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We
offer Mathematics Course for students of Class XI th under TARGET IIT BATCH. This
includes syllabus of IITJEE and AIEEE. The course is of 2
years duration.
Detailed syllabus is as follows.
CLASS XI th :- UNIT 1 - 9
CLASS XII th :- UNIT 10 - 16
MATHEMATICS
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UNIT 1: |
CO-ORDINATE GEOMETRY: |
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Cartesian
system of rectangular co-ordinates in a plane, distance
formula, section formula, locus and its equation, translation
of axes, slope of a line, parallel and perpendicular
lines, intercepts of a line on the coordinate axes.
Straight lines
Various forms of equations of a line, intersection of
lines, angles between two lines, conditions for concurrence
of three lines, distance of a point from a line, equations
of internal and external bisectors of angles between
two lines, coordinates of centroid, orthocentre and
circumcentre of a triangle, equation of family of lines
passing through the point of intersection of two lines.
Circles, conic sections
Standard form of equation of a circle, general form
of the equation of a circle, its radius and centre,
equation of a circle when the end points of a diameter
are given, points of intersection of a line and a circle
with the centre at the origin and condition for a line
to be tangent to a circle, equation of the tangent.
Sections of cones, equations of conic sections (parabola,
ellipse and hyperbola) in standard forms, condition
for y = mx + c to be a tangent and point (s) of tangency.
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UNIT 2: |
SETS, RELATIONS
AND FUNCTIONS: |
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Sets and their representation; Union, intersection and
complement of sets and their algebraic properties; Power
set; Relation, Types of relations, equivalence relations,
functions;. one-one, into and onto functions, composition
of functions. |
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UNIT 3: |
COMPLEX
NUMBERS AND QUADRATIC EQUATIONS: |
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Complex numbers
as ordered pairs of reals, Representation of complex numbers
in the form a+ib and their representation in a plane,
Argand diagram, algebra of complex numbers, modulus and
argument (or amplitude) of a complex number, square root
of a complex number, triangle inequality, Quadratic equations
in real and complex number system and their solutions.
Relation between roots and co-efficients, nature of roots,
formation of quadratic equations with given roots. |
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UNIT 4: |
PERMUTATIONS AND COMBINATIONS: |
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Fundamental
principle of counting, permutation as an arrangement
and combination as selection, Meaning of P (n,r) and
C (n,r), simple applications. |
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UNIT 5: |
MATHEMATICAL INDUCTION: |
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Principle of Mathematical
Induction and its simple applications. |
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UNIT 6: |
BINOMIAL THEOREM AND
ITS SIMPLE APPLICATIONS: |
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Binomial
theorem for a positive integral index, general term
and middle term, properties of Binomial coefficients
and simple applications. |
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UNIT 7: |
Trigonometry: |
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Trigonometrical
identities and equations. Trigonometrical functions.
Inverse trigonometrical functions and their properties.
Heights and Distances. |
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UNIT 8: |
MATHEMATICAL REASONING: |
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Statements,
logical operations and, or, implies, implied by, if
and only if. Understanding of tautology, contradiction,
converse and contrapositive. |
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UNIT 9: |
SEQUENCES
AND SERIES: |
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Arithmetic
and Geometric progressions, insertion of arithmetic,
geometric means between two given numbers. Relation
between A.M. and G.M. Sum upto n terms of special series:
Sn, Sn2, Sn3. Arithmetico - Geometric progression.
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UNIT 10: |
STATISTICS AND
PROBABILITY: |
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Measures
of Dispersion: Calculation of mean, median,
mode of grouped and ungrouped data. Calculation of standard
deviation, variance and mean deviation for grouped and
ungrouped data.
Probability: Probability of an event,
addition and multiplication theorems of probability,
Baye?s theorem, probability distribution of a random
variate, Bernoulli trials and Binomial distribution.
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UNIT 11: |
MATRICES AND DETERMINANTS: |
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Matrices,
algebra of matrices, types of matrices, determinants
and matrices of order two and three. Properties of determinants,
evaluation of determinants, area of triangles using
determinants. Adjoint and evaluation of inverse of a
square matrix using determinants and elementary transformations,
Test of consistency and solution of simultaneous linear
equations in two or three variables using determinants
and matrices. |
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UNIT 12: |
LIMIT,
CONTINUITY AND DIFFERENTIABILITY: |
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Real
- valued functions, algebra of functions, polynomials,
rational, trigonometric, logarithmic and exponential
functions, inverse functions. Graphs of simple functions.
Limits, continuity and differentiability. Differentiation
of the sum, difference, product and quotient of two
functions. Differentiation of trigonometric, inverse
trigonometric, logarithmic, exponential, composite and
implicit functions; derivatives of order upto two. Rolle?s
and Lagrange?s Mean Value Theorems. Applications of
derivatives: Rate of change of quantities, monotonic
- increasing and decreasing functions, Maxima and minima
of functions of one variable, tangents and normals. |
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UNIT 13: |
INTEGRAL
CALCULUS: |
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Integral
as an anti - derivative. Fundamental integrals involving
algebraic, trigonometric, exponential and logarithmic
functions. Integration by substitution, by parts and
by partial fractions. Integration using trigonometric
identities.
Evaluation of simple integrals of the type
Integral as limit of a sum. Fundamental Theorem of Calculus.
Properties of definite integrals. Evaluation of definite
integrals, determining areas of the regions bounded by
simple curves in standard form. |
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UNIT 14: |
Differential
Equations: |
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Ordinary differential
equations, their order and degree. Formation of differential
equations. Solution of differential equations by the method
of separation of variables, solution of homogeneous and
linear differential equations of the type:
dy
-- + p (x) y = q (x)
dx |
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UNIT 15: |
Three Dimensional
Geometry: |
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Coordinates
of a point in space, distance between two points, section
formula, direction ratios and direction cosines, angle
between two intersecting lines. Skew lines, the shortest
distance between them and its equation. Equations of
a line and a plane in different forms, intersection
of a line and a plane, coplanar lines. |
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UNIT 16: |
Vector Algebra:
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Vectors
and scalars, addition of vectors, components of a vector
in two dimensions and three dimensional space, scalar
and vector products, scalar and vector triple product. |
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