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Mathematics IIB - 12
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Co-ordinate Geometry
1. Circle
Equation of a circle - Standard form - Centre and Radius - Equation of a circle with a given line Segment as diameter & Equation of circle through three non collinear points parametric equations of a circle
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Positions of a Point in the plane of the circle - Power of a point - Definition of Tangent - Length of Tangent
Position of a straight line in the plane of the circle - conditions for a Straight plane to be a tangent - Chord Joining two points on a circle - Equation of the tangent - at a Point on the Circle - Point of contact - Equation of Normal
Chord of contact - pole and polar - conjugate points and conjugate lines & Equation of Chord with a given middle point
Relative positions of two circles- circles touching eac other externally and internally - Common Tangents - Point of Similitude - Equation of Tangents from an External Points
Sphere (3- Dimensions) - Cartesian Equation - Finding Centre and Radius
2. System of Circles
Angle Between two intersecting circles
Radical Axis of two circles - Properties
Chord and Common tangent of two circles - Radical Centre
Coaxial System of circles - Equation of the Coaxial system in the Simplest form - Limiting pois of a Coaxial System
Orthogonal System of a Coaxial System of Circles
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3. Parabola
Conic Sections - Parabola - Equation of Parabola in Standard form - Different forms of Parabola ( Cartesian and Parametric)- Condition for a Straight Line to be a Tangent
Pole and Polar - Finding the Pole of a Given line and Vice Versa
4. Ellipse
Equation of Ellipse in standard form, parametric equations
Equation of tangent and normal at a point on the ellipse (Caresian and Parametric) - Condition for a Straight line to be a Tangent
POle and Polar - Finding the Pole of a Given Line and Viceversa
5. Hyperbola
Equation of Hyperbola in standard form, parametric equations
Equations of Tangent and Normal at a point on the Hyperbola ( Cartesian and Parametric) - Conditions for a straight line to be a tangent - Asymptotes
Pole and Polar - Finding the pole of a given line and Vice versa
CALCULUS
1. Successive Differentiation
Successive Differentiation - 'n' th derivative
Leibnitz Theorem and Its Applications
2. Integration
Integration as the inverse process of Differentiation - Standard forms - Properties of Integrals
Method of Substitution - Integration of Algebraic, Exponential , Logarithmic , Trigonometric and Inverse Trigonometric Functions
Integration by parts
Integration - Partial Fractions Methods
Reduction Formulae
3. Definite Integration
The Definite Integral
Interpretation of definite integral as an area
Fundamental Theorem of Integral Calculus
Properties of Integrals
Reduction of Formulae
4. Numerical Integration
Determination of plane areas Involving 2nd Degree Curves Areas under the Curves sin X and Cos X
Trapezoidal Rule and Applications
Simpson's Rule - Simple Applications
5. Differential Equations:
Formation of Differential Equations - Degree and Order of an Ordinary Differential Equation
Solving Differential Equations by
a. Variable Seperable Method
b. Homogeneous Differential Equation
c. Non Homogeneous Differential Equation
d. Linear Differential Equations
Yearbook
Mathematics
Board of Intermediate Education
Andhra Pradesh
2nd
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Mathematics - 12 IIB
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