# Rajasthan Board Math Syllabus for Class 11

## Rajasthan Board Syllabus for Class 11 Math

**UNIT-I: SET AND FUNCTIONS**

**1. Sets :**

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. Properties of complement 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 sets of reals with itself (up to, 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 functions, 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 :**

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 domain and range of trigonometric functions and their graphs. Expressing sin (x $\pm$ y) and

cos (x $\pm$ y) in terms of sinx, siny, cosx & cosy. Deducing the identities like the following.

tan(x $\pm$ y) = $\frac{tan x \pm tan y}{1 \mp tan x tan y}$, cot(x $\pm$ y) = $\frac{cot x cot y \mp 1}{cot y \pm cot x}$,

sinx + siny = 2 sin$\frac{x + y}{2}$ cos$\frac{x - y}{2}$, cos x + cos y = 2 cos$\frac{x + y}{2}$ cos$\frac{x - y}{2}$,

sinx - siny = 2 cos$\frac{x + y}{2}$ sin$\frac{x - y}{2}$, cos x - cos y = -2 sin$\frac{x + y}{2}$ sin$\frac{x - y}{2}$,

Identities related to sin 2x, cos2x, tan 2x, cos3x and tan 3x. General solution of trigonometric equations of the type sin$\theta$ = sin $\alpha$, cos$\theta$ = cos $\alpha$ and tanq = tan a. Pwof and

simple applications of sine and cosine formulae.

Áflfl⁄UÁáÊ·§Ê ·§ˇÊÊ-11, ¬⁄UËˇÊÊ-2013 31

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.

Need for complex numbers, especially 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 of a complex number.

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.

Fundamental principle of counting. Factorial n.(n!) Permutations and combinations, derivation of formulae and their connections, simple applications.

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle terms in binomial expansion, simple applications.

Sequence and Series. Arithmetic progression (A.P.) arithmetic mean (A.M.) Geometic progression (G.P.), general terms of a G.P., sum of n terms of a G.P., Arithmetic and geometric series, infinite G.P. and its sum, geometric means (G.M.), relation between

A.M. and G.M. Sum to n terms of the special series $\sum^{n}_{k = 1} k$, $\sum^{n}_{k = 1} k^{2}$ and $\sum^{n}_{k = 1} k^{3}$

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 axes, point – slope from, slope – intercept form, two point form, intercepts form and normal form. General equation of a line equation of families of lines passing through the point of intersection of two lines. Distance of point from a line.

Sections of a cone: Circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting line as a degenerated case of a conic section. Standard equation and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.

Limit of function introduced as rate of change of distance function and geometric

meaning $\lim_{x \to 0} \frac{log_{e}(1 + x)}{x}$, $\lim_{x \to 0} \frac{e^{x} - 1}{x}$. 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.

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 wards difference between contradiction, converse and contra positive.

.

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

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’ & ‘or’ events.

Prescribed Books :

Mathematics -NCERT's Book Published under Copyright

simple applications of sine and cosine formulae.

Áflfl⁄UÁáÊ·§Ê ·§ˇÊÊ-11, ¬⁄UËˇÊÊ-2013 31

**UNIT-II: ALGEBRA****1. Principle of Mathematical Induction:**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 :**Need for complex numbers, especially 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 of a complex number.

**3. Liner 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.

**4. Permutations & Combinations :**Fundamental principle of counting. Factorial n.(n!) Permutations and combinations, derivation of formulae and their connections, simple applications.

**5. Binomial Theorem :**History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle terms in binomial expansion, simple applications.

**6. Sequence and Series :**Sequence and Series. Arithmetic progression (A.P.) arithmetic mean (A.M.) Geometic progression (G.P.), general terms of a G.P., sum of n terms of a G.P., Arithmetic and geometric series, infinite G.P. and its sum, geometric means (G.M.), relation between

A.M. and G.M. Sum to n terms of the special series $\sum^{n}_{k = 1} k$, $\sum^{n}_{k = 1} k^{2}$ and $\sum^{n}_{k = 1} k^{3}$

**UNIT- III: COORDINATE GEOMETRY****1. 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 axes, point – slope from, slope – intercept form, two point form, intercepts form and normal form. General equation of a line equation of families of lines passing through the point of intersection of two lines. Distance of point from a line.

**2. Conic Sections :**Sections of a cone: Circle, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting line as a degenerated case of a conic section. Standard equation and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

**3. Introduction of 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. Limits and Derivatives :**Limit of function introduced as rate of change of distance function and geometric

meaning $\lim_{x \to 0} \frac{log_{e}(1 + x)}{x}$, $\lim_{x \to 0} \frac{e^{x} - 1}{x}$. 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**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 wards difference between contradiction, converse and contra positive.

.

**UNIT – VI: STATISTICS & PROBABILITY****1. Statistics :**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 :**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’ & ‘or’ events.

Prescribed Books :

Mathematics -NCERT's Book Published under Copyright

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