Mathematics
UNIT 1: Sets, Relations and Functions
Representation of sets and basic operations on sets
Union, intersection and complement of sets
Algebraic properties of set operations
Power set and its properties
Relations and their types
Equivalence relations
Functions and their representation
One-one, onto and many-one functions
Composition of functions
UNIT 2: Complex Numbers and Quadratic Equations
Complex numbers as ordered pairs
Algebra of complex numbers
Modulus and argument of a complex number
Geometrical representation of complex numbers
Quadratic equations in real numbers
Quadratic equations in complex numbers
Nature of roots of quadratic equations
Formation of quadratic equations with given roots
UNIT 3: Matrices and Determinants
Types of matrices
Algebra of matrices
Determinants and their properties
Evaluation of determinants
Area of triangles using determinants
Adjoint and inverse of a square matrix
Solution of linear equations using matrices and determinants
UNIT 4: Permutations and Combinations
Fundamental principle of counting
Permutations as arrangements
Combinations as selections
Meaning and use of P(n, r)
Meaning and use of C(n, r)
Applications of permutations and combinations
UNIT 5: Binomial Theorem and Its Applications
Binomial theorem for positive integral index
General term of a binomial expansion
Middle term of a binomial expansion
Simple applications of the binomial theorem
UNIT 6: Sequence and Series
Arithmetic progression and its properties
Geometric progression and its properties
Insertion of arithmetic means
Insertion of geometric means
Relation between arithmetic mean and geometric mean
Sum of first n terms of sequences and series
UNIT 7: Limit, Continuity and Differentiability
Concept of limit of a function
Left-hand and right-hand limits
Continuity of a function
Differentiability of a function
Derivative as a rate of change
Differentiation of standard functions
Product, quotient and chain rules
Differentiation of trigonometric functions
Differentiation of inverse trigonometric functions
Differentiation of exponential and logarithmic functions
Applications of derivatives to monotonicity
Applications of derivatives to maxima and minima
UNIT 8: Integral Calculus
Indefinite integrals and standard integrals
Integration using substitution method
Integration using partial fractions
Definite integrals and their properties
Evaluation of definite integrals
Area under simple curves
Area between curves in standard forms
UNIT 9: Differential Equations
Formation of differential equations
Order and degree of differential equations
Solution of differential equations by separation of variables
Solution of homogeneous differential equations of first order
UNIT 10: Coordinate Geometry
Cartesian coordinate system
Distance and section formulas
Slope of a straight line
Equations of straight lines
Distance of a point from a line
Locus of a point
Equation of a circle in standard and general form
Tangents and normals to a circle
Parabola and its standard equations
Ellipse and its standard equations
Hyperbola and its standard equations
UNIT 11: Three Dimensional Geometry
Coordinates of a point in space
Distance between two points in space
Section formula in three dimensions
Direction ratios and direction cosines
Angle between two lines in space
Equation of a line in three dimensions
Skew lines and shortest distance between them
UNIT 12: Vector Algebra
Vectors and scalars
Addition and subtraction of vectors
Components of a vector in two and three dimensions
Scalar (dot) product of vectors
Vector (cross) product of vectors
Applications of vector products
UNIT 13: Statistics and Probability
Measures of dispersion
Mean deviation
Standard deviation and variance
Probability of an event
Addition theorem of probability
Conditional probability
Bayes’ theorem
Probability distribution of a random variable
UNIT 14: Trigonometry
Trigonometric ratios and identities
Properties of trigonometric functions
Inverse trigonometric functions
Properties of inverse trigonometric functions
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