Syllabus
1. Relations and Functions
- Definition of Reflexive, Symmetric and Transitive relations, Equivalence relation
- Types of functions, injective(one-one), surjective(onto) and bijective functions
- Composition of functions, invertible functions, inverse of a function
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
- Simplification and its application of inverse trigonometric functions
- Solution of Inverse trigonometric equations
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
- To find the inverse of a matrix by elementary transformations
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
- Slope of tangents and normals, equation of tangents and normals
- 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
- Approximations and errors
- Rolle's Theorem and its applicability
- Lagrange's Mean Value Theorem and its applicability
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)
- Integrals by limit of a sum
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
- Formation 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
- Scalar triple product
- Properties and application of scalar triple product
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
- Equation of plane cartesian forms (three point form and intercept form)
- Vector equation of plane and normal form
- Angle between two planes, Angle between a line and a plane
- Foot of perpendicular, coordinates of image
- Intersection of line and plane
- Equation of plane containing two coplanar lines
- Equation of plane passing through the line of intersection of two planes
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