तथा व्युत्क्रमणीय फलन
  • द्वि-आधारी संक्रियाएँ

प्रतिलोम त्रिकोणमितीय फलन

  • आधारभूत संकल्पनाएँ
  • प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म

 

इकाई 2. बीजगणित (Algebra)

आव्यूह

  • आव्यूह
  • आव्यूहों के प्रकार
  • आव्यूहों पर संक्रियाएँ
  • आव्यूह का परिवर्त
  • सममित तथा विषम सममित आव्यूह
  • आव्यूह पर प्रारंभिक संक्रिया (आव्यूह रूपांतरण)
  • व्युत्क्रमणीय आव्यूह

सारणिक

  • सारणिक
  • सारणिकों के गुणधर्म
  • त्रिभुज का क्षेत्रफल
  • उपसारणिक और सहखंड
  • आव्यूह के सहखंडज और व्युत्क्रम
  • सारणिकों और आव्यूहों के अनुप्रयोग

 

इकाई 3. कलन (Calculus)

सातत्य तथा अवकलनीयता

  • सातत्य
  • अवकलनीयता
  • चरघातांकी तथा लघुगणकीय फलन
  • लघुगणकीय अवकलन
  • फलनों के प्राचलिक रूपों के अवकलज
  • द्वितीय कोटि का अवकलज
  • माध्यमान प्रमेय

अवकलज के अनुप्रयोग

  • राशियों के परिवर्तन की दर
  • वर्धमान और ह्रासमान फलन
  • स्पर्श रेखाएँ और अभिलंब
  • सन्निकटन
  • उच्चतम और निम्नतम

समाकलन

  • समाकलन को अवकलन के व्युत्क्रम प्रक्रम के रूप में
  • समाकलन की विधियाँ
  • कुछ विशिष्ट फलनों के समाकलन
  • आंशिक भिन्नों द्वारा समाकलन
  • खंडशः समाकलन
  • निश्चित समाकलन
  • कलन की आधारभूत प्रमेय
  • प्रतिस्थापन द्वारा निश्चित समाकलनों का मान ज्ञात करना
  • निश्चित समाकलनों के कुछ गुणधर्म

समाकलनों के अनुप्रयोग

  • साधारण वक्रों के अंतर्गत क्षेत्रफल
  • दो वक्रों के मध्यवर्ती क्षेत्र का क्षेत्रफल

अवकल समीकरण

  • आधारभूत संकल्पनाएँ।
  • अवकल समीकरण का व्यापक एवं विशिष्ट हल
  • दिए हुए व्यापक हल वाले अवकल समीकरण का निर्माण
  • प्रथम कोटि एवं प्रथम घात के अवकल समीकरणों को हल करने की विधियाँ

सदिश बीजगणित

  • कुछ आधारभूत संकल्पनाएँ
  • सदिशों के प्रकार
  • सदिशों का योगफल
  • एक अदिश से सदिश का गुणन
  • दो सदिशों का गुणनफल

 

इकाई 4. सदिश बीजगणित और त्रि-विमीय ज्यामिति  (Vectors and 3-Dimensional Geometry)

त्रि-विमीय ज्यामिति

  • रेखा के दिक्-कोसाइन और दिक्-अनुपात
  • अंतरिक्ष में रेखा का समीकरण
  • दो रेखाओं के मध्य कोण
  • दो रेखाओं के मध्य न्यूनतम दूरी
  • समतल
  • दो रेखाओं का सह-तलीय होना
  • दो समतलों के बीच का कोण
  • समतल से दिए गए बिंदु की दूरी
  • एक रेखा और एक समतल के बीच का कोण

 

इकाई 5. रैखिक प्रोग्रामन (Linear Programming)

रैखिक प्रोग्रामन

  • रैखिक प्रोग्रामन समस्या और उसका गणितीय सूत्रीकरण
  • रैखिक प्रोग्रामन समस्याओं के भिन्न प्रकार

इकाई 6. प्रायिकता (Probability)

प्रायिकता

  • सप्रतिबंध प्रायिकता
  • प्रायिकता का गुणन नियम
  • स्वतंत्र घटनाएँ।
  • बेज़-प्रमेय
  • यादृच्छिक चर और इसके प्रायिकता बंटन
  • बरनौली परीक्षण और द्विपद बंटन

Blueprint of Bihar Board Inter Mathematics Question Paper 2020

We hope you find this information on “Bihar board Inter Mathematics Syllabus” useful. We will suggest you read other important articles of Biharboard.xyz to related to inter exam pattern, syllabus, preparation tips, etc. 

Deepak Jha

Deepak Jha

Budding Researcher Two-Part Teacher One part Entrepreneur One Part Content Writer One part Football Enthusiast. Too many parts? 2 Times UGC Qualified.

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