Sets, Relations and Functions
Sets and their Representations, Union, intersection and complements of
sets, and their algebraic properties, Relations, equivalence relations,
mappings, one-one, into and onto mappings, composition of mappings.
Complex number in the form a+ib and their representation in a plane.
Argand diagram. Algebra of complex numbers, Modulous and Arguments (or
amplitude) of a complex number, square root of a complex number. Cube roots of
unity, triangle – inequality.
Matrices and Determinants
Determinants and matrices of order two and three, properties of
determinants, Evaluation of determinants. Area of triangles using
determinants, Addition and multiplication of matrices, adjoint and inverse of
matrix. Test of consistency and solution of simultaneous linear equations
using determinants and matrices
Quadratic equation 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; Symmetric functions of
UNIT 5: Permutation and
Fundamental principle of counting; Permutation as an arrangement. Meaning of
P(n,r) and C(n,r). Simple applications.
Mathematical Induction and Its applications
Binomial Theorem and its Applications
Binomial Theorem for a positive integral index; general term and middle
term; Binomial Theorem for any index. Properties of Binomial Co-efficients.
Simple applications for approximations.
Sequences and Series
Arithmetic, Geometric and Harmonic progressions. Special cases of Sn,
Sn2, Sn3 . Arithmetic-Geometric Series, Exponential and Logarithmic series.
Polynomials, rational, trigonometric, logarithmic and exponential
functions, Inverse functions. Graphs of simple functions. Limits, Continuity;
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
three. Applications of derivative: monotonic functions, Maxima and minima of
functions of one variable.
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. Integral as limit of a sum. Properties of definite
integrals. Evaluation of indefinite integrals; Determining areas of the
regions bounded by simple curves.
Ordinary differential equations, their order and degree. Solution of
differential equations by the method of separation of variables. Solution of
homogeneous and linear differential equations.
TWO AND THREE DIMENSIONAL GEOMETRY
UNIT 12: Two
Recall of Cartesian system of Rectangular co-ordinates in a plane,
distance formula, area of a triangle, condition for the collinearity of three
points and section formula, centroid and in-centre of a triangle, locus and
its equation, translation of axes, slope of a line, parallel and perpendicular
lines, intercepts of a line on the coordinate axes.
The straight line and pair of straight
Various forms of equations of a line, intersection of lines, angles between
two lines, conditions for concurrency of three lines, distance of point from a
line, coordinates of orthocentre and circumcentre of triangle, equation of
family of lines passing through the point of intersection of two lines,
homogeneous equation of second degree in x and y, angle between pair of lines
through the origin, combined equation of the bisectors of the angles between a
pair of lines, condition for the general second degree equation to represent a
pair of lines, point of intersection and angle between two lines represented
by S = O and the factors of S.
Circles and system of Circles
Standard form of equation of a circle, general form of the equation of a
circle, its radius and centre, equation of a circle in the parametric form,
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 the circle, length of the tangent,
equation of the tangent, equation of a family of circles through the
intersection of two circles, condition for two intersecting circles to be
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.
Three dimensional Geometry
Coordinates of a point in space, distance between the points; Section
formula, direction ratios and direction cosines, angle between two
intersecting lines, equations of a line and a plane in different forms;
intersection of a line and a plane, coplanar lines, equation of a sphere, its
centre and radius. Diameter form of the equation of a sphere.
Vectors and Scalars, addition of vectors, components of a vector in two
dimensions and three dimensional space, scalar and vector products, vector
triple product. Application of vectors to plane geometry.
Measures of Central Tendency and Dispersion
Calculation of Mean, median and mode of grouped and ungrouped data.
Calculation of standard deviation, variance and mean deviation for grouped and
Probability of an event, addition and multiplication theorems of
probability and their applications; Conditional probability; Probability
distribution of a random variable; Binomial distribution and its properties.
Trigonometrical ratios, identities and equations. Inverse
trigonometric functions and their properties. Properties of triangles,
solution of triangles. Heights and Distances.
Resultant of Coplanar forces; moments and couples. Equilibrium of three
Speed and velocity, average speed, instantaneous speed, acceleration
and retardation, resultant of two velocities, relative velocity and its simple
applications. Motion of a particle along a line, moving with constant
acceleration. Motion under gravity. Laws of motion, Projectile motion.