HSC Science (Electronics) 11thMaharashtra State Board
Share

# Mathematics and Statistics 11th HSC Science (Electronics) Maharashtra State Board Topics and Syllabus

SubjectMathematics and Statistics

## Topics with syllabus and resources

100.00 Measurement of Angles
• Need & concept
• Revision of directed angle (+ve and –ve angles), zero angle, straight angle, angles in standard position, coterminal angles, angles in quadrant & quadrantal angles.
• Sexagesimal system, circular system, relation between degree measure and radian measure.
• Theorem: Radian is a constant angle. Length of an arc of a circle (s = r. θ, θ is in radians) (without proof). Area of the sector of a circle A = ½ r2 . θ, θ is in radians (without proof).
200.00 Trigonometric Functions
• Need & concept
• Trigonometric functions with the help of standard unit circle, signs of trigonometric functions in different quadrants, trigonometric functions of particular angles (00 , 300 , 450 , 600 , 900 , 1800 , 2700 , 3600 )
• domain and range of trigonometric functions, periodicity of functions
• fundamental identities
• graphs of trigonometric functions, Graph of y = a sin bx, y = a cos bx, trigonometric functions of negative angles.
300.00 Trigonometric Functions of Compound Angles
• Introduction
• trigonometric functions of sum and difference, trigonometric functions of multiple angles (upto double and triple angles only), trigonometric functions of half angles.
400.00 Factorization Formulae
• Introduction
• Formulae for conversion of sum or difference into products, formulae for conversion of product into sum or difference
• trigonometric functions of angles of a triangle
500.00 Locus
• Introduction
• Definition and equation of locus, points of locus, shift of the origin.
600.00 Straight Line
• Revision.
• Inclination of a line, slope of a line, equation of lines parallel to coordinate axes, intercepts of a line, revision of different forms of equations of a line, slope-point form, slope-intercept form, two point form, double intercept form, other forms of equations of a line, parametric form, normal form, general form,
• Theorem 1 : A general linear equation Ax + By+ C =0, provided A and B are not both zero, simultaneously, always represents straigh tline.
• Theorem 2 : Every straight line has an equation of the form Ax +By + C = 0, where A, B and C are constants (without proof),
• Reduction of general equation of a line into normal form, intersection of two lines, parallel lines, perpendicular lines, identical lines,
• condition for concurrency of three lines, angle between lines, distance of a point from a line,
• distance between two parallel lines,
• equations of bisectors of angle between two lines,
• family of lines,
• equation of a straight line parallel to a given line,
• equation of a straight line perpendicular to a given line,
• equation of family of lines through the intersection of two lines
700.00 Circle and Conics
• Revision
• standard equation, centre-radius form, diameter form, general equation, parametric equations of standard equation,
• Conics Napees – Intersection of Napees of a cone and Plane, introduction,
• focus-directrix property of parabola, ellipse, hyperbola, parabola,
• standard equation (different forms of parabola), parametric equations, ellipse, standard equation, hyperbola, standard equation, parametric equations.
• Application of conic section
800.00 Vectors
• Definition
• magnitude of a vector, free and localized vectors, types of vectors, zero vector, unit vector, equality at vectors, negative of a vector, collinear vectors, coplanar vectors, coinitial vectors, like and unlike vectors, scalar multiple of a vector
• triangle law, parallelogram law, polygon law
• properties of addition of vectors
• three dimensional co-ordinate geometry, coordinate axes & coordinate planes in space, co-ordinates of a point in space, distance between two points in a space, unit vectors along axes, position vector of a point in a space
• product of vectors, scalar product, definition, properties, vector product, definition, properties
• simple applications, work done by force, resolved part of a force, moment of a force.
900.00 Linear Inequations

Linear inequations in one variable

• solution of linear inequation in one variable & graphical solution
• solutions of system of linear inequations in one variable

Linear inequations in two variables

• solution of linear inequations in two variables & graphical solution,
• solutions of system of linear inequations in two variables,
• Replacement of a set or domain of a set, Transposition
1000.00 Determinants
• Revision
• determinant of order three, definition, expansion
• properties of determinants
• minors & co-factors
• applications of determinants
• condition of consistency
• area of a triangle
• Cramer’s rule for system of equations in three variables.
1100.00 Matrices
• Introduction, concepts, notations, order
• types of matrices – zero matrix, row matrix, column matrix, square matrix, determinant of a square matrix, diagonal matrix, scalar matrix, identity matrix, triangular matrices, singular & non-singular matrices, transpose of a matrix, symmetric & skew symmetric matrices,
• operations on matrices – equality, addition, subtraction, multiplication of a matrix by a scalar,
• simple properties multiplication of matrices – definition
• properties of matrix multiplication
• properties of transpose of a matrix - (A')' = A, (KA)' = KA', (AB)' = B'A'.
1200.00 Sets, Relations and Functions

1201.00 Set

Revision, subset, proper improper subset and their properties, union, intersection, disjoint sets, empty set, finite & infinite sets, equal sets, equivalent sets, universal set, Venn diagrams, complement of a set, difference of two sets, power set, ordered pairs, equality of ordered pairs, Cartesian product of two sets, No. of elements in the Cartesian product of two finite sets, Cartesian product of the reals with itself

1202.00 Relations

definition of relation, pictorial diagrams, domain, codomain and range of a relation, types of relations, one-one, many-one, binary equivalence relation

1203.00 Functions

function as a special kind of relation, pictorial representation of a function, domain, codomain and range of a function, equal functions

types of functions - constant function, identity function, one-one function, onto function, into function, even & odd functions, polynomial function, rational function, modulus function signum & greatest integer, exponential function, logarithmic function, functions with their graphs, sum, difference, product, quotient of functions, scalar multiplication, composite function, inverse function, binary operations, real valued function of the real variable, domain and range of these functions

1300.00 Logarithms
• Introduction, definition, properties
• laws of logarithms, change of base,
• characteristics & mantissa – method of finding characteristics, method of finding mantissa, method of finding antilogarithm
1400.00 Complex Numbers
• Introduction,
• need for complex numbers,
• definitions –(real parts, imaginary parts, complex conjugates, modulus, argument),
• algebra of complex numbers – equality, addition, subtraction, multiplication, division, powers and square root of a complex number, higher powers of i, DeMoivre’s formula – (without proof), square root of a complex number,
• properties of complex numbers – properties of addition of complex numbers, 1) Closure Property 2) Commulative Law 3) Associative law 4) Existence of additive identity 5) Existence of additive inverse.
• Properties of product of complex numbers – Existance of multiplicative identity –
• Existance of multiplicative inverse, properties of conjugate & modulus of complex numbers, Argand Diagram
• representation of a complex number as a point in plane, geometrical meaning of modulus and argument, polar representation of complex numbers, Fundamental theorem of algebra, cube roots of unity
•  solution of quadratic equations in the complex number system, cube roots of unity
1500.00 Sequences and Series
• Revision - sequence, A.P.,
• Sum of first n terms of A.P.,
• properties of A.P.,
• geometric progression – introduction, general term, sum of the first ‘n’ terms, (n terms from the end of G.P.) containing finitely many terms & sum to infinite terms,
• properties of G.P., H.P. as a special type of A.P,
• Means – arithmetic mean, geometric mean, harmonic mean,
• relation between A.M., G.M., H.M.,
• Arithmetico-Geometric sequence, special series, sum of cube of first n natural numbers, sum of cube of first n odd natural nos., exponential & logarithmic series.
1600.00 Permutations and Combinations
• Introduction,
• fundamental principle of counting, factorial notation, permutations, when all r objects are distinct, when all r objects are not distinct, circular permutations, simple applications,
• combinations – definition, properties, relations between permutations and combinations, simple applications
1700.00 Mathematical Induction and Binomial Theorem
• Principle of mathematical induction,
• simple applications,
• binomial theorem – binomial theorem for positive integers, general term, particular term, properties of binomial coefficient with simple application, binomial theorem for any index (without proof), particular cases of binomial theorem,
• simple applications.
1800.00 Limits
• Introduction of concept,
• meaning of x→a, 83 the limit of a function, fundamental theorem on limits,
• algebra of limits – standard limits, without proof,
• limits at infinity – concepts, simple problems.
1900.00 Differentiation
• Definition : derivative,
• derivative at a point,
• geometrical significance of derivative, physical significance (velocity as a rate of change of displacement),
• derivatives from first principle - of trigonometric functions, logarithmic functions, algebraic functions, exponential functions,
• rules of differentiation –derivative of sum, difference, product and quotient
2000.00 Integration
• Definition of integration as antiderivative,
• geometrical interpretation of indefinite integrals,
• algebra of integrals – integrals of some standard functions, rules of integration
2100.00 Statistics
• Measures of dispersion – range,
• quartile & quartile deviation (for grouped and ungrouped data),
• comparison of two frequency distributions with same mean,