### Integral calculus

**Integral calculus :** Integration as a reverse process of differentiation, indefinite integral of standard functions.

Integration by parts. Integration by substitution and partial fraction.

Maths related to High School Mathematics, Madhyamik Mathematics, Engineering Mathematics, and Graduation level Mathematics

**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.

**Ellipse and Hyperbola :** Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.

**Straight line :** Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two parallel lines.

**Trigonometry**

Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions. Co-ordinate geometry of two dimensions

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**Probability :** Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.

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