Jagran Josh
Unit-I: SETS AND FUNCTIONS
Marks
Periods
09
12
Sets and their representations, Empty set, Finite and Infinite sets, Equal sets, Subsets, Subsets of the set of real numbers especially intervals (with notations), Universal set, Venn diagrams, Union and Intersection of sets, Difference of sets, Complement of a set.
2. Relations and Functions:
08
12
Cartesian product of sets, Number of elements in the cartesian product of two finite sets, Cartesian product of the reals with itself(upto R×R×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 function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs, Sum, difference, product and quotients of functions.
3. Trigonometric Functions:
09
13
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. Sings of trigonometric functions and sketch of their graphs, Expressing sin (x+y) and cos(x+y) interms of sinx, siny, cosx and cosy, Deducing the identities like following:
Unit-II: ALGEBRA
1. Complex Numbers and Quadratic Equations:
06
12
Need for complex numbers, especially √-1, to be motivated by inability to solve every quadratic equation, Brief description of algebraic properties of complex numbers, The modulus and the conjugate of a complex number. Argand plane and polar representation.
2. Linear Inequalities:
04
06
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number-line.
3. Permutations and Combinations:
07
12
Fundamental principle of counting, Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.
4. Binomial Theorem:
07
12
Statement and proof of the binomial theorem for positive integral indices, Pascal’s triangle, simple applications.
5. Sequence and Series:
06
13
Sequence and Series. Geometric progression (G.P.), general term of a GP., sum of n terms of a GP. geometric mean(G.M.), relation between A.M. and GM
Unit-III: COORDINATE GEOMETRY
1. Straight Lines:
08
14
Brief recall of 2D from earlier classes. Slope of a line and angle between two lines, Various forms of equations of a line, parallel to axes, point-slope form, slope-intercept form, two-point form, intercept form and General equation of a line, Distance of a point from a line.
2. Conic Sections:
08
14
Sections of a cone: Circle, ellipse, parabola, hyperbola, a point, a straight line and 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.
3. Introduction to Three-dimensional Geometry:
04
08
Coordinate axes and coordinate planes in three dimensions, Coordinates of a point, Distance between two points
Unit-IV: CALCULUS
Limits and -Derivatives
12
22
Intuitive idea of limits. 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: STATISTICS AND PROBABILITY
1. Statistics:
07
18
Measure of Dispersion, Range, Mean deviation, variance and standard deviation of ungrouped/ grouped data.
2. Probability:
05
12
Events, Occurrence of events, ‘not’, ‘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’& ‘or’ events.
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