Application of Calculus : Tangents and normals, conditions of tangency. Determination of monotonicity, maxima and minima. Differential coefficient as a measure of rate.
Motion in a straight line with constant acceleration.
Geometric interpretation of definite integral as area, calculation of area bounded by elementary curves and straight lines. Area of the region included between two elementary curves.
Integral calculus : Integration as a reverse process of differentiation, indefinite integral of standard functions.
Integration by parts. Integration by substitution and partial fraction.
Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically. Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only).
Circle : Equation of a circle with a given center and radius. Condition that a general equation of second degree in x, y may represent a circle. Equation of a circle in terms of endpoints of a diameter . Parametric equation of a circle. Intersection of a line with a circle.
Conics : Definition, Directrix, Focus and Eccentricity, classification based on eccentricity.
Parabola :Standard equation. Reduction of the form x = ay²+by+c or y = ax²+bx+c to the standard form y² = 4ax or x² = 4ay respectively. Elementary properties and parametric equation of a parabola.
