Mathematics 12 Mathematics 12

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 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