| UNIT |
TOPICS |
| Unit-I: Sets and Functions |
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.
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 (upto R x R x R).
· 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.
· Sum, difference, product and quotients of functions.
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. |
| Unit-II: Algebra |
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
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 and polar
representation of complex numbers.Statement of Fundamental Theorem of Algebra, solution of
quadratic equations (with real coefficients) in the complex number system.Square root of a
complex number.
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
Permutations and Combinations
·Fundamental principle of counting.Factorialn. (n!) Permutations and combinations, derivation of Formulae for n
h and their connections, simple applications.
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.
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 |
Straight Lines
· Brief recall of two dimensional geometry 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 and 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.
Conic Sections
· Sections of a cone: circles, 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 parabola, ellipse and hyperbola.Standard equation of a circle.
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 |
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 scope of tangent of the
curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial
and trigonometric functions.
|
| Unit-V: Mathematical Reasoning |
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 among
contradiction, converse and contra positive. |
| Unit-VI: Statistics and Probability |
Statistics
· Measures of Dispersion: Range, Mean deviation, variance and standard deviation of
un grouped/grouped data. Analysis of frequency distributions with equal means but different
variances.
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 other theories of earlier classes. Probability of an event,
probability of ‘not’, ‘and’ and ‘or’ events. |
