Go BackMATHEMATICS - II(A)
MATHEMATICS - II(B)
Mathematics 12
MATHEMATICS - II(A)
UNIT I: COMPLEX NUMBERS
- Geometrical and Polar representation of complex number in Argand plane-Argand diagram
UNIT II: DE MOIVRE’S THEOREM
- Introduction
- De Moivre’s Theorem- Integral and Rational Indices
- nth roots of unity-Geographical Interpretations- Illustrations
UNIT III: QUADRATIC EXPRESSIONS
- Introduction
- Quadratic Expressions
- Equations in one Variable
- Sign of quadratic expressions-Change in signs and Maximum and Minimum
- Quadratic Inequations
UNIT IV: THEORY OF EQUATIONS
- Introduction
- Relation between the roots and the coefficients in an Equation
- Solving an equation when two or more of its roots are connected by certain relations
- Equations with real coefficients - occurrence of complex roots in conjugate pairs and its consequences
- Transformation of equations - Reciprocal equations
UNIT V: PERMUTATIONS AND COMBINATIONS
- Introduction
- Permutations of n dissimilar things taken r at a time
- Permutations when repetitions are allowed
- Circular Permutations
- Permutations with Constant repetitions
- Combinations- Definitions and Certain Theorems
UNIT VI: BINOMIAL THEOREM
- Introduction
- Binomial Theorem for Rational Index
- Approximations using Binomial Theorem
UNIT VII: PARTIAL FRACTIONS
- Introduction
- Rational Fractions
- Partial Fractions of f(x)/g(x), when g(x) contains non-repeated linear factors
- Partial Fractions of f(x)/g(x), when g(x) contains repeated and I or non-repeated linear factors
- Partial Fractions of f(x)/g(x), when g(x) contains irreducible factors
UNIT VIII: MEASURE OF DISPERSION
- Introduction
- Range
- Mean Deviation
- Variance and Standard Deviation of ungrouped /grouped data
- Coefficient of Variation and analysis of frequency distributions with equal means but different variances
UNIT IX: PROBABILITY
- Introduction
- Random Experiments and Events
- Classical definition of probability
- Axiomatic approach and addition theorem of probability
- Independent and Dependent events
- Conditional Probability
- Multiplication Theorem
UNIT X: RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
- Introduction
- Random Variables
- Theoretical discrete distributions Binomial and Poisson distributions
MATHEMATICS - II(B)
UNIT I: CIRCLE
- Introduction
- Position of a point in the plane of a circle Definition of a tangent
- Position of a straight line in the plane of a circle condition for a line to be tangent
- Chord of contact and polar
- Relative Positions of two circles
UNIT II: SYSTEM OF CIRCLES
- Introduction
- Angle between two intersecting circles
- Radical axis of two circles
UNIT III: PARABOLA
UNIT IV: ELLIPSE
- Introduction
- Parametric equations
- Equation of tangent and normal at a point on the ellipse
UNIT V: HYPERBOLA
- Introduction
- Equation of Tangent and Normal at a point on the hyperbola
UNIT VI: INTEGRATION
- Introduction
- Integration as the inverse process of differentiation, standard forms and properties of integrals
- Method of substitution-Integration of algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions-Integration by parts
- Integration by the method of substitution-Integration of algebraic and trigonometric functions
- Integration by parts-Integration of exponential, logarithmic and inverse trigonometric functions
- Integration- Partial fractions method
- Reduction formulae
UNIT VII: DEFINITE INTEGRALS
- Introduction
- Define Integral as the limit of sum
- Interpretation of definite integral as an area
- The Fundamental Theorem of Integral Calculus
- Properties, Reduction Formulae
- Applications of definite integral to areas
UNIT VIII: DIFFERENTIAL EQUATION
- Introduction
- Formation of differential equations-Degree and order of an ordinary differential Equation
- Solving Differential Equations
- Variables separable method
- Homogenous Differential Equation
- Non-Homogeneous Different Equations
- Linear Differential Equations
BETA
