Class XI: Mathematics Syllabus
MATHEMATICS CLASS - XI (Full Marks 100)
ALGEBRA -30 Marks
Surds and Indices :
Fundamental laws of Surds and Indices, simple applications.
Arithmetic Progression : (A.P.)
Definition of A.P., Common difference, General term, Summation of first n terms. Sum of first n-natural numbers, A.M.
Geometric Progression : (G. P.)
Definition of G.P., Common ratio, General term, Summation of first n-terms, G.M.
Logarithms :
Definition, General properties of logarithms.
Complex numbers :
Complex numbers in the form a + ib, Real and imaginary parts of a complex number, Geometrical representation of complex numbers, Complex Conjugate, Modulus and Argument of a complex number, Algebra of complex numbers, (fundamental operations). Triangle inequality | 
and also 
. Cube roots of unity and their properties.
Theory of Quadratic Equations :
Quadratic equations with real coefficients. Fundamental theorem of Algebra (Statement only). Roots, relations between roots and coefficients of a quadratic equation, Nature of roots, formation of quadratic equation,
common root ax2 + bx + c. (a, b, c are rational numbers).
Permutation and Combination :
Defination of Permutation. Permutation of n different things taken .jpg "r( \le n)")
at a time; Permutation of n things, not all different; Permutation with repetitions (circular permutation excluded).
Definition of Combination; Combination of n different things taken r at a time; Combination of n things when things are not all different; Basic properties.
TRIGONOMETRY [ 25 Marks ]
The associated angles :
(+ ve or -ve) , 
, 
, 
, 
.
The Trigonometrical ratios of compound angles :
Sum and difference formula for  - \cos (A \pm B).jpg "\sin (A \pm B) , \cos (A \pm B)")
etc.
Sum and difference as products. ( 
are all acute angles)
Multiple and submultiple angles :
Simple problems; Finding the values of sine, cosine and tangent of the angle 
General solutions of Trigonometrical equations :
Trigonometrical inverses:
Specific mention of principal values.
Properties of triangles :
Basic relations between sides, angles, circum radius. Area of triangles of the form Vi be sin A. Simple and direct applications.
COORDINATE GEOMETRY OF TWO DIMENSIONS
[14 Marks]
(All discussions should be made in terms of rectangular Cartesian co-ordinate system)
Basic Ideas :
Distance formula, Section formula, Area of a triangle, condition of collinearity of three points in a plane.
Polar coordinates; Transformation from Cartesian to polar coordinates and vice-versa.
Parallel transformation of Axes.
Concept of locus. Elementary locus problems.
Equations of straight lines : Slope of a line. Slope in terms of co-ordinates of two points on it. Equations of coordinate axes, equation of lines parallel to coordinate axes, slope— intercept form, gradient / slope form, equation of the line through two given points, intercept form, symmetric form, normal form; Every first degree equation represents a straight line.
Angle between two lines; conditions of perpendicularity and parallelism of two lines; Equation of a line parallel to a given line. Equation of a line perpendicular to a given line. Distance of a point from a straight line.
Equations of Circles : Standard equation x2 + y2 = a2. Equation of a circle with a given centre and radius. Equation of the form x2 + y2 + 2gx + 2fy + c = 0 represents a circle. Equation of a circle in terms of the co-ordinates of the end points of a diameter. Parametric equation of a circle.
SETS, RELATIONS AND MAPPINGS
110 Marks
Idea of Sets, Finite and infinite sets, Empty set, universal set, subsets, Power set, Venn diagram, Complement of a set, operation on sets (Union, intersection, difference of two sets, De-Morgan laws) Inclusion / Exclusion formula for two or three finite sets. Cartesian product of sets.
Idea of relations, mappings, range and domain, injective, surjective and bijective mapping, Composition of mappings, Inverse of a mapping.
DIFFERENTIAL CALCULUS [15 Marks ]
Idea of number system :
Integer, Rational, Irrational and real number.
Variables and functions : Variables, Functions of single variable, Geometrical representations of functions of the form :
ax + b, ( a ,b rational ), -{1 \over x}(x \ne 0)-\left- x \right--{{\left- x \right-} \over x}-(x \ne 0)-{x-2}-\sin x-\cos x-\tan x.jpg "\sqrt x (x \succ 0),{1 \over x}(x \ne 0),\left| x \right|,{{\left| x \right|} \over x},(x \ne 0),{x^2},\sin x,\cos x,\tan x")
Idea of rational functions; Idea of Exponential and logarithmic functions. Increasing and Decreasing functions, odd and even functions.
Limit and Continuity :
Idea of Limit of a function with more stress on geometrical and intuitive approach. Algebra of limits (Statement only, no proof), 
(n, a positive or negative integer (
) (statement only) proof of } \over {(x - a)}} - n{a-{n - 1}}.jpg "{\lim }\limits_{x \to a} {{({x^n} - {a^n})} \over {(x - a)}} = n{a^{n - 1}}")
where n is a positive integer. Use of the limits (without proof) 
, 
, } \over x}.jpg "{\lim }\limits_{x \to 0} {{\log (1 + x)} \over x}")
,
(n = rational number) limit of a function of a function (statement only). Simple applications of the above limits. Idea of continuity of a function at a point. (Geometric and intritive approach), simple applications.
Derivative / Differential coefficients of functions :
Derivative of a constant function, xn (n-rational), sinx, cosx, ex, logx from first principle. Working rule of derivative of xn (n is a real number); Rules of differentiation of sum, product and quotient of two functions (Statement only). Differential coefficients of tanx, cotx, secx, cosecx, sin-1x , cos-1x, tan-1x , cosec-1x , sec-1x , cot-1x .
VECTOR [6 Marks ]
Vectors and scalars. Equal vectors, Unit vector, Zero vector, Position Vector of a point in terms of i and j, Localized and free vectors, Collinear vectors, Negative of a vector, Components of a vector; Addition of vectors, Multiplication of a vector by a scalar. Position vector of a point dividing a line segment in a given ratio. Application of vectors in geometry (Simple geometrical problems).
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