TERM 1
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. Venn diagrams. Union and
Intersection of 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 set of reals with itself ( R x R only).Definition of relation, pictorial diagrams, domain,
co-domain and range of a relation. Function as a special type of relation. 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 functions, with their graphs.
Unit-II: Algebra
1. Complex Numbers and Quadratic Equations
Need for complex numbers, especially√−1, to be motivated by inability to solve some of the quardratic
equations. Algebraic properties of complex numbers. Argand plane. Statement of Fundamental Theorem
of Algebra, solution of quadratic equations (with real coefficients) in the complex number system.
2. 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., infinite G.P. and its sum, geometric mean (G.M.),
relation between A.M. and G.M.
Unit-III: Coordinate Geometry
1. Straight Lines
Brief recall of two dimensional geometry from earlier classes. 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 and normal form. General equation of a line. Distance of a point from a line.
Unit-IV: Calculus
1. Limits
Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and
logarithmic functions
Unit-V: Statistics and Probability
1. Statistics
Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped
data.
TERM - II
Unit-I: Sets and Functions
1. Trigonometric Functions
Positive and negative angles. Measuring angles in radians and in degrees and conversion from one
measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity
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
applications. Deducing identities like the following:
Identities related to sin2x, cos2x, tan2 x, sin3x, cos3x and tan3x.
Unit-II: Algebra
1. 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 method of finding a solution
of system of linear inequalities in two variables.
2. Permutations and Combinations
Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, formula
for nPr and nCr, simple applications.
Unit-III: Coordinate Geometry
1. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola. Standard equations and simple properties of
parabola, ellipse and hyperbola. Standard equation of a circle.
2. 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. Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically. Definition of
Derivative, relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of
functions. Derivatives of polynomial and trigonometric functions.
Unit-V: Statistics and Probability
1. Probability
Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’,
‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Probability of an event, probability of
‘not’, ‘and’ and ‘or’ events
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