Topics Name. Marks
I Sets and Functions 29II Algebra 37
III Co-ordinate Geometry. 13
IV. Calculus 6
V Mathematical Reasoning. 3
VI Statistics and Probability. 12
Total 100 marks
Course Syllabus
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 Sets
*Practical Problems based on sets
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 sets of real (up to R × R)
*Definition of Relation
*Pictorial diagrams
*Domain
*Co-domain
*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,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 of one into other
*Definition of trigonometric functions with the help of unit circle
*Truth of the 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 application
*Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and 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 1: 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 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 and polar representation of complex numbers
*Statement of Fundamental Theorem of Algebra
*Solution of quadratic equations in the complex number system
*Square root of a complex number
Chapter 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
Chapter 4: Permutations and Combinations
*Fundamental principle of counting Factorial n (n!)
*Permutations and combinations
*Derivation of formulae and their connections *Simple applications.
Chapter 5: 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
Chapter 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.)
*Relation between A.M. and G.M.
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
*Brief recall of two dimensional geometries 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
*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 2: Conic Sections
*Sections of a cone −
Circles-Standard equation of a circle,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 −ParabolaEllipse,Hyperbola
Chapter 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
Chapter 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
Trigonometric, exponential and logarithmic functions
*Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions
*The derivative of polynomial and trigonometric functions
Unit-V: Mathematical Reasoning
Chapter 1: 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 between contradiction, converse and contrapositive
Unit-VI: Statistics and Probability
Chapter 1: Statistics
*Measures of dispersion −Range,Mean deviation,Variance
*Standard deviation of ungrouped/grouped data
*Analysis of frequency distributions with equal means but different variances.
Chapter 2: 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 the theories of earlier classes
*Probability of −An event
*probability of 'not', 'and' and 'or' events
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