## Saturday, November 24, 2007

### CBSE +1 Math

COURSE STRUCTURE

Class XI

One Paper Three Hours Max Marks. 100

Units Marks

I. SETS AND FUNCTIONS 29

II. ALGEBRA 37

III. COORDINATE GEOMETRY 13

IV. CALCULUS 06

V. MATHEMATICAL REASONING 03

VI. STATISTICS AND PROBABILITY 12 100

UNIT-I: SETS AND FUNCTIONS

1. Sets : (12) Periods

Sets and their representations. Empty set. Finite & Infinite sets. Equal sets.Subsets. Subsets

of the 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.

2. Relations & Functions: (14) Periods

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of

two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of

relation, pictorial diagrams, domain. codomain 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 & 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: (18) Periods

Positive and negative angles. Measuring angles in radians & in degrees and conversion

from one measure to another. Definition of trigonometric functions with the help of

unit circle. Truth of the identity sin 2 x + cos 2 x=1, for all x. Signs of trigonometric

functions and sketch of their graphs. Expressing sin (x+y) and cos (x+y) in terms of

sinx, siny, cosx & cosy. Deducing the identities like the following:

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric

equations of the type sin.... = sin á , cos.... = cos á and tan.... = tan á .

UNIT-II: ALGEBRA

1. Principle of Mathematical Induction: (06) Periods

Processes 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.

2. Complex Numbers and Quadratic Equations: (10) Periods

Need for complex numbers, especially , to be motivated by inability to solve every

quadratic equation. Brief description of 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.

3. Linear Inequalities: (10) Periods

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.

Solution of system of linear inequalities in two variables- graphically.

4. Permutations & Combinations: (12) Periods

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations,

derivation of formulae and their connections, simple applications.

5. Binomial Theorem: (08) Periods

History, statement and proof of the binomial theorem for positive integral indices. Pascal's

triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series: (10) Periods

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., geometric mean

(G.M.), relation between A.M. and G.M. Sum to n terms of the special series Ó n, Ó n 2 and

Ó n 3 .

UNIT-III: COORDINATE GEOMETRY

1. Straight Lines: (09) Periods

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, intercepts form and normal form. General equation of a line. Distance of a

point from a line.

2. Conic Sections: (12) Periods

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 (08) Periods

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point.

Distance between two points and section formula.

UNIT-IV: CALCULUS

1. Limits and Derivatives: (18) Periods

Derivative introduced as rate of change both as that of distance function and geometrically,

intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve,

derivative of sum, difference, product and quotient of functions. Derivatives of polynomial

and trigonometric functions.

UNIT-V: MATHEMATICAL REASONING

1. Mathematical Reasoning: (08) Periods

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 & PROBABILITY

1. Statistics: (10) Periods

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped

data. Analysis of frequency distributions with equal means but different variances.

2. Probability: (10) Periods

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' & 'or' events.

Class XI

One Paper Three Hours Max Marks. 100

Units Marks

I. SETS AND FUNCTIONS 29

II. ALGEBRA 37

III. COORDINATE GEOMETRY 13

IV. CALCULUS 06

V. MATHEMATICAL REASONING 03

VI. STATISTICS AND PROBABILITY 12 100

UNIT-I: SETS AND FUNCTIONS

1. Sets : (12) Periods

Sets and their representations. Empty set. Finite & Infinite sets. Equal sets.Subsets. Subsets

of the 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.

2. Relations & Functions: (14) Periods

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of

two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of

relation, pictorial diagrams, domain. codomain 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 & 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: (18) Periods

Positive and negative angles. Measuring angles in radians & in degrees and conversion

from one measure to another. Definition of trigonometric functions with the help of

unit circle. Truth of the identity sin 2 x + cos 2 x=1, for all x. Signs of trigonometric

functions and sketch of their graphs. Expressing sin (x+y) and cos (x+y) in terms of

sinx, siny, cosx & cosy. Deducing the identities like the following:

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric

equations of the type sin.... = sin á , cos.... = cos á and tan.... = tan á .

UNIT-II: ALGEBRA

1. Principle of Mathematical Induction: (06) Periods

Processes 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.

2. Complex Numbers and Quadratic Equations: (10) Periods

Need for complex numbers, especially , to be motivated by inability to solve every

quadratic equation. Brief description of 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.

3. Linear Inequalities: (10) Periods

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.

Solution of system of linear inequalities in two variables- graphically.

4. Permutations & Combinations: (12) Periods

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations,

derivation of formulae and their connections, simple applications.

5. Binomial Theorem: (08) Periods

History, statement and proof of the binomial theorem for positive integral indices. Pascal's

triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series: (10) Periods

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., geometric mean

(G.M.), relation between A.M. and G.M. Sum to n terms of the special series Ó n, Ó n 2 and

Ó n 3 .

UNIT-III: COORDINATE GEOMETRY

1. Straight Lines: (09) Periods

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, intercepts form and normal form. General equation of a line. Distance of a

point from a line.

2. Conic Sections: (12) Periods

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 (08) Periods

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point.

Distance between two points and section formula.

UNIT-IV: CALCULUS

1. Limits and Derivatives: (18) Periods

Derivative introduced as rate of change both as that of distance function and geometrically,

intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve,

derivative of sum, difference, product and quotient of functions. Derivatives of polynomial

and trigonometric functions.

UNIT-V: MATHEMATICAL REASONING

1. Mathematical Reasoning: (08) Periods

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 & PROBABILITY

1. Statistics: (10) Periods

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped

data. Analysis of frequency distributions with equal means but different variances.

2. Probability: (10) Periods

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' & 'or' events.