Chse maths previous year questions

Chse maths previous 10 year Questions paper 12th odisha

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2018 to 2008: Download

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Modified Syllabus 2020-21

MATHEMATICS (+2 2nd year)

UNIT-I: Relations and Functions
1. Relations and Functions
Types of relations; reflexive, symmetric, transitive and equivalence relations. One to
one and onto functions, composite functions, inverse of function. Binary operations.

2. Inverse Trigonometric Functions
Definition, range, domain, principle value branch.

3. 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

UNIT II: Algebra
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 (restrict to square matrices of order 2).
concept of elementary row and column operations

2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors,co-factors and applications of determinants in finding the area ofa triangle, Adjoint and
inverse of a square matrix. solving system of linear equations in two or three variables(having unique solution) using inverse of a matrix.

UNIT-III : Differential Calculus
1. Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, chain rule, derivatives 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 derivativesNo problems on Mean Value Theorems.

2. Applications of Derivatives
Applications of derivatives:, increasing and decreasing functions, tangents and normals,, maxima and minima (first derivative test motivate 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).

UNIT-IV Integral Calculus

2. Applications of Derivatives

Applications of derivatives:, increasing and decreasing functions, tangents and normals, , maxima and minima (first derivative test motivate geometrically and second derivative test given as a provabletool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

UNIT-IV Integral Calculus

1. Integrals

Integration as inverse process of differentiation. Integration of a variety of functions bys substitution by partial fractions and by parts, Evaluation of simple integrals of the types and problems based on them.Fundamental Theorem of Calculus (without proof). Basic properties of definiteintegrals and evaluation of definite integrals.

2. 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).

3. Differential Equations.

Definition, order and degrec, general and particular solutions of a differential cquation.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:p-q where p and q are functions ofr or constants.

UNIT-V: Vectors and Three-Dimensional Geometry

1. Vectors

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratiosof a vector. Types of vectors (equal, unit, zero, parallel and collincar vectors). position vector ofa point, negative of a vector, components of a vector, addition of veetors, multiplication ofavector 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 andvector 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.

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.

Books Recommended:

Bureau's Higher Secondary (+2) Elements of Mathematics, Part-11, Published by Odisha

State Bureau of Text Book Preparation and Production, Bhubaneswar.

MATHEMATICS

(+2 First Year)

UNIT- I: Sets and Functions

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, Ven diagrams, Union and Intersection of sets, Difference of sets, complement of a set, Properties of Complement of Sets, Practical Problems based on sets.

2. Relations & Functions

Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the sets of real (up to 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 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 function,

with their graphs.

3. Trigonometric Functions

Positive and negative angles. Measuring angles in radians and in degrees and conversion of

one into other. Definition of trigonometric functions with the help of unit circle. Truth of Signs of trigonometric functions. Domain and range of

trigonometric functions and their graphs. 

UNIT-II: Algebra

1. Principle of Mathematical Induction

Process of the proof by induction, motivation 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.

2. Complex Numbers and Quadratic Equations Need for complex numbers, especially 1, to be motivated by inability to solve some of the quadratic_equations; Algebraic properties of complex numbers. Argand plane.Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex system. cube roots of unity and its properties

3. 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 solution of system of linear inequalities in two variables.

4. Permutations and Combinations

Fundamental principle of counting, factorial n. (n!), Permutations and combinations,

simple applications.

5. Binomial Theorem

History, statement No problems on Binomial Theorem

6. 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., Arithmetic and

Geometric series, infinite G.P. and its sum, geometric mean (G.M.), Harmonic (mean)

relation between A.M., GM. and H.M.,

UNIT -1I: Co-ordinate Geometry

1. Straight Lines

Brief recall of two dimensional geometry from earlier classes. Slope ofa line and angle

between two lines. Various forms of equations of a line: parill9/106oint-slope

form, slope-intercept form, two-point form, intercept form and ndal fořm. 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,.

2. Conic Sections

Sections ofa cone: circles, cllipse, parabola, hyperbola; Standard equations and simple

properties of Circle, parabola, ellipse and hyperbola.

3. 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

1. 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,

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