bcece Mathematics syllabus and recommended books

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    This article is made by our expert to answer one of the popular searched results about BCECE Math syllabus and recommended Books. Bihar Combined Entrance Competitive Examination (BCECE) is a state level engineering entrance examination conducted by the Bihar Combined Entrance Competitive Examination Board (BCECEB). Every year lac of Aspirants appears for the state level entrance examination of BCECE to get admission in various government and private engineering colleges spread all across The state.

    BCECE Bihar Combined Entrance Competitive Examination
    BCECE Bihar Combined Entrance Competitive Examination

    The BCECE Exam is conducted in two stages, namely, stage 1 (Pre) and stage 2 (Mains) for admission to the various Undergraduate courses in engineering and agriculture. Appearing candidates are advised to thoroughly go through BCECE Math syllabus 2017 in order to have a complete grip on the subject and prepare for the entrance exam as per the prescribed syllabus only. Let us have a detailed look at the BCECE Math syllabus.

    SETS AND FUNCTIONS

    (A) Sets:
    Sets and their representations, Empty set, Finite & Infinite sets.Equal sets, Subsets, Subsets of the set of real number especially intervals (with notations).Powerset, Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement of a set.

    (B) Relation & Functions:
    Ordered pairs, the Cartesian product of sets, Number of elements in the Cartesian product of two finite sets. Cartesian product of the 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 kind of relation from one set to another. Pictorial representation of a function, domain, co-domain & range of a function. A real-valued function of the real variable, domain, and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs, Sum, difference, product and quotients of functions.

    (C) Trigonometric Functions:
    positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identify sin2x + cos2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x, & cosy. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x, and tan3x. A general solution of trigonometric equations of the type sin? = sina, cos? = cosa and tan? = tana. Proof and simple application of sine and cosine formula.

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    ALGEBRA (I)

    (A) A principle of Mathematical Induction :
    Processes 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.

    (B) Complex Numbers and Quadratic Equations:
    Need for complex numbers, especially v-1, to be motivated by an inability to solve every quadratic equation. A brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers.Statement of Fundamental Theorem of Algebra, the solution of quadratic equations in the complex number system.

    (C) 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. A solution of a system of linear inequalities in two variables – graphically.

    (D) Permutation & Combination :

    The fundamental principle of counting. Factorial n. (n!) Permutation and combinations, derivation of formula and their connections, simple applications.

    (E) Binomial Theorem:
    History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

    (F) Sequence & Series:
    Sequence and Series. Arithmetic progression (A.P.) arithmetic mean (A.M.) Geometric progression (G.P.), a general term of a G.P. Sum of n terms of a G.P., geometric mean (G.M.), a relation between A.M. and G. M. Sum to n terms of the special series,?n and ?n2 and ?n3.

    CO-ORDINATE GEOMETRY (I)

    (A) Straight Lines :
    The brief recall of 2D from earlier classes. The slope of a line and angle between two lines. Various forms of equations of a line: parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. The general equation of a line, Distance of a point from a line.

    (B) Conic Section :
    Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and 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.

    (C) Introduction to Three Dimensional Geometry :
    Coordinate axes and coordinate planes in three dimensions, Coordinates of a point. The distance between two points and section formula.

    CALCULUS (I)

    Derivative introduced as a rate of change both as that of distance function and geometrically, intuitive idea of a limit. Definition of derivative, relate it to a slope of the tangent of the curve, a derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

    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 – a difference between contradiction, converse, and contrapositive.

    STATISTICS & PROBABILITY (I)

    (A) Statistics :
    A measure of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data. Analysis of frequency distributions with equal means but different variances.

    (B) Probability :
    Random experiments: outcomes, sample spaces (set representation). Events: occurrence of events, ‘not’, ‘and’ ‘or’ events, exhaustive events, mutually exclusive events Axiomatic (set-theoretic) probability, connections with the theories of earlier classes. A probability of an event, a probability of ‘not’ ‘and’ & ‘or’ events.

    RELATIONS AND FUNCTIONS.

    (A) 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.

    (B) Inverse Trigonometric Functions :
    Definition, range, domain principal value branches. Graphs of inverse trigonometric functions Elementary properties of inverse trigonometric functions.

    ALGEBRA (II)

    (A) Matrices :
    A concept, notation, order, equality types of matrices zero matrix transpose of a matrix, symmetric and skew-symmetric matrices, Addition, multiplication and scalar multiplication of matrices, 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 (restrict to square matrices of order 2). The 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).

    (B) 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 a number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.

    CALCULUS (II)

    (A) Continuity and Differentiability :
    Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. The concept of exponential and logarithmic functions and their derivatives. Logarithmic differentiation. The derivative of functions expressed in parametric forms. Second order derivatives, Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

    (B) Applications of Derivatives :
    Applications of derivatives: a rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima, and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principle and understanding of the subject as well as real-life situations).

    (C) Integrals :
    Integration as an inverse process of differentiation. Integration of a variety of functions by substitution by partial fractions and by parts, only simple integrals. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

    (D) Applications of the Integrals :
    Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).

    (E) Differential Equations :
    Definition, order, and degree, general and particular solutions of a differential equation. Formation of the differential equation whose general solution is given. A solution of differential equations by the method of separation of variables, 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.

    VECTORS AND THREE DIMENSIONAL GEOMETRY (II)

    (A) Vectors :
    Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. Types of vectors (equal unit zero parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, an addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, a projection of a vector on a line. Vector (cross) product of vectors.

    (B) Three – dimensional Geometry :
    Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, a shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. The distance of a point from a plane.

    LINEAR PROGRAMMING

    Introduction, definition of 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, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

    PROBABILITY (II)

    Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of a haphazard variable. Repeated independent (Bernoulli)trials and Binomial distribution.

    Mathematics books recommended for bcece 2018

    Before you start practicing math problems, you need to have the basic idea about the theories and the syllabus material asked in the examination and what can be better than NCERT class 11th and 12th Mathematics Textbooks. So if you have made your mind for the Bihar Engineering Entrance Examination then start preparing the basics of math from the NCERT Text Books. It will act as a note for your Revision. Once you will complete the NCERT and solidify your ground concepts, you can further go to these prescribed books for practice sets.

    • Objective Mathematics by A. Das Gupta
    • Trigonometry and Coordinate Geometry by S.L. Loney
    • Calculus by G.N. Berman

     

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