Organisation : Maharashtra State Board of Secondary & Higher Secondary Education
Announcement : Std-XII Mathematics & Statistics HSC Syllabus
Mathematics & Statistics (40)
(For Arts and Science)
Std. XI & XII
Mathematics is the language of all sciences and is perhaps the only subject which merits this distinction. Mathematics is the backbone of all sciences and it is an inseparable part of human life.
Higher Secondary is a launching stage from where students would go to either for academic education in Mathematics or professional courses like Engineering and Computer Technology, Physical and Biological Sciences. Hence to fulfil the needs of students, it is utmost important to make the study of Mathematics more meaningful by acquainting the student with many branches of mathematics.
This will help them in developing Mathematical tools to be used in the professional education. Apart from motivating topics from real life situations and other subject areas, major thrust is also on application of various concepts.
The proposed syllabus has been designed in accordance with National Curriculum Framework 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students.
To enable the students
1) to acquire knowledge and critical understanding, particularly by way of motivation and visualization of basic concepts, terms, principles, symbols and mastering the underlying processes and skills.
2) to apply the knowledge and skills in Mathematics and related problems from other subjects, by more than one method.
3) to develop positive attitude to think, analyze and articulate logically.
4) to develop interest in Mathematics by participating in various related competitions and self-learning.
5) to acquaint students with different aspects of Mathematics used in real life.
6) to develop an interest in students to study Mathematics as a discipline.
7) to develop awareness of the need for national integration, protection of an environment, removal of social barriers, elimination of sex biases and observance of small family norm.
8) to develop reverence and respect towards great mathematicians for their contribution to the field of Mathematics.
9) to develop interest in the subject by participating in related competitions.
Std. XII : PART – 1
1. Mathematical Logic
Statements – Introduction, sentences and statement, truth value of statement, open sentences, compound statement, quantifier and quantified statements, logical connectives : conjunction, disjunction, negation, implication/ conditional, biconditional, truth tables of compound statements, examples related to real life and mathematics, statement patterns and logical equivalence – tautology, contradiction, contingency, duality, negation of compound statement, contrapositive, converse, inverse, algebra of statements-idempotent law, associative law, commutative law, distributive law, identity law, complement law, involution law, DeMorgan’s laws, difference between converse, contrapositive, contradiction, application-introduction to switching circuits (simple examples).
Elementary transformation of a matrixrevision of cofactor and minor, elementary row transformation, elementary column transformation, inverse of a matrixexistance and uniqueness of inverse of a matrix, inverse by elementary transformation, adjoint method, application-solution of system of linear equations by – reduction method, inversion method.
3. Trigonometric functions
Trigonometric equations-general solution of trigonometric equation of the type
4. Pair of straight lines
Pair of lines passing through origincombined equation, homogenous equation, theorem-the joint equation of a pair of lines passing through origin and its converse, acute angle between the lines represented by ax2+2hxy+by2=0, condition for parallel lines, condition for perpendicular lines, pair of lines not passing through origin-combined equation of any two lines, condition that the equation ax2+2hxy+by2+2gx+2fy+c=0 should represent a pair of lines (without proof), acute angle between the lines (without proof), condition of parallel and perpendicular lines, point of intersection of two lines.
Tangent of a circle-equation of a tangent at a point to 1) standard circle,2) general circle, condition of tangency only for line y = mx + c to the circle x2 + y2 = a2, tangents to a circle from a point outside the circle, director circle, length of tangent segments, normal to a circle-equation of normal at a point.
Tangents and normals-equations of tangent and normal at a point for parabola, ellipse, hyperbola; condition of tangency for parabola; ellipse, hyperbola; tangents in terms of slope for parabola, ellipse, hyperbola, tangents from a point outside conics, locus of points from which two tangents are mutually perpendicular, properties of tangents and normals to conics (without proof).
Revision, Collinearity and coplanarity of vectors : linear combination of vectors, condition of collinearity of two vectors,conditions of coplanarity of three vectors, section formula : section formula for internal and external division, midpoint formula, centroid formula, scaler triple product : definition, formula, properties, geometrical interpretation of scalar triple product, application of vectors to geometrymedians of a triangle are concurrent, altitudes of a triangle are concurrent, angle bisectors of a triangle are concurrent, diagonals of a parallelogram bisect each other and converse, median of trapezium is parallel to the parallel sides and its length is half the sum of parallel sides, angle subtended on a semicircle is right angle.
8. Three dimensional geometry
Direction cosines and direction ratios: direction angles, direction cosines, direction ratios, relation between direction ratio and direction cosines, angle between two lines, condition of perpendicular lines.
Equation of line passing through given point and parallel to given vector, equation of line passing through two given points, distance of a point from a line, distance between two skew lines, distance between two parallel lines (vector approach).
Equation of plane in normal form, equation of plane passing through the given point and perpendicular to given vector, equation of plane passing through the given point and parallel to two given vectors, equation of plane passing through three noncollinear points, equation of plane passing through the intersection of two given planes, angle between two planes, angle between line and plane, condition for the coplanarity of two lines, distance of a point from a plane (vector approach)
11 Linear programming problems
Introduction of L.P.P. definition of constraints, objective function, optimization, constraint equations, nonnegativity restrictions, feasible and infeasible region, feasible solutions, Mathematical formulation-mathematical formulation of L.P.P. different types of L.P.P. problems, graphical solutions for problem in two variables, optimum feasible solution.