BIHAR BOARD EXAM LATEST UPDATE
The Class 11 exams depend on the schools, as they decide when to conduct the exams. Usually, the Class 11 exams are held a few months before the final board exams. This gives you the opportunity to prepare for the final board exams and also mentally prepare for them. Therefore, it is better to contact your school regarding the Class 11 exams, and also take advantage of the complete information provided here for the final board exam.
Bihar School Examination Board [BSEB] has announced class 12 Board exams date. This year class 12th board exam will be started from 01 February 2025 and will last upto 15 February 2025, it will take around 15 days to complete the class 12th board exam. The board will conduct the class 12 exam in two shifts. The first-shift exams are conducted from 9:30 am to 12:45 pm while the second shift exam will be from 2 pm to 5:15 pm. The board is going to start the practical exams on January 10, 2025. The last practical exam will be on January 20, 2025.
NCERT SYLLABUS
| Chapter |
| Sets |
| Relations and Functions |
| Trigonometric Functions |
| Principle of Mathematical Induction |
| Complex Numbers and Quadratic Equations |
| Linear Inequalities |
| Permutations and Combinations |
| Binomial Theorem |
| Sequences and Series |
| Straight Lines |
| Conic Sections |
| Introduction to three Dimensional Geometry |
| Limits and Derivatives |
| Mathematical Reasoning |
| Statistics |
| Probability |
Unit-I: Sets and Functions
Chapter 1 : Sets
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets, Subsets, Subsets of a set of real numbers especially intervals (with notations). Power set. Universal Set, Venn diagrams, Union and Intersection of sets. Difference of sets, Complement of a set, Properties of Complement.
Chapter 2 : Relations & Functions
Ordered pairs, Cartesian product of sets, Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of Relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation, Pictorial representation of a function, domain, co-domain and range of A function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, Signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.
Chapter 3 : Trigonometric Functions
Positive and negative angles, Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:
tan (x±y) = tanx ± tany/ 1 -+ tanx tany
cot (x±y) = cotx coty -+1 / coty ± cotx
sin alpha (±) sin beta = 2sin(1/2) (alpha ± beta) cos(1/2) (alpha -+ beta)
cos alpha + cos beta = 2cos(1/2) (alpha + beta) cos(1/2) (alpha - beta)
cos alpha - cos beta = - 2sin(1/2) (alpha + beta) sin(1/2) (alpha - beta)
Identities related to sin2x, cos2x, tan2x, sin3x, cos3xand tan3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.
Unit-II: Algebra
Chapter 4 : Principle of Mathematical Induction
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.
Chapter 5 : Complex Numbers and Quadratic Equations
Need for complex numbers, especially1, to be motivated by inability to solve some of quadratic equations. Algebraic properties of complex numbers. Argand plane and polar
representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.
Chapter 6 : Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.
Chapter 7 : Permutations and Comb
...
BIHAR BOARD EXAM LATEST UPDATE
The Class 11 exams depend on the schools, as they decide when to conduct the exams. Usually, the Class 11 exams are held a few months before the final board exams. This gives you the opportunity to prepare for the final board exams and also mentally prepare for them. Therefore, it is better to contact your school regarding the Class 11 exams, and also take advantage of the complete information provided here for the final board exam.
Bihar School Examination Board [BSEB] has announced class 12 Board exams date. This year class 12th board exam will be started from 01 February 2025 and will last upto 15 February 2025, it will take around 15 days to complete the class 12th board exam. The board will conduct the class 12 exam in two shifts. The first-shift exams are conducted from 9:30 am to 12:45 pm while the second shift exam will be from 2 pm to 5:15 pm. The board is going to start the practical exams on January 10, 2025. The last practical exam will be on January 20, 2025.
NCERT SYLLABUS
| Chapter |
| Sets |
| Relations and Functions |
| Trigonometric Functions |
| Principle of Mathematical Induction |
| Complex Numbers and Quadratic Equations |
| Linear Inequalities |
| Permutations and Combinations |
| Binomial Theorem |
| Sequences and Series |
| Straight Lines |
| Conic Sections |
| Introduction to three Dimensional Geometry |
| Limits and Derivatives |
| Mathematical Reasoning |
| Statistics |
| Probability |
Unit-I: Sets and Functions
Chapter 1 : Sets
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets, Subsets, Subsets of a set of real numbers especially intervals (with notations). Power set. Universal Set, Venn diagrams, Union and Intersection of sets. Difference of sets, Complement of a set, Properties of Complement.
Chapter 2 : Relations & Functions
Ordered pairs, Cartesian product of sets, Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (up to R x R x R). Definition of Relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation, Pictorial representation of a function, domain, co-domain and range of A function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, Signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.
Chapter 3 : Trigonometric Functions
Positive and negative angles, Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x + cos2x = 1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities like the following:
tan (x±y) = tanx ± tany/ 1 -+ tanx tany
cot (x±y) = cotx coty -+1 / coty ± cotx
sin alpha (±) sin beta = 2sin(1/2) (alpha ± beta) cos(1/2) (alpha -+ beta)
cos alpha + cos beta = 2cos(1/2) (alpha + beta) cos(1/2) (alpha - beta)
cos alpha - cos beta = - 2sin(1/2) (alpha + beta) sin(1/2) (alpha - beta)
Identities related to sin2x, cos2x, tan2x, sin3x, cos3xand tan3x. General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a.
Unit-II: Algebra
Chapter 4 : Principle of Mathematical Induction
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.
Chapter 5 : Complex Numbers and Quadratic Equations
Need for complex numbers, especially1, to be motivated by inability to solve some of quadratic equations. Algebraic properties of complex numbers. Argand plane and polar
representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.
Chapter 6 : Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line.Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.
Chapter 7 : Permutations and Combinations
Fundamental principle of counting. Factorial n.(n!) Permutations and combinations, derivation of Formulae form pr and ncr and their connections, simple applications.
Chapter 8 : Binomial Theorem
Historical perspective, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications.
Chapter 9 : Sequence and Series
Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums.
Unit- III : Coordinate Geometry
Chapter 10 : Straight Lines
Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.
Chapter 11 : Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
Chapter 12 : Introduction to Three-dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
Unit- IV : Calculus
Chapter 13 : Limits and Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.
Unit- V : Mathematical Reasoning
Chapter 14 : Mathematical Reasoning
Mathematically acceptable statements. Connecting words/ phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics. Validating the statements involving the connecting words, difference among contradiction, converse and contrapositive.
Unit- VI : Statistics and Probability
Chapter 15 : Statistics
Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different
variances.
Chapter 16 : Probability
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.
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