Syllabus

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1. Relations and Functions

• Definition of Reflexive, Symmetric and Transitive relations, Equivalence relation
• Types of functions, injective(one-one), surjective(onto) and bijective functions

2. Inverse Trigonometric Functions

• Domain and range of inverse trigonometric functions, principal values
• Properties of inverse trigonometric functions
• Derivation of properties of inverse trigonometric functions and its application

3. Matrices

• Definition, Order and Formation of Matrices
• Equality, addition and subtraction of matrices
• Matrix Equation, word problems on addition and subtration of matrices
• Multiplication of matrices
• Types of matrices and its application
• Problems based on Principle of mathematical induction (PMI)
• Transpose, symmetric and skew symmetric matrices

4. Determinants

• Minors and cofactors of matrices and determinants, expansion of determinants
• Properties of determinants and its application
• Solution of determinants equations
• Application of determinants
• Adjoint and inverse of a matrix, properties of adjoint and inverse
• To solve the system of linear equations using matrix method, consistency and inconsistency

5. Continuity and differentiability

• Basis concept of Continuity and problems based on continuity
• Properties of continuous functions and its applications
• Differentiability and problems on differentiability
• Basic formulae of differentation, product rule, quotient rule and chain rule of differentiation
• Differentiation of implicit functions and problems based on implicit functions
• Differentiation of Inverse trigonometric functions
• Differentiation of logarithmic functions
• Differentiation of infinite series
• Differentiation of parametric functions
• Differentiation of a function with respect to another function
• Higher order derivatives (second order derivative, third order derivatives)
• Parametric functions in higher order derivatives

6. Application of derivatives

• Basic concept of application of derivatives, Rate of change
• Important problems on rate of change, Marginal revenue and marginal cost
• Increasing and decreasing functions
• Maxima and minima introduction, first order derivative test
• Higher order derivative test
• Word problems related to two dimensional figures
• Absolute maxima and absolute minima

7. Integrals

• Indefinite integrals introduction, formulae
• Basic Integration of trigonometric functions
• Indefinite integrals by substitution method
• Standard form of indefinite integrals 
• Integration by parts
• Problems in the form of e^x(f(x)+f'(x))
• Problems in the form of e^x sinx and e^x cosx
• Integrals of some special form
• Integrals using partial fractions
• Miscellaneous problems based on indefinite integrals
• Definite integrals introduction, substitution method
• Properties of definite integrals and its applications (f(x)=f(a-x))
• Properties of definite integrals and its applications (modulus functions)
• Properties of definite integrals and its applications (odd and even functions)

8. Application of Integrals

• Area under curves (Circles and circle with straight line)
• Area under curves (Parabolas and parabolas with circle)
• Area under curves (Inequality based problems)
• Area under curves (Modulus functions and Ellipse based problems)
• Area under curves (Straight lines)Area under curves (Trigonometric functions and Miscellaneous problems)

9. Differential Equations

• Order and degree of differential equations
• Solution of differential equations by variable seperable method
• Solution of homogeneous differential equations
• Solution of linear differential equations
• Word problems on solution of differential equations

10. Vectors

• Vector introduction, types of vectors and resultant of vectors, triangle law, addition and subtraction of vectors
• Position vectors, component of vectors, magnitude of vector and unit vector
• Section formula and its application
• Scalar or dot product of vectors, projection of vectors
• Cross or vector product of vectors, Application of cross product, area of parallelogram and triangle by vector method

11. Three Dimensional Geometry

• Introduction of three dimensional geometry, direction ratios and direction cosines
• Equation of straight line in vector and cartesian forms
• Angle between two straight lines
• Length of perpendicular, foot of perpendicular and coordinate of image
• Point of intersection of intersecting lines
• Distance between two skew lines, distance between two parallel lines

12. Linear Programming

• Manufacturing problems
• Diet problems
• Transportation problems
• Miscellaneous problems

13. Probability

• Conditional probability
• Multiplication theorem, Independent events
• Problems on independent events
• Total probability, Baye's theorem
• Probability distribution, its mean, variance and standard deviation
• Problems on probability distribution

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